Split (1)

train · ~1.24B rows (showing the first 1.67M)

text stringlengths 8 1.01M
More About This Textbook Overview Fully up-to-date with Levels 2 and 3 of the BTEC Engineering Specifications Containing 1000 worked problems, 1750 further problems and 238 multiple-choice questions and answers Real-world situations and engineering examples put the theory into context John Bird's approach to mathematics, based on numerous worked examples supported by problems, is ideal for students of a wide range of abilities. Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills, making this a thoroughly practical introduction to the mathematics engineering that students need to master. This book presents a logical topic progression rather than following the structure of a particular syllabus, and is suitable for all Level 3 vocational students, early Foundation Degree students and for any introductory course involving engineering mathematics. However, the coverage has been carefully matched to the mathematics units within the 2010 Level 2 and 3 BTEC National Specifications. In this sixth edition there is new material on logarithms, exponential functions, vectors, and methods of alternating waveforms. The book now includes even more problems to work through. Ideal for use as tests or homework, full solutions to the revision tests are supplied on the accompanying instructor's website. Audience: Students following vocational engineering courses / first year undergraduates. Suitable for all Level 3 engineering programmes, and core units at Level 3. Matched to New BTEC National specifications: Mathematics for Technicians; Further Mathematics for Technicians; AVCE: Applied Mathematics for Engineering; Further Mathematics for Engineering. Product Details Meet the Author John Bird is the former Head of Applied Electronics in the Faculty of Technology at Highbury College, Portsmouth, UK. More recently, he has combined freelance lecturing at the University of Portsmouth, with examiner responsibilities for Advanced Mathematics with City and Guilds, and examining for the International Baccalaureate Organisation. He is the author of over 125 textbooks on engineering and mathematical subjects, with worldwide sales of one million copies. He is currently a Senior Training Provider at the Defence School of Marine Engineering in the Defence College of Technical Training at HMS Sultan, Gosport, Hampshire
Helping students through their GCSE maths course, this title provides short units to facilitate quick learning. Thoroughly covering the range of Intermediate topics, the explanations are designed to work from the basics up to examination standard. Synopsis: Edexcel GCSE Mathematics 16+ helps students through their maths course in a year, whether they are new to GCSE or preparing to retake the exam. It provides coverage of all the key intermediate tier topics. Edexcel GCSE Mathematics 16+ helps students through their maths course in a year, whether they are new to GCSE or preparing to retake the exam. It provides coverage of all the key intermediate tier topics
This is a basic or beginning algebra textbook that helps students understand the central ideas of algebra, and does not short change basic skills. It is a learning system appropriate for community... More > college classes, home school students, and parents who would like to help their children learn math. The exercises (see below) are purchased separately.< Less A thorough explanation of signed numbers focusing on basic ideas and methods for computing with negative numbers. It also includes useful, full-page tables that summarize and clarify notation issues... More > that occur with multiple signs, parentheses, exponents, and mixed numbers.< Less A careful, step-by-step explanation of factoring in algebra. In addition to basic insights, it teaches a systematic factor-by-grouping method for factoring trinomials. This method either produces the... More > desired factors or makes it easy to determine that there are none.< Less This is a complete set of basic algebra exercises in the form of work sheets, spiral bound. Answers to all problems are included. Students who use "Algebra from the Beginning" as a textbook... More > will need this workbook. These exercises can also be used for extra practice, to review, or to prepare for math placement tests.< Less
Calculus may not seem very important to you but the lessons and skills you learn will be with for your whole lifetime! Calculus is the mathematical study of continuous change. It helps you practice and develop your logic/reasoning skills. It throws challenging problems your way which make you think. Although you may never use calculus ever again after school or college, you will definitely hold on to the lessons that calculus teaches you. Things like time management, how to be organized, how to accomplish things on time, how to perform under pressure, how to be responsible are just some of the things Calculus helps you become proficient in. Traits that will help you succeed. Calculus plays a big role in most universities today as students in the fields of economics, science, business, engineering, computer science, and so on are all required to take Calculus as prerequisites. Our Pre-Calculus guide is a preliminary version of Calculus containing over 300 rules, definitions, and examples that provides you with a broad and general introduction of this subject. A valuable pocket reference to have on your phone. Even if you dont use Calculus, this app sure is a cool way to show-off some high IQ! Like all our 'phoneflips', this fast and lightweight application navigates quick, has NO Adverts, NO In-App purchasing, never needs an internet connection and will not take up much space on your phone! Portrait & Landscape mode supported13 total 5 9 4 1 3 0 2 1 1 2 A Google User Don't waste your money I've taken pre-calculus and calculus 1 and nothing that we covered is in this app. A Google UserA Google User Awesome! helped my weird brother study during the summer.. A Google User Ripped off This is a total waste of money. Does not cover quadratics, logarithms, exponents, or polynomials. A Google User I'm an advanced mathematics student and I can't express enough in words how much this helped me in getting things done quickly. Has loads of equations User reviews A Google User A Google User October 7, 2011 Don't waste your money I've taken pre-calculus and calculus 1 and nothing that we covered is in this app. poweredCalculus has been known to bring students to tears. Now you have an expert in your corner. This application contains a rich collection of examples, tutorials and solvers, crafted by a professional math tutor with over 20 years of applied mathematics and teaching experience. "Calculus Pro" covers:The TOP precalculus math game to help you get ready for college calculus. Join thousands of precalculus students who love to use games + learning to prepare for algebra, trigonometry, geometry and calculus. Designed by expert educators, master mathematicians and amazing game designers, ThUMP is The Ultimate Math Practice for helping you improve every skill in high school mathematics. From numbers to exponents to equations and graphs, all precalculus math topics are covered here. Mathtoons works closely with leading colleges and universities to combine cutting edge educational research with vibrant game features to make precalculus practice hugely successful. THEWIREDHOMESCHOOL.COM: "What a great app! Many math concepts are covered in this colourful and fun bundle of electronic goodness!" APPSFORHOMESCHOOLING.COM: "A math practice app for older children - a pre-calculus math game for high schoolers? Rare find!" Students use ThUMP to achieve: * Faster recall of math facts * Increased understanding of algebra * Better preparation for college and university * Quick problem solving skills Kymmee12, "Such a great interactive tool for learning math!" Em Rivers, "I love using it!" CSogers, "I wish this app was around when I was in school!" This app takes education to a wholeNow you can learn about differentiation and integration minus the boring bits of simply going through equations and formulas FEATURES: - 6 Complete Chapters to cover the fundamentals of Calculus including: Introduction to Differentiation, Applications of Differentiation, Transcendental Functions, Introduction to Integration, Applications of Integration, and Integration Techniques. - 3 Feature Videos to introduce the topic to you - Fully narrated tutorials guide you on the basic concepts of Calculus - Fun-to-watch videos introduce you to the world of Calculus; learn about fun facts Track your progress from the Navigation Menu - Try the sample math questions and check your answers against model solutions Unsure about the Calculus Interactive App Full Edition? Try out the FREE Lite Edition ⇒ CH 8 Infinite Sequences and Series Sequence Series The Integral Test and Estimates of Sums The Comparison Test Alternating Series Absolute Convergence and The Ratio and Root Test Power Series Taylor and Maclaurin Series The Calculus Math App takes education to aIf you like the lite version, you can now get the full version of the app here FEATURES: - Watch narrated tutorials guide you on the basic concepts of Calculus including Differentiation and Integration - Fun-to-watch videos introduce you to the world of Calculus; learn about the history of Calculus Try the sample questions and check your answers against model solutions Calculus - The Brain Trainer. This brain game gives you: Memory, attention, and math skills improvement. Speeds up your abilitySame GREAT content, but now in HD and, optimized for both phones and tablets! Mistakes in grammar or punctuation can be annoying to a reader and quickly draws attention away from what is being written. These types of mistakes cause the reader to focus on the grammar instead of what is being communicated, leads them to question on how well educated the person is, and significantly reduces the impact of your message. Proper grammar and punctuation not only helps you control the flow of writing, but also helps to accurately and effectively convey your message in the best possible way. For decades we have been delivering content that is concise, relevant, easy to follow and best of all, easy to understand! The 'Punctuation & Capitalization' guide is used by academics, writers, and teachers around the world and is one of the most comprehensive and complete reference guides available today. Everything you need in one download! Release Notes: The old version of this app was first published in 2009. It has now been deprecated and is no longer supported. This version is optimized for HD content, phones and tablets. Guarantee: • If you purchase our guide and not completely satisfied, please play nice and give us a chance to make it right by emailing admin @ phoneflips.com, BEFORE posting a negative review. Thank you! Privacy Policy: • There are no marketing pop-ups, advertising or any other prompts to purchase anything via this app • This app collects no information or data from you, your device or even your order. Ever. • Your business is none of our business. :) 40. Cone 41. Sphere 42. Symmetry 43. Perimeter & Area of Polygons 45. Area of Triangle & Circle 46. Area and Volume of Solids 47. Area and Volume of Cube, Rectangular solid 48. Area and Volume of Cylinder, Cone & Sphere 49. Area and Volume of Right Prism and Pyramid Like all our 'phoneflips', this lightweight application has NO Adverts, never needs an internet connection and won't take up much space on your phone. Portrait & Landscape mode supported. A COMPLETE REMAKE OF OUR ORIGINAL AND POPULAR PRE-ALGEBRA GUIDE - NOW WITH SUPPORT FOR BOTH PHONES AND TABLETS A Hard-copy Best-seller. Our guide will take you step-by-step through the basic building blocks of Algebra giving you a solid foundation for further studies in our easy-to-follow and proven format! Need some practice? No problem. As an in-App purchase, we offer two 'Practice Packs' that will help you practice the rules covered in this reference guide. The PDF's you buy are yours to keep and can be viewed, emailed or printed giving you a great way to get the most out of this guide. Please note: The practice packs are NOT yet interactive. You will need to print them out and scribble on them with one of those old fashioned pencil devices :) From our old version: ★★★★★ "Easy to understand This app makes pre algebra easy to deal with... Down to earth explanation, quick and easy to learn" ★★★★★ "An excellent app its worth buying..Thank you for creating this app..I LOVE IT!!" ★★★★★ "Older adult back in school loving it I' m in my 50's and heck deep in Pre-algebra class in college. This app makes for a fantastic way to study while waiting for your appointments in-line, anywhere. The examples along with the explanations are clear, intuitive, and really simple for someone who has not been to this type of schooling for over forty years. AND! I never took algebra in high school. The developer broke it down into several categories similar to my syllabus. It is really great. I contacted the developer and says he is working on a workbook and should be out in a couple of months. I will be continuing to take a class of this nature in summer so this will help. I am hoping he comes out with an algebra 1 too. :-) Thanks Mike!"Don't waste time trying to search the internet in a disaster, this must-have app will help you and your family prepare and rebound from almost any DISASTER quickly and safely. Topics cover everything you'd expect from a Disaster Readiness quick reference guide and includes sections on how to make your own Disaster Supplies Kit, how to re-charge your phone when there is no electricity, how to purify water and even where to get pills to protect yourself from nuclear radiation! With over 175,000 quick reference guides in print we've been delivering content that is relevant, professionally summarized, and bang on to-the-point. Now this great content has been improved and is available for your mobile device! Offline Access ** In a disaster there will always be a chance wireless communications and/or the internet will be unavailable. Googling wont be possible. By having this content local on your phone means it will be available whenever and wherever you need it. The Disaster Readiness Guide is an app we hope you'll never need, but when you need it, you'll need it bad. Disasters hit when you least expect it, grab your copy now! Landscape & Portrait modes supported. Guarantee: • If you purchase our guide and not completely satisfied, play nice and give us a chance to make it right by emailing admin @ phoneflips.com BEFORE posting a negative review. Thank you! Privacy Policy: • There are no marketing pop-ups, advertising or any other prompts whatsoever to purchase anything via this app • This app collects no information or data from you, your device or your order. Ever. • Your business in none of our business. :) Being a babysitter is the ultimate "Role Model" position. Working in a family's home adds a level of responsibility that other jobs may not have. Babysitters have the unique opportunity to positively influence children in their own surroundings. Everyone has memories of their childhood babysitter. By making your babysitting jobs fun, you will become that unforgettable babysitter in that child's memory. Our Babysitting guide covers everything needed to provide a professional and complete caregiving service. It offers important safety information and very useful tips for Babysitters, Nannies, other caregivers and parents too - all local on your phone! (no internet needed) In society high paying jobs demand someone who can take complicated situations and simplify them to a level that everyone can understand. Knowing math gives you the competitive edge needed to compete for good paying jobs. Math helps your mind to reason and organize complicated situations and problems into clear, simple, and logical steps and this reference guide helps you do this. Used by teachers & students in our hard-copy format since 1974, our new mobile Math 2 guide is still one of the most concise and easy to follow guides on the market today - but now mobile - to well over 400 rules, definitions and examples covering fractions, decimals, ratios, proportions, percent, probability, graphs, square roots, metric conversions and more.
iGraphmatica By Keith Hertzer Description Graphmatica is a powerful, easy-to-use, equation plotter with numerical and calculus features: - Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. - Data plotting and curve-fitting. - Up to 999 graphs on screen at once. - Numerically solve and graphically display tangent lines and integrals. - Find critical points, solutions to equations, and intersections between Cartesian functions. - AutoSquare keeps your graphs from getting squashed as you zoom or enable helper panes; or disable it in General Settings so you can scale each axis independently by pinching horizontally or vertically. - Print your graphs, copy to clipboard or export to Photo Album. - Share graph documents with friends or Graphmatica for Mac or Windows via email or iTunes. - Online help and demo files make getting up to speed a snap. In summary, a great tool for students and teachers of anything from high-school algebra through college calculus. What's New in Version 2.3.2 - Differentiable single-variable equations / inequalities (e.g. 1/x - 2 > 0) are now solved and rendered more accurately by a new algorithm that uses Newton's method to find all of the potential solutions and boundaries. - Improved display of equation parsing errors to indicate the position of the problem where applicable. - Fixed crash when computing critical points for equations containing an expression like "x+0". - Fixed a number of issues with displaying "holes" in graphs and the Find Critical Points dialog box. - Fixed issues with persisting custom colors for graphs and reverting to the default color scheme. - Fixed performance issue with custom keyboards when large items are on the clipboard.
These courses promote students' understanding and appreciation of mathematics and develop quantitative and problem solving skills. Each course uses the computer to aid in exploration and computation. Various topics are offered each semester
Math 98 - Introductory and Intermediate Algebra Fall 2009 Professor: Carrie Naughton Office: Library L247 Office Hours: MW 5:00-5:50 pm, Thursday 3:00 – 5:00 pm, online Tuesday 7:00-8:00 pm (may vary) or by appt. Phone: 651-554-3785 Email: cnaught@inverhills.mnscu.edu Website: (similar material and gradebook available on D2L) Prerequisite: Recommendation based on the results of the Inver Hills Assessment Inventory or a grade of a C or better in Math 0092. This course is designed for college students who want a self-paced course to learn or review introductory and intermediate algebra topics in preparation for college algebra or precalculus. Students planning to take Math for Liberal Arts, Statistics or Math for Decision Making as their last math course would be better served by taking Math 96. This course does not satisfy any graduation distribution requirements. Learning Outcomes: For Math 94, the student should be able to: 1) Translate words into algebraic expressions, equations, and inequalities. 2) Identify and use the properties of real numbers and classify numbers into appropriate subsets. 3) Simplify expressions: numerical, polynomial, rational, and radical. 4) Solve: linear, literal, quadratic, and radical equations and linear inequalities. 5) Solve applications using the equations and inequalities from Objective 4. 6) Use laws of exponents to simplify expressions with integer exponents. 7) Identify and use connections between linear equations, their slope, their intercepts, and their graphs. 8) Graph nonlinear equations by point plotting. For Math 99, the student should be able to: 1) Solve certain types of linear and nonlinear equations and inequalities, and modeling applications based on these types of equations and inequalities. 2) Demonstrate appropriate manipulation of polynomials. 3) Demonstrate appropriate symbolic manipulation of rational expressions, solving certain types of rational equations, and modeling applications based on rational equations. 4) Manipulate expressions involving rational exponents and radicals. 5) Graph linear equations and model applications based on linear equations and their graphs. 6) Solve systems of linear equations using matrices, and modeling applications based on linear systems. 7) Graph quadratic functions, and model applications based on quadratic functions. 8) Demonstrate proper symbolic manipulation of exponential and logarithmic expressions, solving of exponential and logarithmic equations, and modeling exponential and logarithmic applications. Text: Algebra, A Combined Approach, 3rd Edition by Elayn Martin-Gay You will need the My Math Lab Software which should come shrink-wrapped with the textbook. You will also need a coursepack with my name on the cover. Calculators: A scientific calculator is highly recommended. I recommend a TI 30XII. Math Center: Help is available in the Math Learning Center. The hours are M-Th: 9-6, and F: 9-1. Important Dates: August 24, Classes begin November 11, Holiday September 7, Holiday November 25, Last Day to Withdraw September 30, Student Success Day November 26-27, Holiday October 15-16, No class December 16, Final Exam 6 – 8 pm Grading Criteria for Math 94: Groupwork: 5 activities worth 5 points each Homework: work for each test and practice exam worth about 20 points Chapter Tests: 6Grading Criteria for Math 99: Groupwork: 5 activities worth 5 points each Homework: work for each test and practice exam worth about 20 points Chapter Tests: 5Grade Scale: A = 90-100% B = 80-87% Please note that you must earn a C = 70-79% minimum grade of "C" (70%) D = 60-69% in order to qualify for the next NC = Below 60 math course. P = Minimum of 70 You MUST earn at least 70% in the Math 94 portion of the course in order to move on to Math 99. You MUST earn at least 70% in the Math 99 portion of the course to pass Math 98. If so, your final Math 98 grade will be based on total points earned from both Math 94 and 99. If you only pass the Math 94 portion, then you will get a grade for Math 94 on your transcript. If you pass both Math 94 and 99, then you will get a grade for Math 98 on your transcript that will count as a prerequisite for higher level courses. Homework: Daily homework will not be graded or collected in this course. It is meant to provide you with review and practice of material relevant to each Chapter test. You may do as much or as little HW as needed to pass the Chapter tests with 85% mastery. Homework and practice problems are available from the textbook and also from My Math Lab. However, you must turn in your work, written neatly on a piece of paper, for each Chapter Test that you pass with 85%. There are also practice midterms and final exam review sheets that must be completed and turned in for points before you will be allowed to take the midterm and final exam. Work for each Chapter Test will be worth a maximum of 2 points. Review sheets for the midterms and finals will be worth 5 points each. Groupwork: A groupwork activity will be given at least once a week. You are expected to work with your classmates to answer questions based on the material covered in class that day. Each activity will be worth 5 points. You will be given 15 groupwork activities (1 per week), however only 5 will be recorded towards your Math 94 grade and 5 towards your Math 99 grade, so you can drop your 5 lowest scores. If you miss an activity, then that will be one of the activities that you drop. No late assignments will be accepted. Please note that on all activities and paper-pencil Midterms and Finals, I will be evaluating your solutions, not just your answers. A correct answer with no supporting work will earn little credit, but an incorrect answer with good reasoning and a small error will earn more credit. I expect that you will be showing work as completely as you can. Exams: There will be 6 Chapter Tests given online in My Math Lab for the Math 94 portion and 5 Chapter Tests given online for the Math 99 portion of the course. You must pass each test with 85% success or higher. If not, you may retake the tests. I strongly recommend that you get help on the material before retaking the test. You can get help by doing more HW on My Math Lab, using additional My Math Lab and textbook support (like video lectures, chapter reviews, etc.), getting help in class, going to the math center, or getting a peer tutor. There will also be a paper-pencil Midterm Exam and Final Exam for both Math 94 and Math 99. You must pass the Midterm Exam with a 75% success rate. If not, then three retakes will be available until success is achieved. However, there will only be one chance to achieve 70% success or higher on the Final Exam. Each Chapter Test is due by Sunday at midnight. Please refer to your calendar for the due dates of each Chapter Test, Midterm and Final Exam. You will not be allowed to take your Midterms or Final Exams unless each of the prerequisite Chapter Tests have been passed with 85% or higher. Attendance: Even though no official attendance is taken, regular attendance is recommended. A schedule of recommended deadlines will be provided on My Math Lab. This is meant to give you guidelines on when tests should be completed so that both Math 94 and Math 99 can be completed in one semester. Going slower than the suggested calendar will jeopardize your ability to complete both courses in one term. If you fail to complete all of Math 99 this semester, then you will only get credit for Math 94, assuming you pass Math 94. Technology:  You will need daily access to a high-speed internet connection (DSL, cable modem, or equivalent).  You will need to download all plug-ins for MyMathLab. Once you purchase the MyMathLab access code and register on MyMathLab, you can go through the Installation Wizard to download all necessary plug-ins. These are required to watch video lectures, work through guided practice problems and take Chapter Tests.  You may want access to a printer in order to print off copies of the activities and blank notes pages for the Video Lectures.  You may need to upgrade to the latest version of Windows Media Player in order to view my Video Lectures. You can download it by visiting  You need to have a back-up plan in case your main computer access is not available. Make sure that you know of a library, coffee house, friend, computer lab, or some other source where you can get on-line to access course materials and take tests. Internet disruptions or computer malfunctions are NOT acceptable excuses for missing deadlines. If you need technical assistance, please visit the Inver Hills computer lab (1 st floor of the Library) for help. Video Lectures: Online video lectures created by your instructor are available on D2L (under Content) and also on the instructor's webpage. These are meant to provide you with additional resources for learning the content of the course. You can print off blank notes pages first, then watch the videos and take notes as you listen. These videos should be one of the major resources you use to learn the material. The video lectures provide some examples and content that is not necessarily covered in the textbook, yet is required for the course and exams. MyMathLab tends to give problems that are slightly easier in difficulty than what is expected in the course, so please refer to the video lectures and HW activities to get a good idea of what to expect on the midterm and final exam. Other Policies: As a courtesy to all, please be sure that your cell phone and pager are turned off during class. Be on time. It is very disruptive to those around you if you come in late. Be courteous. Be in class to be successful. You are responsible for what happens in class whether you are in attendance or not. Do not cheat. Any cheating will result in a zero on that test, quiz, homework or classwork. Other actions may be taken at the discretion of the instructor. Access/Accommodations: I would like to make sure that all the materials, discussions and activities that are part of the course are accessible to you. If you would like to request accommodations or other services, please contact me as soon as possible. It is also possible to contact the Disability Services Office, L-224; phone, 651/450-8628; TTY, 651/450-8369. Satisfactory Academic Progress: Students need to maintain both a cumulative GPA of 2.0 and cumulative completion rate of at least 67% of all attempted credits for each term of attendance. If a student fails to meet these requirements, they will be placed on academic and/or financial aid probation. Suggestions for successfully completing this course: 1. Follow the Weekly Schedule; don't take weeks off from the course. 2. Start working on HW and groupwork activities as soon as possible. I have no problem with students working together to complete activities; in fact, I strongly encourage it! 3. Watch all of my Video Lectures posted on the Content page of D2L. These lectures cover all of the material in the course including some topics not found in the textbook, but covered on the Midterm and Final Exam. These Video Lectures should be your first step towards learning the material. 4. Make sure you use all of your resources to learn the course material. Read through the text; watch my Video Lectures as well as those on MyMathLab; work through guided problems on MyMathLab; work through suggested homework problems in the text and on MyMathLab; and use the Multimedia Library on MyMathLab to view sample problems, animations, video clips, etc. 5. Attend office hours. 6. Get help on HW and groupwork activities in the Math Center or with a free Peer Tutor. Work together with fellow students! 7. SHOW YOUR WORK on all groupwork activities, Tests, Midterms and Finals. 8. Take a Chapter Test as soon as you feel you understand the material that the test covers well; don't leave Tests until the day or night before the deadline. 9. DON'T FALL BEHIND!!! (It bears repeating!) 10. Ask for help when you need
This course includes prime numbers, linear and polynomial congruences, law of quadratic reciprocity, algebraic numbers and integers, other topics in number theory and unsolved problems in number theory. This course may not be offered annually. OBJECTIVES: It is the purpose of this course to present to the student an introduction to an area of pure mathematics which, although it does not abound in practical application, has intrigued many non-professionals people, as well as the greatest mathematicians from the time of the ancient Greeks to the present.
0130166367 9780130166364 Beginning and Intermediate Algebra:This book now offers an integrated program that contains videos, supplements, and multimedia courseware that includes a Companion Website and MathPro Explorer 4.0, where readers can address the variety of styles and backgrounds found in the field of algebra. Emphasizes problem-solving, critical thinking and compelling applications, in a way that readers will find easy to understand. Incorporates many of the features that make the Martin-Gay series so successful--including its accessible writing style and user-friendly accents to the book. KEY" This book will appeal to readers who have mastered arithmetic concepts and need a review of, or introduction to, specific algebra topics. Back to top Rent Beginning and Intermediate Algebra 2nd edition today, or search our site for K. Elayn textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Prentice Hall.
stud... More: lessons, discussions, ratings, reviews,... An algebra practice program for anyone working on simplifying expressions and solving equations. Create your own sets of problems to work through in the equation editor, and have them appear on all ofAlgebra Concepts is a tool for introducing many of the difficult concepts that are necessary for success in higher level math courses. This program includes a special feature, the Algebra Tool Kit, wh... More: lessons, discussions, ratings, reviews,... Algebra Concepts is an interactive learning system designed to provide instruction in mathematics at the 7th grade enrichment through adult levels. The instructional goals for Algebra Concepts include
MAT0028 Developmental Mathematics II View in Catalog 4credit hour(s)\| Fall \| Spring \| Summer Prerequisite(s): appropriate placement score or grade of C or better in MAT0018. This course is for students who possess basic arithmetic skills and have some background in algebra, but have not demonstrated the algebra skills necessary to be successful in college-level mathematics. The course is designed to supplement and strengthen the skills the student possesses and to give the student the skills required for satisfactory completion of MAT1033. The course focuses on algebraic concepts and skills for solving equations and inequalities, applying the laws of exponents to simplify polynomials, factoring polynomial expressions and using factoring to solve equations, graphing linear equations in two variables, and performing basic operations with radical expressions. Contact: 4 hours, including 1 lab hour. Students must earn a grade of C or better in this course before enrolling in MAT1033. Does not count toward A.A. degree or A.S. degree.
Mastery of calculus requires understanding how integration computes areas and business profit and acquiring a stock of techniques. Further methods solve equations involving derivatives ("differential equations") for population growth or pollution levels. Exponential and logarithmic functions and trigonometric and inverse functions play an important role. This course is the right starting point for students who have seen derivatives, but not necessarily integrals, before. Class Format: lecture Requirements/Evaluation: evaluation will be based primarily on homework, quizzes, and/or exams Additional Info: Additional Info2: Prerequisites: MATH 130 or equivalent; students who have received the equivalent of advanced placement of AB 4, BC 3 or higher may not enroll in MATH 140 without the permission of instructor Enrollment Preference: Department Notes: students who have higher advanced placement must enroll in MATH 150 or above
College and Career Readiness Standards for Mathematics Draft for Review and Comment July 16, 2009 DRAFT • CONFIDENTIAL Contents Introduction 2, 3 College and Career Readiness Standards for Mathematics 4 22 – Mathematical Practices 5, 6 Number 7 Expressions 8 Equations 9 Functions 10 Quantity 11 Modeling 12 Shape 13 Coordinates 14 Probability 15 Statistics 16 Explanatory Problems 17 22 – How Evidence Informed Decisions in Drafting the Standards 23, 24 Sample of Works Consulted 25 28 – Exemplars for the draft Math Standards can be found at 1 DRAFT  CONFIDENTIAL Introduction and Overview of the Organization Ten Mathematical Principles form the backbone of these standards. Each principle is accompanied by an explanation that describes the coherent view students are expected to have of a specific area of mathematics. With this coherent view, students will be better able to learn more mathematics and use the mathematics they know. The principles pull together topics previously studied and target topics yet to be learned in post-secondary programs. Each principle consists of a statement of a Coherent Understanding of the principle, together with Core Concepts, Core Skills, and Explanatory Problems that exemplify and delimit the range of tasks students should be able to do. These standards, like vectors, specify direction and distance for students to be ready for college and careers: 1. Direction—The Coherent Understanding The Coherent Understandings attempt to communicate the mathematical coherence of the knowledge students should take into college and careers. They are intended to tell teachers, 'This is how your students should see the mathematics in this area in order to aim them towards mastering it.' 2. Distance—The Concepts, Skills and Explanatory Problems Collectively, these statements and sets of problems define and clarify the level of expertise students should reach if they are to be prepared for success in college and career. They are a. statements of concepts students must know and actions students must be able to take using the mathematics; and b. examples of the problems and other assignments they must be able to complete. In addition to the Mathematical Principles, the standards also contain a set of Mathematical Practices that are key to using mathematics in the workplace, in further education and in a 21st Century democracy. Students who care about being precise, who look for hidden structure and note regularity in repeated reasoning, who make sense of complex problems and persevere in solving them, who construct viable arguments and use technology intelligently are more likely to be able to apply the knowledge they have attained in school to new situations. These mathematical practices are described and tied to examples. Taken together, the explanations of the mathematical principles, the associated concepts and skills and the mathematical practices form the College and Career Readiness Standards for Mathematics. 2 DRAFT  CONFIDENTIAL Overview of the Mathematical Principles Number. Procedural fluency in operations with real numbers and strategic competence in approximation are grounded in an understanding of place value. The rules of arithmetic govern operations and are the foundation of algebra. Expressions. Expressions use symbols and efficient notational conventions about order of operations, fractions and exponents to express verbal descriptions of computations in a compact form. Equations. An equation is a statement that two expressions are equal, which may result from expressing the same quantity in two different ways, or from asking when two different quantities have the same value. Solving an equation means finding the values of the variables in it that make it true. Functions. Functions describe the dependence of one quantity on another. For example, the return on an investment is a function of the interest rate. Because nature and society are full of dependencies, functions are important tools in the construction of mathematical models. Quantity. A quantity is an attribute of an object or phenomenon that can be measured using numbers. Specifying a quantity pairs a number with a unit of measure, such as 2.7 centimeters, 42 questions or 28 miles per gallon. Modeling. Modeling uses mathematics to help us make sense of the real world—to understand quantitative relationships, make predictions, and propose solutions. Shape. Shapes, their attributes, and the relations among them can be analyzed and generalized using the deductive method first developed by Euclid, generating a rich body of theorems from a few axioms. Coordinates. Applying a coordinate system to Euclidean space connects algebra and geometry, resulting in powerful methods of analysis and problem solving. Probability. Probability assesses the likelihood of an event. It allows for the quantification of uncertainty, describing the degree of certainty that an event will happen as a number from 0 through 1. Statistics. We often base decisions or predictions on data. The decisions or predictions would be easy to make if the data always sent a clear signal, but the signal is usually obscured by noise. Statistical analysis aims to account for both the signal and the noise, allowing decisions to be as well informed as possible. 3 DRAFT  CONFIDENTIAL College and Career Readiness Standards for Mathematics 4 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Mathematical Practices Proficient students expect mathematics to make sense. They take an active stance in solving mathematical problems. When faced with a non-routine problem, they have the courage to plunge in and try something, and they have the procedural and conceptual tools to carry through. They are experimenters and inventors, and can adapt known strategies to new problems. They think strategically. The mathematical practices described below bind together the five strands of mathematical proficiency: procedural fluency, conceptual understanding, strategic competence, adaptive reasoning, and productive disposition.a Students who engage in these practices discover ideas and gain insights that spur them to pursue mathematics beyond the classroom walls.b They learn that effort counts in mathematical achievement.c These are practices that expert mathematical thinkers encourage in apprentices. Encouraging these practices should be as much a goal of the mathematics curriculum as is teaching specific content topics and procedures.d 1. They care about being precise. Mathematically proficient students organize their own ideas in a way that can be communicated precisely to others, and they analyze and evaluate others' mathematical thinking and strategies based on the assumptions made. They clarify definitions. They state the meaning of the symbols they choose, are careful about specifying units of measure and labeling axes, and express their answers with an appropriate degree of precision. They would never say "let v be speed and let t be elapsed time" but rather "let v be the speed in meters per second and let t be the elapsed time in seconds." They recognize that when someone says the population of the United States in June 2008 was 304,059,724, the last few digits are meaningless. 2. They construct viable arguments. Mathematically proficient students understand and use stated assumptions, definitions and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They break things down into cases and can recognize and use counterexamples. They use logic to justify their conclusions, communicate them to others and respond to the arguments of others. 3. They make sense of complex problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for the entry points to its solution. They consider analogous problems, try special cases and work on simpler forms. They evaluate their progress and change course if necessary. They try putting algebraic expressions into different forms or try changing the viewing window on their calculator to get the information they need. They look for correspondences between equations, verbal descriptions, tables, and graphs. They draw diagrams of relationships, graph data, search for regularity and trends, and construct mathematical models. They check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" 5 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL 4. They look for structure. Mathematically proficient students look closely to discern a pattern or stand back to get an overview or shift their perspective, and they transfer fluently between these points of view. For example, in �� 2 + 5�� + 6 they can see the 5 as 2 + 3 and the 6 as 2 × 3 They recognize the significance of an existing line in a geometric figure or add an auxiliary line to make the solution of a problem clear. They also can step back and see complicated things, such as some algebraic expressions, as single objects that they can manipulate. For example, they might determine that the value of 5 − 3 �� − �� 2 is at most 5 because �� − �� 2 is non- negative.d 5. They look for and express regularity in repeated reasoning. Mathematically proficient students pay attention to repeated calculations as they are carrying them out, and look both for general algorithms and for shortcuts. For example, by paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, ��−2 they might abstract an equation of the line of the form = 3. By noticing the telescoping in the ��−1 2 expansions of �� − 1 �� + 1 , �� − 1 �� + �� + 1 , and �� − 1 �� 3 + �� 2 + �� + 1 , they might derive the general formula for the sum of a geometric series. As they work through the solution to a problem, they maintain oversight over the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.d 6. They make strategic decisions about the use of technological tools. Mathematically proficient students consider the available tools when solving a mathematical problem, whether pencil and paper, graphing calculators, spreadsheets, dynamic geometry or statistical software. They are familiar enough with all of these tools to make sound decisions about when each might be helpful. They use mathematical understanding, attention to levels of precision and estimation to provide realistic levels of approximation and to detect possible errors. a) The term proficiency is used here as it was defined in the 2001 National Research Council report Adding it up: Helping children learn mathematics. The term was used in the same way by the National Mathematics Advisory Panel (2008). b) Singapore standards c) National Mathematics Advisory Panel (2008) d) Cuoco, A. , Goldenberg, E. P., and Mark, J. (1996). Journal of Mathematical Behavior, 15 (4), 375-402; Focus in High School Mathematics. Reston, VA: NCTM, in press. 6 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Number Core Concepts  Students understand that: Core Skills  Students can and do: A Standard algorithms are based on place value and the 1 Use standard algorithms with procedural  rules of arithmetic. fluency. B Fractions represent numbers. Equivalent fractions have 2 Use mental strategies and technology with the same value. strategic competence.  C All real numbers can be located on the number line. 3 Compare numbers and make sense of their magnitude. A Coherent Understanding of Number. Procedural fluency Include positive and negative numbers in operations with real numbers and strategic competence in expressed as fractions, decimals, powers and approximation are grounded in an understanding of place roots. Limit to square and cube roots. Include very large and very small numbers. value. The rules of arithmetic govern operations and are the foundation of algebra. 4 Solve multi-step problems involving The place value system bundles units into 10s, then 10s into fractions and percentages. 100s, and so on, providing a method for naming large numbers. Subdividing in a similar way extends this to the decimal system Include situations such as simple interest, tax, markups/markdowns, gratuities and for naming all real numbers and locating them on a number commissions, fees, percent increase or line. This system is the basis for efficient algorithms. Numbers decrease, percent error, expressing rent as a represented as fractions, such as rational numbers, can also be percentage of take-home pay, and so on. Students should also be able to solve located on the number line by seeing them as numbers problems of the three basic forms: 25 expressed in different units (for example, 3/5 is three fifths). percent of 12 is what? 3 is what percent of Operations with fractions depend on applying the rules of 12? and 3 is 25 percent of what? and understand how these three problems are arithmetic: related. • Numbers can be added in any order with any grouping and multiplied in any order with any grouping. 5 Use estimation to solve problems and • Multiplication by 1 and addition of 0 leave numbers detect errors. unchanged. • All numbers have additive inverses, and all numbers 6 Give answers to an appropriate level of except zero have multiplicative inverses. precision. • Multiplication distributes over addition. Mental computation strategies are opportunistic uses of  The term procedural fluency as used in this document these rules, which, for example, allow one to compute the has the same meaning as in the National Research product 5×177×2 at a glance, obtaining 1770 instantly rather Council report Adding it up: Helping children learn mathematics. Specifically, "Procedural fluency refers to than methodically working from left to right. knowledge of procedures, knowledge of when and how Sometimes an estimate is more appropriate than an exact to use them appropriately, and skill in performing them flexibly, accurately, and efficiently" (p. 121). value. For example, it might be more useful to give the length of  The term strategic competence as used in this a board approximately as 1 ft 43 in, rather than exactly as 2 ft; 4 document has the same meaning as in the National Research Council report Adding it up: Helping children an estimate of how long a light bulb lasts helps in determining learn mathematics. Specifically, "Strategic competence the number of light bulbs to buy. In addition, estimation and refers to the ability to formulate mathematical problems, represent them, and solve them" (p. 124). approximation are useful in checking calculations. Connections to Expression, Equations and Functions. The rules of arithmetic govern the manipulations of expressions and functions and, along with the properties of equality, provide a foundation for solving equations. 7 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Expressions Core Concepts  Students understand that: Core Skills  Students can and do: A Expressions represent computations with symbols 1 See structure in expressions and standing for numbers. manipulate simple expressions with procedural fluency. B Complex expressions are made up of simpler See Explanatory Problems. expressions. 2 Write an expression to represent a C Rewriting expressions serves a purpose in solving quantity in a problem. problems. 3 Interpret an expression and its parts in A Coherent Understanding of Expressions. Expressions terms of the quantity it represents. use symbols and efficient notational conventions about order of See Explanatory Problems. operations, fractions and exponents to express verbal descriptions of computations in a compact form. For example, p + 0.05p expresses the addition of a 5% tax to a price p. Reading an expression with comprehension involves analysis of its underlying structure, which may suggest a different but equivalent way of writing it that exhibits some different aspect of its meaning. For example, rewriting p + 0.05p as 1.05p shows that adding a tax is the same as multiplying by a constant factor. Heuristic mnemonic devices are not a substitute for procedural fluency, which depends on understanding the basis of manipulations in the rules of arithmetic and the conventions of algebraic notation. For example, factoring, expanding, collecting like terms, the rules for interpreting minus signs next to parenthetical sums, and adding fractions with a common denominator are all instances of the distributive law; the interpretation we give to negative and rational exponents is based on the extension of the exponent laws for positive integers to negative and rational exponents. When simple expressions within more complex expressions are treated as single quantities, or chunks, the underlying structure of the larger expression may be more evident. Connections to Equations and Functions. Setting expressions equal to each other leads to equations. Expressions can define functions, with equivalent expressions defining the same function. 8 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Equations Core Concepts  Students understand that: Core Skills  Students can and do: A An equation is a statement that two expressions are equal. 1 Understand a word problem and restate it as an equation. B Solving is a process of algebraic manipulation guided by Extend to inequalities and systems. logical reasoning. C Completing the square leads to a formula for solving 2 Solve equations in one variable using quadratic equations. manipulations guided by the rules of arithmetic and the properties of equality. D Equations not solvable in one number system might be Solve linear equations with procedural solvable in a larger system. fluency. For quadratic equations, include solution by inspection, by factoring, or by using the quadratic formula. See Explanatory A Coherent Understanding of Equations. An equation is a Problems. statement that two expressions are equal, which may result from expressing the same quantity in two different ways, or from asking 3 Rearrange formulas to isolate a quantity when two different quantities have the same value. Solving an of interest. equation means finding the values of the variables in it that make Exclude cases that require extraction of roots or inverse functions.* it true. The solutions of an equation in one variable form a set of numbers; the solutions of an equation in two variables form a set 4 Solve systems of equations. of ordered pairs, which can be graphed in the plane. Equations can Focus on pairs of simultaneous linear equations in two variables. Include algebraic be combined into systems to be solved simultaneously. techniques, graphical techniques and solving An equation can be solved by successively transforming it into by inspection. one or more simpler equations. The process is governed by deductions based on the properties of equality. For example, one 5 Solve linear inequalities in one variable can add the same constant to both sides without changing the and graph the solution set on a number solutions, but squaring both sides might lead to extraneous line. solutions. Some equations have no solutions in a given number system, stimulating the formation of expanded number systems 6 Graph the solution set of a linear (integers, rational numbers, real numbers and complex numbers). inequality in two variables on the Strategic competence in solving includes looking ahead for coordinate plane. productive manipulations and anticipating the nature and number of solutions. A formula expressing a general relationship among several  Exclusions of this sort are modeled after variables is a type of equation, and the same solution techniques Singapore's standards, which contains similar used to solve equations can be used to rearrange formulas. For exclusions and limitations to help define the example, the formula for the area of a trapezoid, �� = �� 1 +�� 2 ℎ, can desired level of complexity. 2 be solved for h using the same deductive steps. Like equations, inequalities can involve one or more variables and can be solved in much the same way. Many, but not all, of the properties of equality extend to the solution of inequalities. Connections to Functions, Coordinates, and Modeling. Equations in two variables can define functions, and questions about when two functions have the same value lead to equations. Graphing the functions allows for the approximate solution of equations. Equations of lines are addressed under Coordinates, and converting verbal descriptions to equations is addressed under Modeling. 9 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Functions Core Concepts  Students understand that: Core Skills  Students can and do: A A function describes the dependence of one quantity on 1 Recognize proportional relationships and another. solve problems involving rates and ratios. B The graph of a function f is a set of ordered pairs (x, f(x)) 2 Describe the qualitative behavior of in the coordinate plane. common types of functions using expressions, graphs and tables. C Common functions occur in parametric families where Use graphs and tables to identify: intercepts; each member describes a similar type of dependence. intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetries; and A Coherent Understanding of Functions. Functions periodicity. Explore the effects of parameter describe the dependence of one quantity on another. For changes (including shifts and stretches) on the graphs of these functions using example, the return on an investment is a function of the technology. Include linear, power, quadratic, interest rate. Because nature and society are full of polynomial, simple rational, exponential, dependencies, functions are important tools in the construction logarithmic, trigonometric, absolute value and step functions. See Explanatory of mathematical models. Problems. Functions in school mathematics are often presented by an algebraic rule. For example, the time in hours it takes for a 3 Analyze functions using symbolic plane to fly 1000 miles is a function of the plane's speed in manipulation. miles per hour; the rule T(s) = 1000/s expresses this Include slope-intercept and point-slope form dependence algebraically and is said to define a function, of linear functions; factored form to find whose name is T. The graph of a function is a useful way of horizontal intercepts; vertex form of quadratic functions to find maximums and visualizing the dependency it models, and manipulating the minimums; and manipulations as described expression for a function can throw light on its properties. under Expressions. See Explanatory Sometimes functions are defined by a recursive process which Problems. can be modeled effectively using a spreadsheet or other technology. 4 Use the families of linear and exponential Two important families of functions are characterized by functions to solve problems. laws of growth: linear functions grow at a constant rate, and For linear functions f(x) = mx + b, understand exponential functions grow at a constant percent rate. Linear b as the intercept or initial value and m as the slope or rate of change. For exponential functions with an initial value of zero describe proportional functions f(x) = abx, understand a as the relationships. intercept or initial value and b as the growth Connections to Expressions, Equations, Modeling and factor. See Explanatory Problems. Coordinates. Functions may be defined by expressions. The graph of a function f is the same as the solution set of the 5 Find and interpret rates of change. equation y = f(x). Questions about when two functions have the Compute the rate of change of a linear function and make qualitative observations same value lead to equations, whose solutions can be visualized about the rates of change of nonlinear from the intersection of the graphs. Since functions express functions. relationships between quantities, they are frequently used in modeling. 10 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Quantity Core Concepts  Students understand that: Core Skills  Students can and do: A The value of a quantity is not specified unless the units 1 Use units consistently in describing real- are named or understood from the context. life measures, including in data displays and graphs. B Quantities can be added and subtracted only when they are of the same general kind (lengths, areas, speeds, etc.). 2 Know when and how to convert units in computations. C Quantities can be multiplied or divided to create new Include the addition and subtraction of types of quantities, called derived quantities. quantities of the same general kind expressed in different units; averaging data given in mixed units; converting units for A Coherent Understanding of Quantity. A quantity is an derived quantities such as density and speed. attribute of an object or phenomenon that can be measured using numbers. Specifying a quantity pairs a number with a 3 Use and interpret derived quantities and unit of measure, such as 2.7 centimeters, 42 questions or 28 units correctly in algebraic formulas. miles per gallon. For example, the length of a football field and the speed of 4 Use units as a way to understand light are both quantities. If we choose units of miles per problems and to guide the solution of second, then the speed of light has the value 186,000 miles per multi-step problems. second. But the speed of light need not be expressed in second Include examples such as acceleration; per hour; it may be expressed in meters per second or any currency conversions; people-hours; social science measures, such as deaths per other unit of speed. A speed of 186,000 miles per second is the 100,000; and general rate, such as points per same as a speed of meters per second. "Bare" numerical values game. See Explanatory Problems. such as 186,000 and do not describe quantities unless they are paired with units. Speed (distance divided by time), rectangular area (length multiplied by length), density (mass divided by volume), and population density (number of people divided by area) are examples of derived quantities, obtained by multiplying or dividing quantities. It can make sense to add two quantities, such as when a child 51 inches tall grows 3 inches to become 54 inches tall. To be added or subtracted, quantities must be expressed in the same units, but even then it does not always make sense to add them. If a wooded park with 300 trees per acre is next to a field with 30 trees per acre, they do not have 330 trees per acre. Converting quantities to have the same units is like converting fractions to have a common denominator before adding or subtracting. Doing algebra with units in a calculation reveals the units of the answer, and can help reveal a mistake if, for example, the answer comes out to be a distance when it should be a speed. Connections to Number, Expressions, Equations, Functions and Modeling. Operations described under Number and Expressions govern the operations one performs on quantities, including the units involved. Quantity is an integral part of any application of mathematics, and has connections to solving problems using equations, functions and modeling. 11 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Modeling Core Concepts  Students understand that: Core Skills  Students can and do: A Models abstract key features from situations to help us 1 Model numerical situations. solve problems. Include readily applying the four basic operations in combination to solve multi-step quantitative B Models can be useful even if their assumptions are problems with dimensioned quantities; making estimates to introduce numbers into a situation oversimplified. and get a problem started; recognizing proportional or near-proportional relationships A Coherent Understanding of Modeling. Modeling uses and analyzing them using characteristic rates and mathematics to help us make sense of the real world—to ratios. understand quantitative relationships, make predictions, and propose solutions. 2 Model physical objects with geometric shapes. A model can be very simple, such as a geometric shape to Include common objects that can reasonably be describe a physical object like a coin. Even so simple a model idealized as two- and three-dimensional geometric shapes. Identify the ways in which the involves making choices. It is up to us whether to model the actual shape varies from the idealized geometric solid nature of the coin with a three-dimensional cylinder, or model. whether a two-dimensional disk works well enough for our purposes. For some purposes, we might even choose to 3 Model situations with equations, inequalities adjust the right circular cylinder to model more closely the and functions. way the coin deviates from the cylinder. Include situations well described by a linear In any given situation, the model we devise depends on a inequality in two variables or a system of linear number of factors: How exact an answer do we want or inequalities that define a region in the plane; situations well described by linear, quadratic or need? What aspects of the situation do we most need to exponential equations or functions; and situations understand, control, or optimize? What resources of time that can be well described by inverse variation. and tools do we have? The range of models we can create and analyze is constrained as well by the limitations of our 4 Model situations with common functions. mathematical and technical skills. For example, modeling a Include identifying a family that models a problem physical object, a delivery route, a production schedule, or a and identify a particular function of that family adjusting parameters. Understand the recursive comparison of loan amortizations each requires different nature of situations modeled by linear and sets of tools. Networks, spreadsheets and algebra are exponential functions. powerful tools for understanding and solving problems drawn from different types of real-world situations. 5 Model data with statistics. The basic modeling cycle is one of (1) apprehending the Include replacing a distribution of values with a important features of a situation, (2) creating a measure of its central tendency; modeling a mathematical model that describes the situation, (3) bivariate relationship using a trend line or a linear regression line. analyzing and performing the mathematics needed to draw conclusions from the model, and (4) interpreting the results 6 Compare models for a situation. of the mathematics in terms of the original situation. Connections to Quantity, Equations, Functions, Shape and Include recognizing that there can be many models that relate to a situation, that they can Statistics. Modeling makes use of shape, data and algebra to capture different aspects of the situation, that they represent real-world quantities and situations. In this way can be simpler or more complex, and that they can the Modeling Principle relies on concepts of quantity, have a better or worse fit to the situation and the questions being asked. equations, functions, shape and statistics. 7 Interpret the results of applying the model in the context of the situation. Include realizing that models do not always fit exactly and so there can be error; identifying simple sources of error and being careful not to over-interpret models. 12 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Shape Core Concepts  Students understand that: Core Skills  Students can and do: A Shapes, their attributes, and their measurements can be 1 Use geometric properties to solve multi-step analyzed deductively. problems involving shapes. Include: measures of angles of a triangle sum to B Right triangles and the Pythagorean theorem are focal 180°; measures of vertical, alternate interior and points in geometry with practical and theoretical corresponding angles are equal; measures of supplemental angles sum to 180°; two lines importance. parallel to a third are parallel to each other; points on a perpendicular bisector of a segment C Congruent shapes can be superimposed through rigid are equidistant from the segment's endpoints; and the radius of a circle is perpendicular to the transformations. tangent at the point of intersection of the circle and radius. See Explanatory Problems. D Proportionality governs the relationship between measurements of similar shapes. 2 Prove theorems, test conjectures and identify logical errors. A Coherent Understanding of Shape. Shapes, their Include theorems about angles, parallel and attributes, and the relations among them can be analyzed and perpendicular lines, similarity and congruence of triangles. generalized using the deductive method first developed by Euclid, generating a rich body of theorems from a few axioms. 3 Solve problems involving measurements. The analysis of an object rests on recognition of the points, lines and surfaces that define its shape: a circle is a set of points Include measurement (length, angle measure, area, surface area, and volume) of a variety of in a plane equidistant from a fixed point; a cube is a figure figures and shapes in two- and three- composed of six identical square regions in a particular three- dimensions. Compute measurements using dimensional arrangement. Precise definitions support an formulas and by decomposing complex shapes into simpler ones. See Explanatory Problems. understanding of the ideal, allowing application to the real world where geometric modeling, measurement, and spatial 4 Construct shapes from a specification of their reasoning offer ways to interpret and describe physical properties using a variety of tools. environments. We can also analyze shapes, and the relations of congruence Include classical construction techniques and construction techniques supported by modern and symmetry, through transformations such as translations, technologies. reflections, and rotations. For example, the line of reflective symmetry in an isosceles triangle assures that its base angles 5 Solve problems about similar triangles and are equal. scale drawings. The study of similar right triangles supports the definition of Include computing actual lengths, areas and sine, cosine and tangent for acute angles, and the Pythagorean volumes from a scale drawing and reproducing a theorem is a key link between shape, measurement, and scale drawing at a different scale. coordinates. Knowledge about triangles and measurement can be applied in practical problems, such as estimating the amount 6 Apply properties of right triangles and right of wood needed to frame a sloping roof. triangle trigonometry to solve problems. Connections to Coordinates and Functions. The Pythagorean Include applying sine, cosine and tangent to theorem provides an important bridge between shape and determine lengths and angle measures of a right triangle, the Pythagorean theorem and distance in the coordinate plane. Parameter changes in families properties of special right triangles. Use right of functions can be interpreted as transformations applied to triangles and their properties to solve real-world their graphs. problems. Limit angle measures to degrees. See Explanatory Problems. 7 Create and interpret two-dimensional representations of three-dimensional objects. Include schematics, perspective drawings and multiple views. 13 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Coordinates Core Concepts  Students understand that: Core Skills  Students can and do: A Locations in space can be described using numbers called 1 Translate fluently between lines in the coordinates. coordinate plane and their equations. Include predicting visual features of lines by B Coordinates serve as tools for blending algebra with inspection of their equations, determining geometry and allow methods from one domain to be the equation of the line through two given points, and determining the equation of the used to solve problems in the other. line with a given slope passing through a given point. C The set of solutions to an equation in two variables is a line or curve in the coordinate plane and the solutions to 2 Identify the correspondence between systems of equations in two variables correspond to parameters in common families of intersections of lines or curves. equations and the shape of their graphs. Include common families of equations—the D Equations in different families graph as different sorts of graphs of Ax + By = C, y = mx + b and x = a are curves—such as straight lines, parabolas, circles. straight lines; the graphs of y = a(x – h)2 + k and y = Ax2 + Bx + C are parabolas; and the graph of (x – h)2 + (y – k)2 = r2 is a circle. A Coherent Understanding of Coordinates. Applying a coordinate system to Euclidean space connects algebra and 3 Use coordinates to solve geometric geometry, resulting in powerful methods of analysis and problems. problem solving. Include proving simple theorems Just as the number line associates numbers with locations in algebraically, using coordinates to compute one dimension, a pair of perpendicular axes associates pairs of perimeters and areas for triangles and rectangles, finding midpoints of line numbers with locations in two dimensions. This segments, finding distances between pairs of correspondence between numerical coordinates and geometric points and determining the parallelism or points allows methods from algebra to be applied to geometry perpendicularity of lines. See Explanatory Problems. and vice versa. The solution set of an equation becomes a geometric curve, making visualization a tool for doing and understanding algebra. Geometric shapes can be cast as equations, making algebraic manipulation into a tool for geometric proof and understanding. Coordinate geometry is a rich field for exploration. How does a geometric transformation such as a translation or reflection affect the coordinates of points? What features does the graph have for a rational function whose denominator can be zero? How is the geometric definition of a circle reflected in its equation? Coordinates can also be applied to scale maps and provide a language for talking about direction and bearing. Adding a third perpendicular axis associates three numbers with locations in three dimensions and extends the use of algebraic techniques to problems involving the three-dimensional world we live in. Connections to Shape, Quantity, Equations and Functions. Coordinates can be used to reason about shapes. In applications, coordinates often have dimensions and units (such as lengths and bushels). A one-variable equation of the form f(x) = g(x) may be solved in the coordinate plane by finding intersections of the curves y = f(x) and y = g(x). 14 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Probability Core Concepts  Students understand that: Core Skills  Students can and do: A Probability expresses a rational degree of certainty with 1 Use methods of systematic counting to a number from 0 to 1 where probability of 1 means that compute probabilities. an event is certain. 2 Take probability into account when B When there are n equally likely outcomes the probability making decisions and solving problems. 1 of any one of them occurring is �� and the probability of any combination of outcomes can be computed using the 3 Compute theoretical probabilities and laws of probability. compare them to empirical results. Include one- and two-stage investigations C Probability is an important consideration in rational involving simple events and their decision-making. complements, compound events involving dependent and independent simple events. Include using data from simulations carried A Coherent Understanding of Probability. Probability out with technology to estimate probabilities. assesses the likelihood of an event. It allows for the quantification of uncertainty, describing the degree of certainty 4 Identify and explain common that an event will happen as a number from 0 through 1. misconceptions regarding probability. In some situations, such as flipping a coin, rolling a number cube or drawing a card, where no bias exists for or against any Include misconceptions about long-run versus. short-run behavior (the law of large particular outcome, it is reasonable to assume that the possible numbers) and the "high exposure fallacy" outcomes are all equally likely. From this assumption the laws (e.g., more media coverage suggests of probability give the probability for each possible number of increased probability that an event will occur, which fails to account for the fact that heads, sixes or aces after a given number of trials. Generally media covers mostly unusual events). speaking, if you know the probabilities of some simple events you can use the laws of probability to deduce probabilities of 5 Compute probabilities from a two-way combinations of them. table comparing two events. An important method in such calculations is systematically Include reading conditional probabilities counting all the possibilities in a situation. Systematic counting from two-way tables; do not emphasize often involves arranging the objects to be counted in such a fluency with the related formulas. way that the problem of counting reduces to a smaller problem of the same kind. In some situations it is not known whether an event has been influenced by outside factors. If we question whether a number cube is fair, we can compare the results we get by rolling it to the frequencies predicted by the mathematical model. It is this application of probability that underpins drawing valid conclusions from sampling or experimental data. For example, if the experimental population given a drug is categorized 20 different ways, a manufacturer's claim of significant results in one of the categories is not compelling. Connections to Statistics and Expressions. The importance of randomized experimental design provides a connection with Statistics. Probability also has a more advanced connection with the Expression principle through Pascal's triangle and binomial expansions. 15 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Statistics Core Concepts  Students understand that: Core Skills  Students can and do: A Statistics quantifies the uncertainty in claims based on data. 1 Identify and formulate questions that can be addressed with data; collect and B Random sampling and assignment open the way for organize the data to respond to the statistical methods. question. C Visual displays and summary statistics condense the 2 Use appropriate displays and summary information in large data sets. statistics for data Include univariate, bivariate, categorical and D A statistically significant result is one that is unlikely to be quantitative data. Include the thoughtful selection of measures of center and spread due to chance. to summarize data. A Coherent Understanding of Statistics. We often base decisions or 3 Estimate population statistics using predictions on data. The decisions or predictions would be easy to samples. make if the data always sent a clear signal, but the signal is usually obscured by noise. Statistical analysis aims to account for both the Focus on the mean of the sample, and signal and the noise, allowing decisions to be as well informed as exclude standard deviation. possible. We gather, display, summarize, examine and interpret data to 4 Interpret data displays and summaries discover patterns. Data distributions can be described by a summary critically; draw conclusions and develop statistic measuring center, such as mean or median, and a summary recommendations. statistic measuring spread, such as interquartile range or standard Include paying attention to the context of the deviation. We can compare different distributions numerically using data, interpolating or extrapolating judiciously and examining the effects of these statistics or visually using plots. Data are not just numbers, they extreme values of the data on summary are numbers that mean something in a context, and the meaning of a statistics of center and spread. Include data pattern in the data depends on the context. Which statistics to sets that follow a normal distribution. compare, and what the results of a comparison may mean, depend on the question to be investigated and the real-life actions to be taken. 5 Evaluate reports based on data. We can use scatter plots or two-way tables to examine relationships Include looking for bias or flaws in way the between variables. Sometimes, if the scatter plot is approximately data were gathered or presented, as well as unwarranted conclusions, such as claims linear, we model the relationship with a trend line and summarize the that confuse correlation with causation. strength and direction of the relationship with a correlation coefficient. We use statistics to draw inferences about questions such as the effectiveness of a medical treatment or an investment strategy. There are two important uses of randomization in inference. First, collecting data from a random sample of a population of interest clears the way for inference about the whole population. Second, randomly assigning individuals to different treatments allows comparison of the their effectiveness. Randomness is the foundation for determining the statistical significance of a claim. A statistically significant difference is one that is unlikely to be due to chance; effects that are statistically significant may, nevertheless, be small and unimportant. Sometimes we model a statistical relationship and use that model to show various possible outcomes. Technology makes it possible to simulate many possible outcomes in a short amount of time, allowing us to see what kind of variability to expect. Connections to Probability, Expressions, and Numbers. Inferences rely on probability. Valid conclusions about a population depend on designed statistical studies using random sampling or assignment. 16 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Explanatory Problems [Note: The Explanatory Problems are incomplete in this draft. Explanatory Problems will eventually appear alongside their corresponding standards when the standards move to a two-page format.] The purpose of the Explanatory Problems is to explain certain Core Skills and exemplify the kinds of problems students should be able to do. This feature of the College and Career Readiness Standards has been modeled on the standards of Singapore, Japan, and other high-performing countries—as well as the standards of states like Massachusetts whose standards include such problems. Explanatory Problems have been provided for those Core Skills in which difficult judgments must be made about the desired level of mathematical complexity. For Number and Modeling, no Explanatory Problems were judged necessary to further clarify the Core Skills. Please note that the explanatory problems are specific cases and do not fully cover the content scope of their corresponding Core Skills. Also please note that these problems are not intended to be classroom activities. They are best thought of as parts of the standards statements to which they correspond. Number No Explanatory Problems intended Expressions 1 See structure in expressions and manipulate simple expressions with procedural fluency. Explanatory Problems (a) Expressions in (a) were taken from Perform manipulations such as the following with procedural fluency: Japan COS, 2008 �� + �� 2 = ��2 + 2�� + �� 2 �� − �� 2 = ��2 − 2�� + �� 2 �� + �� − �� = ��2 − �� 2 �� + �� + �� = �� 2 + �� + �� + �� Explanatory Problems (b) Problems in (b) were taken from 2 Hong Kong Secondary 3 Territory- �� 4 Wide Assessment 2007 Simplify �� 2 12�� 3�� Simplify − �� 2 Problem (c) was taken from Explanatory Problem (c) Singapore O Level January 2007 Exam Expand fully �� 1 − �� + 3 Additional Explanatory Problems to come 17 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Expressions, continued 2 Write an expression to represent a quantity in a problem. Explanatory Problems to come Equations 2 Solve equations in one variable using manipulations guided by the rules of arithmetic and the properties of equality. Solve linear equations with procedural fluency. For quadratic equations, include solution by inspection, by factoring, or by using the quadratic formula. Explanatory Problems to come Functions 2 Describe the qualitative behavior of common types of functions using expressions, graphs and tables. Use graphs and tables to identify: intercepts; intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetries; and periodicity. Explore the effects of parameter changes (including shifts and stretches) on the graphs of these functions using technology. Include linear, power, quadratic, polynomial, simple rational, exponential, logarithmic, trigonometric, absolute value and step functions. Explanatory Problems to come 3 Analyze functions using symbolic manipulation. Include slope-intercept and point-slope form of linear functions; factored form to find horizontal intercepts; vertex form of quadratic functions to find maximums and minimums; and manipulations as described under Expressions. Explanatory Problems to come 4 Use the families of linear and exponential functions to solve problems. For linear functions f(x) = mx + b, understand b as the intercept or initial value and m as the slope or rate of change. For exponential functions f(x) = abx, understand a as the intercept or initial value and b as the growth factor. Explanatory Problems to come 18 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Quantity 4 Use units as a way to understand problems and to guide the solution of multi-step problems. Include examples such as acceleration; currency conversions; people-hours; social science measures, such as deaths per 100,000; and general rate, such as points per game. Explanatory Problems to come Modeling No Explanatory Problems intended Shape 1ABCD is a rhombus. Find x. Angle measurements are in degrees. Assessment 2007 A (x+8) D B 42 96 C 19 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Shape, continued 3 Solve problems involving measurements. Include measurement (length, angle measure, area, surface area, and volume) of a variety of figures and shapes in two- and three-dimensions. Compute measurements using formulas and by decomposing complex shapes into simpler ones. Explanatory Problem This problem was taken from Hong Kong Secondary 3 Territory-Wide The figure shows a solid prism. Its base is a right-angled triangle. Find Assessment 2007 its surface area. 5cm 4cm 3cm 6cm 6 Apply properties of right triangles and right triangle trigonometry to solve problems. Include applying sine, cosine and tangent to determine lengths and angle measures of a right triangle, the Pythagorean theorem and properties of special right triangles. Use right triangles and their properties to solve real-world problems. Limit angle measures to degrees. Explanatory Problem to come 20 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Coordinates 3The figure below shows a rectangle ABCD. Find the length of the Assessment 2007 diagonal BD of the rectangle. y B (1, 6) C A x D (-1, -2) 21 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Probability 1 Use methods of systematic counting to compute probabilities. Explanatory Problems to come 2 Take probability into account when making decisions and solving problems. Explanatory Problems to come Statistics 2 Use appropriate displays and summary statistics for data. Include univariate, bivariate, categorical and quantitative data. Include the thoughtful selection of measures of center and spread to summarize data. Explanatory Problems to come 5 Evaluate reports based on data. Include looking for bias or flaws in way the data were gathered or presented, as well as unwarranted conclusions, such as claims that confuse correlation with causation. Explanatory Problems to come 22 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL How Evidence Informed Decisions in Drafting the Standards The Common Core Standards initiative builds on a generation of standards efforts led by states and national organizations. On behalf of the states, we have taken a step toward the next generation of standards that are aligned to college- and career-ready expectations and are internationally benchmarked. These standards are grounded in evidence from many sources that shows that the next generation of standards in mathematics must be focused on deeper, more thorough understanding of more fundamental mathematical ideas and higher mastery of these fewer, more useful skills. The evidence that supports this new direction comes from a variety of sources. International comparisons show that high performing countries focus on fewer topics and that the U.S. curriculum is "a mile wide and an inch deep." Surveys of college faculty show the need to shift away from high school courses that merely survey advanced topics, toward courses that concentrate on developing an understanding and mastery of ideas and skills that are at the core of advanced mathematics. Reviews of data on student performance show the large majority of U.S. students are not mastering the mile wide list of topics that teachers cover. The evidence tells us that in high performing countries like Singapore, the gap between what is taught and what is learned is relatively smaller than in Malaysia or the U.S. states. Malaysia's standards are higher than Singapore's, but their performance is much lower. One could interpret the narrower gap in Singapore as evidence that they actually use their standards to manage instruction; that is, Singapore's standards were set within the reach of hard work for their system and their population. Singapore's Ministry of Education flags its webpage with the motto, "Teach Less, Learn More." We accepted the challenge of writing standards that could work that way for U.S. teachers and students: By providing focus and coherence, we could enable more learning to take place at all levels. However, a set of standards cannot be simplistically "derived" from any body of evidence. It is more accurate to say that we used evidence to inform our decisions. A few examples will illustrate how this was done. For example, systems of linear equations were included by all states, yet students perform surprisingly poorly on this topic when assessed by ACT. We determined that systems of linear equations have high coherence value, mathematically; that this topic is included by all high performing nations; and that it has moderately high value to college faculty. Result: We included it in our standards. A different and more complex pattern of evidence appeared with families of functions. Again, we found that students performed poorly on problems related to many advanced functions (trigonometric, logarithmic, quadratic, exponential, and so on). Again, we found that states included 23 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL them, even though college faculty rated them lower in value. High performing countries included this material, but with different degrees of demand. We decided that we had to carve a careful line through these topics so that limited teaching resources could focus where it was most important. We decided that students should develop deep understanding and mastery of linear and simple exponential functions. They should also have familiarity (so to speak) with other families of functions, and apply their algebraic, modeling and problem solving skills to them—but not develop in-depth mastery and understanding. Thus we defined two distinct levels of attention and identified which families of functions got which level of attention. Why were exponential functions selected in this case, instead of (say) quadratic functions? What tipped the balance was the high coherence value of exponential functions in supporting modeling and their wide utility in work and life. Quadratic functions were also judged to have received enough attention under Equations. These examples indicate the kind of reasoning, informed by evidence, that it takes to design standards aligned to the demands of college and career readiness in a global economy. We considered inclusion in international standards, requirements of college and the workplace, surveys of college faculty and the business community, and other sources of evidence. As we navigated these sometimes conflicting signals, we always remained aware of the finiteness of instructional resources and the need for deep mathematical coherence in the standards. In the pages that follow, the work group has identified a number of sources that played a role in the deliberations described above and more generally throughout the process to inform our decisions. 24 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Sample of Works Consulted I. National Reports and Carnegie Corporation of New York and the Recommendations Institute for Advanced Study, 2009. Online: A. Adding it Up: Helping Children Learn Mathematics. National Council of Teachers J. Principles and Standards for School of Mathematics, Mathematics Learning Mathematics. National Council of Teachers Study Committee, (2001). of Mathematics, (2000). B. Crossroads in Mathematics, 1995 and K. Quantitative Literacy and Mathematical Beyond Crossroads, 2006. Competencies. Niss, Mogen. Last retrieved American Mathematical Association of Two- July 15, 2009, from Year Colleges (AMATYC). C. Curriculum Focal Points for Prekindergarten L. A Research Companion to Principles and through Grade 8 Mathematics: A Quest for Standards for School Mathematics. National Coherence. National Council of Teachers of Council of Teachers of Mathematics, (2003). Mathematics, (2006). M. Focus in High School Mathematics: D. Foundations for Success: Final Report of the Reasoning and Sense Making. National National Mathematics Advisory Panel Council of Teachers of Mathematics. (NMAP), (2008). Reston, VA: NCTM, in press. E. Guidelines for Assessment and Instruction in Statistics Education (GAISE) project II. College Readiness A. ACT College Readiness Benchmarks™ last F. Habits of Mind: An Organizing Principle for retrieved July 14, 2009, from a Mathematics Curriculum. Cuoco, A. , Goldenberg, E. P., and Mark, J. (1996). /pdf/benchmarks.pdf Journal of Mathematical Behavior, 15 (4), B. ACT College Readiness Standards™ 375-402. Last retrieved July 15, 2009, from C. ACT National Curriculum Survey™ sOfMind.pdf. D. Adelman, Cliff. (2006). The Toolbox G. How People Learn: Brain, Mind, Experience, Revisited: Paths to Degree Completion From and School. Bransford, J.D., A.L. Brown and High School Through College. R.R. Cocking, eds.. Committee on Developments in the Science of Learning, /toolboxrevisit/index.html Commission on Behavioral and Social E. Advanced Placement Calculus, Statistics and Sciences and Education, National Research Computer Science Course Descriptions. May Council, (1999). 2009, May 2010. College Board, (2008). H. Mathematics and Democracy, The Case for F. Aligning Postsecondary Expectations and Quantitative Literacy, edited by Lynn Arthur High School Practice: The Gap Defined Steen. National Council on Education and (Policy Implications of the ACT National the Disciplines, 2001. Curriculum Survey Results 2005-2006). Last I. The Opportunity Equation: Transforming retrieved July 14, 2009, from Mathematics and Science Education for Citizenship and the Global Economy. The CSPolicyBrief.pdf 25 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL G. Condition of Education, 2004: Indicator 30, S. Out of Many, One: Towards Rigorous Top 30 Postsecondary Courses, U.S. Common Core Standards from the Ground Department of Education, (2004). Up. Achieve, (2008). H. Condition of Education, 2007: High School T. Ready for College and Ready for Work: Course-Taking. U.S. Department of Same or Different? ACT. Last retrieved July Education, (2007). 14, 2009, from I. Conley, D.T. (2008). Knowledge and Skills eadinessBrief.pdf for University Success U. Ready or Not: Creating a High School J. Conley, D.T. (2007). Toward a More Diploma That Counts. American Diploma Comprehensive Conception of College Project, (2004). Readiness. K. Crisis at the Core: Preparing All Students for V. Rigor at Risk: Reaffirming Quality in the College and Work. ACT, Last retrieved July High School Core Curriculum. ACT, Last 14, 2009, from retrieved July 14, 2009, from isis_report.pdf gor_report.pdf L. Achieve, Inc., Florida Postsecondary Survey, W. The Forgotten Middle: Ensuring that All 2008. Students Are on Target for College and M. Golfin, Peggy, et. al. CNA Corporation. Career Readiness before High School. ACT, (2005). Strengthening Mathematics at the Last retrieved July 14, 2009, from Postsecondary Level: Literature Review and Analysis. /reports/ForgottenMiddle.html N. Camara, W.J., Shaw, E., and Patterson, B. X. Achieve, Inc., Virginia Postsecondary (June 13, 2009). First Year English and Math Survey, 2004. College Coursework. College Board: New York, NY (Available from authors). III. Career Readiness O. CLEP Precalculus Curriculum Survey: A. ACT Job Skill Comparison Charts Summary of Results. The College Board, (2005). B. Achieve's Mathematics at Work, 2008. P. College Board Standards for College Success: Mathematics and Statistics. C. The American Diploma Project Workplace College Board, (2006). Study. National Alliance of Business Study, 2002. oads/about/association/academic/mathem atics-statistics_cbscs.pdf. D. Carnevale, Anthony and Desrochers, Donna. (2002). Connecting Education Standards Q. Miller, G.E., Twing, J., and Meyers, J. and Employment: Course-taking Patterns of "Higher Education Readiness Component Young Workers. (HERC) Correlation Study." Austin, TX: Pearson. dp/ADPWorkplaceStudy.pdf R. On Course for Success: A Close Look at E. Colorado Business Leaders Top Skills, 2006 Selected High School Courses That Prepare All Students for College and Work. ACT. Last F. Hawai'i Career Ready Study: access to living retrieved July 14, 2009, from wage careers from high school, 2007 G. Ready or Not: Creating a High School ccess_report.pdf Diploma That Counts. American Diploma 26 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL Project, (2004). E. England Qualifications and Curriculum Authority. H. States' Career Cluster Initiative. (2008). (2007). Programme of Study for Key Stage Essential Knowledge and Skill Statements. 4, National Curriculum, 2007. (Grades 10- I. WorkKeys Occupational Profiles™ 11) F. Finland occuprof/index.html Finnish National Board of Education. (2003). National Core Curriculum For Upper IV. International Documents Secondary Schools 2003. (Grades 10-12) STANDARDS [High performing countries/countries G. Hong Kong of interest] Learning Objectives for Key Stage 4. (Grades A. Alberta 10-11) Alberta Learning, (2002). Pure Mathematics H. India 10–20–30 (Senior High). (Grades 10-12) o The National Curriculum Framework. B. Belgium (2005). (Grades 9-12). National Council Department for Educational Development: of Educational Research and Training. Core Curriculum. (Grades 9-10 and 11-12) Last retrieved July 13, 2009, from Retrieved June 24, 2009 from iculum/framework05/prelims.pdf o Secondary School Curriculum, (2010). /corecurriculum/corecurriculum.htm (Grades 9-10). Central Board of Education. C. China o Senior School Curriculum, (2010). Compulsory mathematics curriculum for (Grades 11-12). Central Board of senior secondary, as submitted to the APEC Secondary Education. consortium. (Grades 10-12) Last retrieved I. Ireland July 13, 2009, from o Junior Certificate Mathematics Syllabus (Higher, Ordinary and Foundation px?id=1895 Level). (Grades 7-9). National Council for Curriculum and Assessment, (2000). D. Chinese Taipei o The Leaving Certificate Mathematics o Curriculum Guidelines for the Required Syllabus. (Higher, Ordinary and Subject Math in Senior High Schools, as Foundation Level). (Grades 10-12). submitted to the APEC consortium. National Council for Curriculum and (Grades 10-11) Last retrieved July 13, Assessment, (2000). 2009 from J. Japan le.aspx?id=1900 The Courses of Study in Japan, Provisional o Curriculum Guidelines for the Elective and Unofficial Translation, 2004, as Subject Math (I) in Senior High Schools, submitted to the APEC consortium. (Grades as submitted to the APEC consortium. 10-12). Last retrieved July 13, 2009, from (Grades 12) Last retrieved July 13, 2009, from px?id=1896. le.aspx?id=1901 K. Korea 27 COLLEGE AND CAREER READINESS STANDARDS DRAFT  CONFIDENTIAL The Seventh National School Curriculum, as E. EdExcel, General Certificate of Secondary submitted to the APEC consortium. (Grades Education, Mathematics, (2009). 7-10). Last retrieved July 13, 2009, from F. Lundsgaard Hansen, Birthe and Vagn. Reference levels in School Mathematics, px?id=1897 and Education in Europe, National Presentation, Denmark, (2001). Last retrieved July 15, px?id=1898 2009, from L. Singapore _pdf/EMS_NATIONAL_PRESENTATIONS/EM S_DENMARK.pdf Secondary Mathematics Syllabuses, 2007, as submitted to the APEC consortium. (Grades ≈7-10/11). Last retrieved July 13, V. State Documents 2009, from A. California State Standards es/sciences/files/maths-secondary.pdf. B. Florida State Standards C. Georgia State Standards ASSESSMENTS [Key international assessments with global reach] D. Massachusetts State Standards A. Program for International Student E. Mathematics Curriculum Framework Assessment (PISA), (2006). Revision Panel [Revised Progress Report]. Massachusetts Department of B. Trends in International Mathematics and Elementary and Secondary Education, Science Study (TIMSS), (2007). (2009). Last retrieved July 15, 2009, C. International Baccalaureate, Mathematics from Standard Level, (2006 ). 509/item5_report.pdf. D. University of Cambridge International Examinations: General Certificate of F. Minnesota State Standards Secondary Education in Mathematics, (2009
Hi everybody out there, I am caught up here with a set of algebra questions that I find really hard to answer. I am taking Basic Math course and need help with java how to program 7th edition + solution to programming exercises chapter 7. Do you know of any good quality math help software ? To be honest , I am a little skeptical about how useful these software products can be but I really don't know how to solve these questions and felt it is worth a try. First of all, let me welcome you to the world of java how to program 7th edition + solution to programming exercises chapter 7. You need not worry; this topic seems to be difficult because of the many new symbols that it has. Once you learn the basics, it becomes fun. Algebrator is the most preferred tool amongst novice and professionals . You must buy yourself a copy if you are serious at learning this subject. Registered: 24.10.2003 From: Where the trout streams flow and the air is nice Posted: Monday 01st of Jan 09:10 Even I made use of Algebrator to get to know the basic principles of Intermediate algebra a year back. It is worth investing in the purchase of Algebrator since it offers qualitytutoring in Remedial Algebra and is available at a nominal rate. graphing equations, least common measure and decimals were a nightmare for me until I found Algebrator, which is truly the best algebra program that I have ever come across. I have used it through many algebra classes – Algebra 1, Basic Math and Remedial Algebra. Simply typing in the math problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my math homework would be ready. I highly recommend the program. Just click this link to view more details: I think they are offering money back guarantee so you don't have to worry about it. Believe me, it's the best math software I used. I hope you'd get the assistance you are looking for from this software .
More About This Textbook Overview Problem solving has always been a fundamental element of mathematics. This innovative book challenges the perception that solving a problem is merely a means to an end. Focusing on problem solving as a subject in its own right, the contributors present a broad range of practical, theoretical, simple, intricate and purely mathematical examples.
I have checked all links are working and made some happy discoveries along the way where tools have been improved. There are many calculators here from basic to rather more advanced. I will keep these pages regularly updated. On Decision Mathematics for example, check the excellent Linear Programming grapher from zweigmedia.com: Linear Programming Grapher – zweigmedia.com And look at the calculator from zweigmedia for normal distribution probabilities on the Statistics 16+ page, not only are probabilities calculated but a very clear diagram illustrating those probabilities is also provided. Normal Distribution Calculator – Random Science Tools and Calculators The Graphs section has also had a major update with all the Desmos resources gathered together A new slideshow has been added to the page demonstrating WolframAlpha syntax. WolframAlpha can be very useful for checking for example normal probabilities. Each query as you will see in the slides is illustrated with a diagram. It is always useful to sketch a diagram when solving any normal distribution problems. The way to improve your mathematical skills is to do lots of questions (then do some more!) You need to apply what you know and just reading your notes will not help you do that. Worked examples can be very helpful – particularly if you cover up the solution and try answering the question yourself first. If you are looking for questions the following sites provide many for you. Maths Centre (age 16+) An extensive collection of very clear notes and other resources are available from the mathcentre. There are many very clearly worked examples, also exercises (with answers). Check the resource types,choosing Practice & Revision for example would lead you to this Calculus Refresher (under the Chain rule) which is a whole workbook of mixed calculus examples.mathtutorprovides mathcentre resources conveniently structured as a course. mathcentre – Maths Tutor Just the Maths (age 18+) Just the Maths by Tony Hobsonisanother extensive collection of notes which include numerous worked examples and also exercises to try (with answers). These notes are very useful for students in their last years at school and at university. The Maths Teacher (age 11-17) David Smith's site, The Maths Teacher has an extensive collection of videos to help you study Mathematics. GCSE (age 14-16, though many of these resources would be helpful for younger students also) and A-Level (age 16-18) lessons are available. For each topic not only is a video available but also a transcript and exercises with solutions. This makes the site ideal for revision – you have the choice of perhaps just trying the exercises or if you feel you need more help you can watch the video – whatever is right for you. CIMT,The Centre for Innovation in Mathematics Teaching(age 5 – 18) Scroll down this page to see all the material available for students of all ages. The student texts include worked examples in every section. The texts also have exercises which are usually password protected. (Schools can obtain the password from CIMT). Note in particular the Interactive Material (examples with online checking of answers for Year 7 \| Year 8 \| Year 9 (have a look at the topics here which may be useful for slightly older students also). If you choose the GCSE course material for example and scroll down the page you will see all the pupil textbook chapters. Trinity school (age 11-16) Trinity School have very helpful Mathematics resources – many examples for you to try (answers included) Trinity School Nottingham – numerous questions and answers WolframAlpha (age 5 upwards!) If you are trying any exercises you can obviously check the answers given in the notes; remember that you can also check your answers with WolframAlpha. You could make up questions of your own and check the answers on WolframAlpha, for example suppose you want to make sure you can multiply out brackets – make up your own question (writing questions is actually a good way to check your understanding), for example multiply out (x+3)(x+2), write your answer, then check it on WolframAlpha. Perhaps some calculus? Differentiate sinxcosx wrt x. On the subject of WolframAlpha, there are several slideshowson the WolframAlpha page on this blog to help you get used to the syntax. If you are feeling a little unsure on identifying the equation of a straight line then use this Desmos graph and experiment by changing the gradient, intercept or points marked on the line. The image above shows the line y=2x+1. We can see that the intercept is 1 (where the line crosses the y axis) and the gradient is 2. Looking at the graph we can see that the gradient is positive and you can verify that the gradient is 2 by dividing the difference between the y coordinates (6 in this image) by the difference in the x coordinates (3 in this image). Try moving the points, you will see that this ratio remains constant. Compare the second image. We can see that the intercept is 1. Looking at the slope, the gradient is positive. The gradient is given by 2÷4 = 0.5. So the equation of the line is y = 0.5x + 1. .. … … In the third example; looking at the slope of the line we can see it is negative. The gradient is given by 6÷2 which is 3 and the line crosses the y axis at 2 giving the equation of the line as y = ─3x + 2 Since writing this post Desmos have taken the page and created a superior version!
The book has many important features which make it suitable for both undergraduate and postgraduate students in various branches of engineering and general and applied sciences. The important topics interrelating Mathematics & Computer Science are also covered briefly. The book is useful to readers with a wide range of backgrounds... There is a significant difference between designing a new algorithm, proving its correctness, and teaching it to an audience. When teaching algorithms, the teacher's main goal should be to convey the underlying ideas and to help the students form correct mental models related to the algorithm. This process can often be facilitated by... This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come. This Festschrift volume, published in honour of J. Ian Munro, contains contributions written by some of his colleagues, former students, and friends. In celebration of his 66th birthday the colloquium "Conference on Space Efficient Data Structures, Streams and Algorithms" was held in Waterloo, ON, Canada, during August 15-16, 2013.... Ontologies tend to be found everywhere. They are viewed as the silver bullet for many applications, such as database integration, peer-to-peer systems, e-commerce, semantic web services, or social networks. However, in open or evolving systems, such as the semantic web, different parties would, in general, adopt different ontologies. Thus,... Computational and mathematical models provide us with the opportunities to investigate the complexities of real world problems. They allow us to apply our best analytical methods to define problems in a clearly mathematical manner and exhaustively test our solutions before committing expensive resources. This is made possible by assuming... This textbook serves as an introduction to the subject of embedded systems design, using microcontrollers as core components. It develops concepts from the ground up, covering the development of embedded systems technology, architectural and organizational aspects of controllers and systems, processor models, and peripheral devices.... Paying with mobile devices such as mobile phones or smart phones will expand worldwide in the coming years. This development provides opportunities for various industries (banking, telecommunications, credit card business, manufacturers, suppliers, retail) and for consumers. "Newton's Gravity" conveys the power of simple mathematics to tell the fundamental truth about nature. Many people, for example, know the tides are caused by the pull of the Moon and to a lesser extent the Sun. But very few can explain exactly how and why that happens. Fewer still can calculate the actual pulls of the... Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes. This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of potential applications in sensor and cognitive systems engineering. The topics and application include Information Geometry, Differential... This book constitutes the thoroughly refereed post-conference proceedings of the 9th International ICST Conference on Mobile and Ubiquitous Systems: Computing, Networking, and Services, MobiQuitous 2012, held in Beijing, China, Denmark, in December 2012. The revised full papers presented were carefully reviewed and selected from numerous...
Do the Math: Secrets, Lies, and Algebra EPB Tess loves math because it's the one subject she can trust—there's always just one right answer, and it never changes. But then she starts algebra and is introduced to those pesky and mysterious variables, which seem to be everywhere in eighth grade. When even your friends and parents can be variables, how in the world do you find out the right answers to the really important questions, like what to do about a boy you like or whom to tell when someone's done something really bad? Will Tess's life ever stop changing long enough for her to figure it all out? Do the Math #2: The Writing on the Wall Eighth grade, like algebra, has become pretty complicated for Tess. For one thing, there are the patterns she's noticing everywhere—like how charming-on-the-outside Richard keeps playing scary pranks on her, and how annoying copycat Lynn always has to follow what everyone else is doing. Then... Do the Math: Secrets, Lies, and Algebra In the eighth grade, 1 math whiz 1 stolen test (x), 3 cheaters (y), and 2 best friends (z) who can't keep a secret. Oh, and she can't forget the winter dance (d)! Then there's the suspicious guy Tess's parents know, but that's a whole different problem. Can Tess find the solutions?
Essential Steps of Problem Solving in Mathematical Sciences Share the joy Learning how to solve problems in mathematics is simply to know what to look for. Math problems often require established procedures and one must know What & When to apply them. To identify procedures, you have to be familiar with the different problem situations, and be able to collect the appropriate information, identify a strategy or strategies and use the strategy/strategies appropriately. But exercise is must for problem solving. It needs practice!! The more you practice, the better you get. The great mathematical wizard G Polya wrote a book titled How to Solve It in 1957. Many of the ideas that worked then, do still continue to work for us. Given below are the four essential steps of problem solving based on the central ideas of Polya. Essential Step One: Identifying the clues •First of all read the problem carefully understanding each word precisely and underline the clue words in it. As a student I know that this also requires practice. A new problem-solver, in his/her early days, should work on practicing on identifying clues from a problem. Some when it is said that Problems have their solutions in understanding the problems. • Ask yourself if you've seen a problem similar to this one. If so, what is similar about it? What did you do then? If this problem is almost new to you then after using clues, confirm: What facts are you given here? and What you have to find out here? Essential Step Two: The Game Plan • Define your game plan, and ask again that "Have you seen a problem like this before?". • Identify what you did (or what have you to do)? • Define your strategies to solve this problem. •Try out your strategies, using formulae, simplifying, using sketches, guess and check, look for a pattern, graphing etc.. • If your strategy doesn't work, it may lead you to a new strategy that does work. You can find a new strategy iff you know all the concepts related to the topic on which the problem is covered. Essential Step Three: Solving the Problem Use your skills of 'strategy' & 'tactics' to solve the problem. Never go over or out of the focus of the problem. This may cause time waste and errors. This step needs specialization. Essential Step Four: Reflect upon the problem This is very critical step and many students leave this while solving the problems. • Look over the solution you arrived at just. Again look at the problem you had. • Does it look probable? • Did you answer the question exactly? And are you sure of the answer? If yes , then how much? • Did you answer in the language of the problem? • Did you derive the answer in the specified units? At last, applying these steps, also need practice and hard work. If you have any other techniques of problem solving then drop those into the comment box . This will help other readers. About the Author 3 Comments Tinned_Tuna Personally, my method for solving problems (since most of the problems I come up against are well known problems) involves an extra crucial step: Research. If I'm really stuck on a problem, for example, at the moment, I'm looking into how to compile closures (I'm not straight maths, I'm CS/Maths, hence compiler stuff). My main reaction to this? Think about the problem for a good few hours, try to realise where I'm coming unstuck, and finally, I'm going to have to raid the library. Some solutions most people won't hit on simply because they're non-obvious, and in a lot of cases, a lot of work has gone into producing a solution that works. Look at it, see why it works, can it be made to work for your problem, what hurdles might you have to get over for it to work, how does their solution inform your search?
Mathematics This computer program is an exact emulation of a toy which was sold years ago called Magic Designer. There are 2 versions - MS Windows one written in Euphoria and C and one written for the Web for people who do not have a Windows computer. "Curso rapido de calculo diferencial e integral" is a program that may help college and high school students understand and learn the basic concepts of differential and integral calculus. So how to solve some useful exercises using educational videos Program for presentation of geometrical euclidean constructions. Utilises own script language for description of the construction. Construction is performed step by step and detailed report in HTML as well as final result in JPEG/PNG can be exported. Visual BASIC 6.0 program to find the factors between two numbers. Use as an educational tool to help students with factors. Does not find the LCD but use as a learning tool to find the LCD by looking at the factors. Jabaco version runs in any JRE Function Wizard is designed to provide a lightweight, fast, and easy to use application that will integrate, differentiate, calculate maxima and minima, etc. basic polynomials, as well as assist in other tedious polynomial tasks. GraphIte is a mathematical graphing program for Windows platforms built in C++ on the MFC libraries by Mr Soo Reams and Mr Stephen Bennett. Many of the features are not understood by either of the aforementioned, or Tim Cook
Analytic Trigonometry With Application - 9th edition Summary: Featuring updated content, vivid applications, and integrated coverage of graphing utilities, the ninth edition of this hands-on trigonometry text guides readers step by step, from the right triangle to the unit-circle definitions of the trigonometric functions. Examples with matched problems illustrate almost every concept and encourage readers to be actively involved in the learning process. Key pedagogical elements, such as annotated examples, think boxes, cautio...show moren warnings, and reviews, help readers comprehend and retain the materialFriends of the Phoenix Library Phoenix, AZ 2005 Hardcover Good 100% of this purchase will support literacy programs through a nonprofit organization! $9.97 +$3.99 s/h Good bingofred-1 Oviedo, FL 047174655X tight and sound, a nice solid book $12.44 +$3.99 s/h Good E1J1 Orlando, FL Some writing and highlighting. Most of the 500+ pages are clean, bumped corners. Text is eminently readable. Does not include cd's or access codes if applicable133
Summary: Mathematical reform is the driving force behind the organization and development of this new precalculus text. The use of technology, primarily graphing utilities, is assumed throughout the text. The development of each topic proceeds from the concrete to the abstract and takes full advantage of technology, wherever appropriate. The first major objective of this book is to encourage students to investigate mathematical ideas and processes graphically and numerically,...show more as well as algebraically. Proceeding in this way, students gain a broader, deeper, and more useful understanding of a concept or process. Even though concept development and technology are emphasized, manipulative skills are not ignored, and plenty of opportunities to practice basic skills are present. A brief look at the table of contents will reveal the importance of the function concept as a unifying theme. The second major objective of this book is the development of a library of elementary functions, including their important properties and uses. Having this library of elementary functions as a basic working tool in their mathematical tool boxes, students will be able to move into calculus with greater confidence and understanding. In addition, a concise review of basic algebraic concepts is included in Appendix A for easy reference, or systematic review. The third major objective of this book is to give the student substantial experience in solving and modeling real world problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful. Most of the applications are simplified versions of actual real-world problems taken from professional journals and professional books. No specialized experience is required to solve any of the applications
MA.8.2.2 2000 MA.8.2.3 2000 Use estimation techniques to decide whether answers to computations on a calculator are reasonable. MA.8.2.4 2000 Use mental arithmetic to compute with common fractions, decimals, powers, and percents. MA.8.3 2000 - Algebra and Functions Students solve simple linear equations and inequalities. They interpret and evaluate expressions involving integer powers. They graph and interpret functions. They understand the concepts of slope and rate. MA.8.3.1 2000 Write and solve linear equations and inequalities in one variable, interpret the solution or solutions in their context, and verify the reasonableness of the results. MA.8.3.2 2000 Solve systems of two linear equations using the substitution method and identify approximate solutions graphically. MA.8.3.3 2000 Interpret positive integer powers as repeated multiplication and negative integer powers as repeated division or multiplication by the multiplicative inverse. MA.8.3.4 2000 Use the correct order of operations to find the values of algebraic expressions involving powers. MA.8.3.5 2000 Identify and graph linear functions, and identify lines with positive and negative slope. MA.8.3.6 2000 Find the slope of a linear function given the equation and write the equation of a line given the slope and any point on the line MA.8.3.7 2000 Demonstrate an understanding of rate as a measure of one quantity with respect to another quantity. MA.8.3.8 2000 Demonstrate an understanding of the relationships among tables, equations, verbal expressions, and graphs of linear functions. MA.8.3.9 2000 Represent simple quadratic functions using verbal descriptions, tables, graphs and formulas, and translate among these representations. MA.8.3.10 2000 Graph functions of the form y=nx2 and y=nx3 and describe the similarities and differences in the graphs. MA.8.4 2000 - Geometry Students deepen their understanding of plane and solid geometric shapes and properties by constructing shapes that meet given conditions, by identifying attributes of shapes, and by applying geometric concepts to solve problems. MA.8.4.4 2000 MA.8.4.5 2000 Use the Pythagorean Theorem and its converse to solve problems in two and three dimensions. MA.8.5 2000 - Measurement Students convert between units of measure and use rates and scale factors to solve problems. They compute the perimeter, area, and volume of geometric objects. They investigate how perimeter, area, and volume are affected by changes of scale. MA.8.5.1 2000 Convert common measurements for length, area, volume, weight, capacity, and time to equivalent measurements within the same system. MA.8.5.2 2000 Solve simple problems involving rates and derived measurements for such attributes as velocity and density. MA.8.5.3 2000 MA.8.5.4 2000 Use formulas for finding the perimeter and area of basic two-dimensional shapes and the surface area and volume of basic three-dimensional shapes, including rectangles, parallelograms, trapezoids, triangles, circles, prisms, cylinders, spheres, cones, and pyramids. MA.8.5.5 2000 Estimate and compute the area and volume of irregular two-dimensional and three-dimensional shapes by breaking the shapes down into more basic geometric objects. MA.8.6 2000 - Data Analysis and Probability Students collect, organize, represent, and interpret relationships in data sets that have one or more variables. They determine probabilities and use them to make predictions about events. MA.8.6.1 2000 Identify claims based on statistical data and, in simple cases, evaluate the reasonableness of the claims. Design a study to investigate the claim. MA.8.6.2 2000 Identify different methods of selecting samples, analyzing the strengths and weaknesses of each method, and the possible bias in a sample or display. MA.8.6.3 2000 Understand the meaning of, and be able to identify or compute the minimum value, the lower quartile, the median, the upper quartile, the interquartile range, and the maximum value of a data set. MA.8.6.4 2000 Analyze, interpret, and display single- and two-variable data in appropriate bar, line and circle graphs, stem-and-leaf plots and box-and-whisker plots, and explain which types of display are appropriate for various data sets. MA.8.6.5 2000 Represent two-variable data with a scatterplot on the coordinate plane and describe how the data points are distributed. If the pattern appears to be linear, draw a line that appears to best fit the data, and write the equation of that line. MA.8.6.6 2000 Understand and recognize equally likely events. MA.8.6.7 2000 Find the number of possible arrangements of several objects by using the Basic Counting Principle. MA.8.7 2000 - Problem Solving Students make decisions about how to approach problems and communicate their ideas.
Effective Learning & Teaching in Mathematics & Its Applications Mathematics dates from antiquity, built upon the minds of the world's intellectual giants: Euclid, Pythagoras, Archimedes, Newton, Euler, Gauss, Einstein and many, many others. It is perhaps the most developed science, deploying a huge corpus of theory and technique. Music, art and mathematics transcend all cultures but perhaps mathematics most of all is universal, for it is a truly common language, regrettably appreciated by and accessible to far too few of us. Among the sciences, mathematical sciences have undergone extraordinary growth over the last decade, primarily stimulated by advances in computing facilities, both software and hardware. The advancement of science, indeed society more generally, has always depended upon mathematics and will do so even more in the future. Communicating this corpus of knowledge, understanding the theoretical and logical base and deploying this knowledge to the benefit of mankind is one of the biggest challenges facing education at the beginning of this new century (or millennium!). It is therefore pleasing to see a text on Effective Teaching and Learning in Mathematics and its Applications, edited by Peter Kahn and Joseph Kyle, with chapters by leading practitioners in the discipline of mathematics, statistics and operational research. Chapters in the book cover the key areas of assessment (diagnostic, formative, summative), learning developments, course design and reflection, application of mathematics in modelling phenomena, the analysis of data and preparation for future employment. There is also recognition of the need to support the non-specialists who need mathematics or statistics for the full understanding and appreciation of their own discipline. I strongly encourage you to read the chapters of this book, implement and further develop the ideas and concepts relevant to your interests, but to also draw your colleagues' attention to the book as well, for there is much to understand about the learning, teaching and assessment of mathematics, statistics and operational research. Professor John R Blake Director, LTSN Mathematics, Statistics and Operational Research Network School of Mathematics and Statistics, The University of Birmingham
Margate, FL PrecalPrecalculus reviews concepts and skills introduced in Algebra 2 and introduces students to exponential and logarithmic functions, sequences, and series. In order to do well, students must UNDERSTAND the concepts presented not merely ?get the answer.? I have had great success teaching the concep
151+ subjects including precalculus
torn out from the center) to measure understanding. Students will develop foundational math skills needed for higher education and practical life skills with ACE's Math curriculum. This set includes the 4th Edition/Latest Edition Math PACEs 1073-1084 which cover: Whole and mixed numbers, integers, and common fractions. Proper mathematical terminology-dividend, multiplicand, product, simplify, minuend, quotient, numerator, and denominator; how to change fractions and decimals to percent; how to find the number when a percent is known; and data and graphs, mean, mode, median, range, and rank. Business and consumer arithmetic-profit and loss, commission, discounts, bills and receipts, and invoices with discounts; ratio, proportions and percent. Business methods needed to function at home-keeping cash and household accounts, budgets, insurance, and the reading of gas and electric meters. Banking-savings and checking accounts, deposits, interest, and loans. English and metric units of length, volume, weight, and temperature. Basic geometry concepts and symbols, uses a protractor and compass to find perimeter and area of shapes and solids. Equations-variable, sets, and set notation; vocabulary, symbols and word problems.
2 Physics We've already seen some applications of derivatives to physics. In particular, we saw that the rst derivative of a position function is the velocity, and the second derivative is acceleration. Derivative Applications and Related Rates ... 1 Calculus in the Natural and Social Sciences Physics Biology Economics 2 Related Rates Volumes Joe Benson Derivative ... Let's take a minute to examine a few of the instances where derivatives occur in the sciences. Recall that the ... DERIVATIVES AND APPLICATIONS; DEVELOPMENT OF ONE STUDENT'S UNDERSTANDING Gerrit Roorda#, Pauline Vos* and Martin Goedhart# ... derivatives are used inphysics lessons for concepts such as velocity, acceleration or radioactive decay, ... Given clarify the importance and numerous applications of fractional derivatives and integrals, in recent years many articles and books on this subject have been published [3,4]. 1.2. ... Heaviside's operator inphysics, Fluid flows and the design of Weir Notch in Civil and Mechanics, Analysis ! 1! ! Calculus & Physics Calculus is used a lot in the more advanced levels of physics. What it allows the physicist to do is examine motion (or some other physical phenomenon) during infinitesimal (aka teensy-weensy) times or distances. IN MANY VARIABLES WITH APPLICATIONS TO BEAM PHYSICS MARTIN BERZ PROCEEDINGS WORKSHOP ON AUTOMATIC DIFFERENTIATION BRECKENRIDGE, CO, JANUARY 1991 ... Besides the mere computation of derivatives, algorithms for the e fficient composition and using this generalized calculus with Laplace transforms of complex-order derivatives to solve ana-lytically many differential equations inphysics, ... collection of papers on applicationsinphysics edited by Hil-fer [19]. applications of calculus inphysics to reinforce (or perhaps to reteach) calculus concepts. Access to reform calculus materials such as the Calculus ... derivatives and anti-derivatives as something other than equations generated from given equations. What physical meaning can be assigned to the various time derivatives of position and their graphical representations, ... applications (scroll down) ... Students will use Interactive Physics software to simulate collisions. Assessment: Their Applicationsin Mathematical Physics Robert Vein Paul Dale Springer. Preface The last treatise on the theory of determinants, by T. Muir, revised and ... Partial derivatives of this type are applied in Section 4.5.2 on symmetric Toeplitz determinants. many dynamical systems whose equations involved with fractional order derivatives have potential applicationsin many fields of science. ... Applications of fractional calculus inphysics, World Scientific, New Jersey, 2000. Applications of Taylor Series Jacob Fosso-Tande Department of Physics and Astronomy, University of Tennessee ... self consistent field calculation of the second derivatives is very time consuming, thus the optimization usually The Virial Theorem and its applicationsin the teaching of Modern Physics . Celso L. Ladera, Eduardo Alomá y Pilar León Departamento de Física, ... (the force components are given by the derivatives of the potential energy . V) ... This is an intermediate course in distributions with applications to Physics and Engineering. It is addressed to students and teachers wishing to have a deeper ... derivatives of any order. The advantages of this operational calculus in solving Theoretical Developments and ApplicationsinPhysics and Engineering edited by and Université de Bordeaux I. ... symposium on Fractional Derivatives and Their Applications (FDTAs), ASME-DETC 2003, Chicago, Illinois, USA, September 2003; IFAC first
John O'Neill Associate Dean, School of Business Associate Professor of Quantitative Business Analysis Associate Professor of Mathematics Siena Hall 301B (518) 783-2386 joneill@siena.edu QBUS 110 Math for Decision Making II Course Guide Course Description The primary focus of this course is to have students apply appropriate mathematical models to common business situations, developing their ability to analyze and interpret the results. Students will develop their analytical skills through exposure to modeling as well as classical differential and integral calculus. A wide variety of problems from business may be solved using nonlinear functions. For example, a business manager uses the exponential and logarithmic functions to study the growth of money or the decay of new sales volume. Rate of change is an extremely important concept for business managers. Differential calculus is used to measure a rate of change. It can be used to find the marginal profit, marginal cost, and marginal revenue, given the respective profit, total cost, and total revenue functions. Differentiation can be used to minimize average cost, maximize total revenue, and maximize profit. Techniques applied in business situations such as supply and demand analysis, inventory cost modeling, optimization of profit, revenue and average cost, theory of diminishing return and marginal analysis will also be covered. Specific, Assessable Learning Outcomes Compute derivatives for polynomial, logarithmic, exponential functions and more complex functions which are combinations thereof. Use differential calculus to find the marginal profit, marginal cost, and marginal revenue, given the respective profit, total cost, and total revenue functions and then to determine the level of production that maximizes revenue or profit for a product or minimizes the average cost of producing a product. Utilize first and second derivatives to identify critical points, inflection points and associated graphical behavior for a given function. Use implicit differentiation to solve business problems involving the rates of change of two or more variables. An example of this type of problem might include elasticity of demand or maximization of tax revenue. Use integration to find total revenue functions from marginal revenue functions, to find total cost functions from marginal cost functions and to optimize profit from information about marginal cost and marginal revenue. Use definite integrals to find area under a curve. More adept students may use definite integrals to approximate the time/total value of a continuous income stream and/or find Producer's and Consumer's Surplus. Course Outline The development and use of logarithmic and exponential functions and their use in solving common business problems. The development and use of differential calculus to find the rate of change, marginal profit, marginal cost, and marginal revenue, given the respective profit, total cost, and total revenue functions. The development and use of relative maxima and relative minima for finding maximum and/or minimum values of important business functions such as profit, cost, and revenue. The development and use of implicit differentiation techniques from calculus to solve business problems such as elasticity of demand and maximization of taxation revenue. The development and use of integration techniques from calculus to find total revenue functions from marginal revenue functions, to optimize profit from information about marginal cost and marginal revenue, and to find national consumption functions from information about marginal propensity to consume. The development and use of definite integrals from calculus to find area under a curve. Applications of this technique may also include approximating the time/total value of a continuous income stream or determining a consumer's and producer's surplus is also explored. Recommended Teaching Methodology This course will be structured in such a way as to facilitate the use of different methods of instruction. Readings, lectures, multimedia presentations, group discussions, and written assignments will be used throughout the course. Work will be done individually and/or in small groups. The primary focus of the teaching methodologies used will be to prepare the student to understand and apply mathematical tools and reasoning to business situations. Thus, ample time will be devoted to "hands-on" problem solving. The readings will come from the required text as well as additional material to be provided by the instructor. Lectures and group discussions will enable the instructor and students to expand on the material presented in the readings. For all testing situations, a departmentally designed formula sheet will be the only supplemental material accompanying any exam. Assessment Measures The following assessment measures will be used. Assessment devices (quizzes, homework, exams, etc.) should be given throughout the semester, building up to a comprehensive final exam. The final exam will be used to assess the specific assessable learning outcomes enumerated above. Writing and/or oral presentation(s) focusing on major areas of study will be given to students to assess their understanding of mathematics and the ability to communicate quantitative results. Statement of Expectations This course satisfies the quantitative reasoning (CAQ) core requirement for the college and is a pre-business core requirement for the School of Business. As such, any student in the course is required to show a D- level proficiency in the course in order to attain credit for the college core and/or attain credit towards the business major. It is normally taken in the student's second semester of full-time studies. To attain the desired levels of proficiency, it is required that students attend class prepared to participate in interactive learning using tools such as the graphical calculator and textbook. Students should remain actively engaged in the material covered in class. Of course this is not all that is needed, as classroom learning success is also influenced by student preparation outside of class. It is therefore imperative that students complete out-of-class assignments and textbook reading in a timely fashion. Students will develop and retain the knowledge and skill set described above by continual practice, thereby slowly building and adding onto their knowledge base. "Cramming" in the days before a test is not an effective way to learn the skills necessary to employ mathematical reasoning in the business environment. Lastly, it is expected that if you have questions about any course material you will ask those questions so that they may be answered. There are a variety of sources from which answers will come, including (but by no means limited to) the textbook, the QBA Help Lab, a tutor, classmates, and MOST IMPORTANTLY the professor. You can ask questions of the professor in class or after class during the professor's office hours. Remember that an unasked question is an answer never given. Prerequisite Knowledge The most important prerequisites are an interest in the subject, the willingness to commit the necessary resources in terms of time and intellectual effort, and the willingness to actively participate in the learning process. Students should have a fundamental understanding of mathematical reasoning as well as be competent in solving applied algebra problems. Successful completion of Mathematics for Decision Making I (QBUS-100) is required before this course can be taken. The Quantitative Business Analysis department will annually review assessment results for this course. Specifically, assessment results in each of the five learning outcome areas will be analyzed to determine the level of success in achieving these learning outcomes. Any deficiencies in achieving learning outcomes will be addressed and appropriate changes designed to improve the success in achieving these learned outcomes.
Summary: Intended for introductory courses in basic mathematics, this comprehensive text teaches the skills necessary for practical work involving architectural and mechanical drafting, electronics, welding, air conditioning, aviation, and automotive mechanics, and machining and construction. The authors have carefully organized the material to provide flexibility: the text can be used in a lecture class, in a laboratory setting, or for self-paced instruction. Each chapter is...show more divided into frames that present the individual concepts on which the major concepts are based. To ensure student comprehension, each concept is first explained and then illustrated with an example. Questions about the material test students' understanding of the concepts, and the answers are found on the right side of each page. Exercise sets throughout the chapters and self tests at the end of each chapter provide further opportunity for students to master the material. In all, the text presents more than 3,000 problems and exercises
This clear, accessible treatment of mathematics features a building-block approach toward problem solving, realistic and diverse applications, and chapter organizer to help users focus their study and become effective and confident problem solvers. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. The Fourth Edition contains additional modeling and real-data coverage. A conceptual approach to functions is introduced early in the book and revisited in Ch. 5, 6, 7, 8, and 10—readers are exposed to a variety of realistic situations where functions are used to explain and record the changes we observe in the world. A discussion of solving linear equations in Chapter 2 now includes coverage of equations with no solution and equations with infinitely many solutions. The sections on determinants and Cramer's rule have been moved out of Chapter 4 into an appendix. This material can be covered with ease after Section 4.3. Editorial Reviews Booknews Progresses from linear equations and polynomials through to quadratic equations and exponential functions. Bright colors and countless graphics will keep even nodding-off students up to speed. The new edition focuses on real world math problems and includes practice problems with solutions, application problems, and chapter summaries presented in chart form. Annotation c. by Book News, Inc., Portland, Or. Product Details Read an Excerpt problems selftesting. Exercises are paired and graded and are of varying levels and types to ensure that all skills and concepts are covered. As a result, the text offers students an effective and proven learning program suitable for a variety of course formats—including lecturebased classes; discussionoriented classes; distance learning centers; modular, selfpaced courses; mathematics laboratories; and computersupportedSolving Abilities We are committed as authors to producing a textbook that emphasizes mathematical reasoning and problemsolving techniques as recommended by AMATYC, NCTM, AMS, NADE, MAA, and other groups. To this end, the exercise sets are built on a wealth of reallife and realworld and realfriendly writing style. See the walkout example for each type of exercise. Students often find that preparing a similar chapter organizer on their own in higherEQ with QuizmasterEQ; allnew lecture videos; lecture videos digitized on CDspecific site offers students online selfquizzes. Questions are graded, and students can email (<%ISBN%>0130328383) • Complete student text • Answers in place on the same text page as the exercises • Teaching Tips at key points where students historically need extra help • Answers to all exercises in pretests, review problems, tests, cumulative tests, diagnostic pretest, and practice final Instructor's Solutions Manual (<%ISBN%>0130342041) • Detailed stepbystep solutions to the evennumbered exercises • Solutions to every exercise (odd and even) in the diagnostic pretest, pretests, review problems, tests, cumulative tests, and practice final • Solution methods that reflect those emphasized in the text Instructor's Resource Manual with Tests (<%ISBN%>0130342033) • Nine test forms per chaptersix free response, three multiple choice. Two of the freeresponse tests are cumulative in nature. • Two forms of pretests per chapter • Eight forms of final examination • Twenty additional exercises per section • Answers to all tests and additional exercises Media Resources New TestGenEQ with QuizMasterEQ (Windows/Macintosh) (<%ISBN%>0130600237) • Algorithmically driven, textspecific testing program • Networkable for administering tests and capturing grades online • The builtin Question Editor allows you to edit or add your own questions to create a nearly unlimited number of tests and worksheets. • Use the Function Plotter to create graphs. • Sidebyside (<%ISBN%>0130600105) • Enables instructors to create either customized or algorithmically generated practice tests from any section of a chapter or a test of random items • Includes an email function for network users, enabling instructors to send a message to a specific student or an entire group • Provides networkbased reports and summaries for a class or student and for cumulative or selected scores New MathPro 5 Anytime. Anywhere. With Assessment. • The popular MathPro tutorial program available over the Internet • Online tutorial accessanytime and anywhere • Enhanced course management tools Companion Web Site Internet Connections activities have been completely revised and updated. Annotated finks facilitate student navigation. • Site provides online selfquizzes. Questions are graded, and students can email their results to the instructor. • Syllabus Manager gives professors the option of creating their own online custom syllabus. Visit the Web site to learn more. Supplements for Students Printed Resources Student Solutions Manual (<%ISBN%>0130342017) • Solutions to all oddnumbered exercises • Solutions to every (odd and even) exercise found in pretests, chapter tests, reviews, and cumulative reviews • Solution methods that reflect those emphasized in the textbook • Ask your bookstore about ordering. Media Resources New MathPro Explorer 4.0 CDROM (Student version: 0130600229) • Keyed to each section of the text for textspecific tutorial exercises and instruction • Warmanytime and anywhere New Lecture Videos (<%ISBN%>0130600180) • All new videotapes accompany the fourth edition. • Videos are keyed to each section of the text. • Key concepts are explained stepbystep. New Digitized Lecture Videos on CDROM (<%ISBN%>0130600199) • The entire set of Intermediate Algebra, Fourth Edition lecture videotapes in digital form • Convenient access to video tutorial support from home or campus computer • Available shrinkwrapped with the text or standalone New Prentice Hall Tutor Center • Staffed by qualified math instructors and open 5 days a week, 7 hours a day • Text specific tutoring provided via tollfree telephone, fax, or email. • The Prentice Hall Tutor Center is accessed through a registration number that may be bundled with a new textbook or purchased separately. Companion Web Site Internet Connections activities have been completely revised and updated. • Site provides an online study guide via selfquizzes. Questions are graded, and students can email classtestedofout solutions for all the oddnumbered exercises as well as diagnostic pretest, chapter review, chapter test, and cumulative test exercises in this book. (If your college bookstore does not carry the Student Solutions Manual, ask them to order a copy for you. <%ISBN%>0130342017) Watch the videotapes or digitized videos on CD Practice problem solving using the resources available to you. MathPro 5 is the online version of this comprehensive tutorial program. out solutions to the Practice Problems that appear at the end of the text. Studentfriendly application exercises. In every chapter of this book you will find application exercises that are realistic and interesting. Many of the exercises were actually written or suggested by students. As you develop your problemsolving and reasoning skills in this course, you will encounter a number of realPreface- techniques writing-specific site offers students online self-quizzes. Questions are graded, and students can e-mail (ISBN: 0-13-032838-3) • Complete student text • Answers in place on the same text page as the exercises • Teaching Tips at key points where students historically need extra help • Answers to all exercises in pretests, review problems, tests, cumulative tests, diagnostic pretest, and practice final Instructor's Resource Manual with Tests (ISBN: 0-13-034203-3) • Nine test forms per chapter-six free response, three multiple choice. Two of the free-response tests are cumulative in nature. • Two forms of pretests per chapter • Eight forms of final examination • Twenty additional exercises per section • Answers to all tests and additional exercises Media Resources New TestGen-EQ with QuizMaster-EQ (Windows/Macintosh) (ISBN: 0-13-060023-7) • Algorithmically driven, text-specific testing program • Networkable for administering tests and capturing grades online • The built-in Question Editor allows you to edit or add your own questions to create a nearly unlimited number of tests and worksheets. • Use the Function Plotter to create graphs. • Side-by-side- (ISBN: 0-13-060010-5) • Enables instructors to create either customized or algorithmically generated practice tests from any section of a chapter or a test of random items • Includes an e-mail function for network users, enabling instructors to send a message to a specific student or an entire group • Provides network-based reports and summaries for a class or student and for cumulative or selected scores New MathPro 5 Anytime. Anywhere. With Assessment. • The popular MathPro tutorial program available over the Internet • Online tutorial access-anytime and anywhere • Enhanced course management tools Companion Web Site • Internet Connections activities have been completely revised and updated. Annotated finks facilitate student navigation. • Site provides online self-quizzes. Questions are graded, and students can e-mail their results to the instructor. • Syllabus Manager gives professors the option of creating their own online custom syllabus. Visit the Web site to learn more. Media Resources New MathPro Explorer 4.0 CD-ROM (Student version: 0-13-060022-9) • Keyed to each section of the text for text-specific tutorial exercises and instruction • Warm--anytime and anywhere New Lecture Videos (ISBN: 0-13-060018-0) • All new videotapes accompany the fourth edition. • Videos are keyed to each section of the text. • Key concepts are explained step-by-step. New Digitized Lecture Videos on CD-ROM (ISBN: 0-13-060019-9) • The entire set of Intermediate Algebra, Fourth Edition lecture videotapes in digital form • Convenient access to video tutorial support from home or campus computer • Available shrink-wrapped with the text or stand-alone New Prentice Hall Tutor Center • Staffed by qualified math instructors and open 5 days a week, 7 hours a day • Text specific tutoring provided via toll-free telephone, fax, or e-mail. • The Prentice Hall Tutor Center is accessed through a registration number that may be bundled with a new textbook or purchased separately. Companion Web Site • Internet Connections activities have been completely revised and updated. • Site provides an online study guide via self-quizzes. Questions are graded, and students can e-mail class-tested-of--out solutions for all the odd-numbered exercises as well as diagnostic pretest, chapter review, chapter test, and cumulative test exercises in this book. (If your college bookstore does not carry the Student Solutions Manual, ask them to order a copy for you. ISBN: 0-13-034201-7) Watch the videotapes or digitized videos on CD- Practice problem solving using the resources available to you. MathPro 5 is the online version of this comprehensive tutorial program. --out solutions to the Practice Problems that appear at the end of the text. Student-friendly application exercises. In every chapter of this book you will find application exercises that are realistic and interesting. Many of the exercises were actually written or suggested by students. As you develop your problem-solving and reasoning skills in this course, you will encounter a number of real-Introductionfollowing writing
This site is a selection of mathlets designed for "geometry classes to review basic algebra skills in such a way that they... see more This site is a selection of mathlets designed for "geometry classes to review basic algebra skills in such a way that they can check their answers and/or get hints as to how to proceed. The idea behind these "procedure-based" dynamic worksheets is to provide students the opportunity to review and practice algebra skills with problems they create, while at the same time providing a means for students to check their answers and to get a hint if needed. The hints will walk the student through the problem in a step by step manner.״ ״Created by a high school math teacher with over 25 years of experience in the classroom. Develop your algebraic equation... see more ״Created by a high school math teacher with over 25 years of experience in the classroom. Develop your algebraic equation solving skills through playing a Bingo game. This game will take you step by step through the process of learning how to solve the most basic equation up through multiple-step equations by way of 13 different levels and it will allow you to choose from a variety of Bingo games from straight-line Bingo through multiple patterns of Bingo all the way up to Black-out Bingo if you choose. The game will keep track of your time and points to be able to compete with others as well as yourself.״״This game is great for Pre-Algebra and Algebra I students who are just learning how to solve equations as well as for Algebra II and even Precalculus students needing to review their equation solving skills. It can also be used an Algebra tutorial for anyone preparing for a standardized test such as the S.A.T. or A.C.T.״This app costs $.99 ״Have you forgotten most of your algebra? Algebra Touch will refresh your skills using touch-based techniques built from the... see more ״Have you forgotten most of your algebra? Algebra Touch will refresh your skills using touch-based techniques built from the ground up for your iPhone/iPad/iPod Touch. Say you have x + 3 = 5. You can drag the 3 to the other side of the equation. Enjoy the wonderful conceptual leaps of algebra, without getting bogged down by the tedium of traditional methods. Drag to rearrange, tap to simplify, and draw lines to eliminate identical terms. Easily switch between lessons and randomly-generated practice problems. Create your own sets of problems to work through in the equation editor, and have them appear on all of your devices with iCloud. (there is a version of this app for OSX as well!) Current material covers: Simplification, Like Terms, Commutativity, Order of Operations, Factorization, Prime Numbers, Elimination, Isolation, Variables, Basic Equations, Distribution, Factoring Out, Substitution.״This app costs $1.99 ״Punflay's popular Mathomatix series is back! And this time its cutie pie Al the Zebra who's ready to play cool algebra games... see more ״Punflay's popular Mathomatix series is back! And this time its cutie pie Al the Zebra who's ready to play cool algebra games with your kids! Learning Algebra is never going to be the same with Mathomatix: Alzebra. The app is designed to teach basic functional algebra to kindergarteners and is based on National and California Standards. The vivid colors, unique characters and exciting animations are sure to capture the curiosity and attention of children. There are five different games, all aimed at improving the various Algebra skills introduced in Kindergarten.Pizza Mania: Get ready for a Pizza party! Simply select the right toppings and make your own pizzas! This fun game helps in strengthening identifying, sorting and classifying skills. Your kids will be hungry for more!Tummy Time: This game has cute animals that are hungry all the time. See your child's hand-eye coordination improve as they use the accelerometer to feed the right food to the right animal. Space Rock: Teaching object patterns can leave most parents perplexed. But this fun game set in outer space will encourage the young kindergartener to reason out the patterns and fill them in; cool special effects will leave them giggling! Jump-a-Sound: An interactive sound pattern game, Jump-a-Sound will encourage your kids to listen to a sound sequence and recreate it. The little chipmunk that jumps greedily at the rewards will have you laughing. Number Strike: Bring the bowling alley to your living room with this great number pattern game. Simply aim and flick the ball at the correct pin to complete the pattern, and learn all about numbers! An exciting and challenging game for kids! Al Zebra's rewards will leave your kindergartener shrieking with delight and sharing it with friends and family. They can win everything from a cool surf board to an astronaut suit! And while they are having a great time learning, you can finally get that downtime you deserve! Grab the app right away!״This is a free app. ״Do you need to measure angles with your device? Are you studying or working? Get the ideal app to measure angles with... see more ״Do you need to measure angles with your device? Are you studying or working? Get the ideal app to measure angles with several nice features such as: * Camera view. * Pause angle. * Switch cameras. * Designed for: iPhone, iPad and iPod Touch. * Easy to use.״This is a free app a parent struggling to help your child with geometry homework, this is a short book that will help you. It covers plane geometry and touches on beginning trigonometry. You will find 70 illustrations and 25 problems with detailed solutions. Whether you are new to geometry or just need to brush up on the things you learned in school, this is the book for you. Give your child the gift of learning along with you. This book can be useful for students as well. ' ״Jumbo Calculator is great for anyone wanting the ease of use of a large buttoned calculator. While sadly you can't feel the... see more ״aring and square-rooting. One size fits all.״This is a free app
is a self-contained introduction to the theory of distributions, sometimes called generalized functions. Most books on this subject are either intuitive or else rigorous but technically demanding. Here, by concentrating on the essential results, the authors have introduced the subject in a way that will most appeal to non-specialists, yet is still mathematically correct. Topics covered include: the Dirac delta function, generalized functions, dipoles, quadrupoles, pseudofunctions and Fourier transforms. The self-contained treatment does not require any knowledge of functional analysis or topological vector spaces; even measure theory is not needed for most of the book. The book, which can be used either to accompany a course or for self-study, is liberally supplied with exercises. It will be a valuable introduction to the theory of distributions and their applications for students or professionals in statistics, physics, engineering and economics. less
Book Description:Paperback. Book Condition: New. 2nd. 15mm x 19mm x 249mm. Paperback. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 358 pages. 0.862. Bookseller Inventory # 9780941355711 Book Description:Paperback. Book Condition: New. Paperback. Math Matters, first published in 2000, quickly became an invaluable resource for math educators nationwide, helping them clarify their own understanding of the math concepts they are required to teach. This important book contains activities and discussions on key elementary topics such as whole number computation, fractions, algebra, geometry, and measurement. The scope in this second edition has now been expanded to address key topics in the middle school math curriculum as well, including sections on integers, exponents, similarity, the Pythagorean Theorem, and more. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN, Momence,IL, Commerce,GA. book. Bookseller Inventory # 97809413557
Offering 10+ subjects including calculus calculus
What's New in Mathematica 9 Jon McLoone Mathematica 9 adds major computational areas and introduces a new interface paradigm—further expanding Mathematica's unrivaled base of algorithmic, knowledge, and interface capabilities. Get an overview of what's new in Mathematica 9 in this video. Channels: Mathematica Mathematica seamlessly integrates computational ability with a sophisticated development environment and a range of immediate deployment options. In this video, Tom Wickham-Jones briefly describes the advantages of Mathematica as a technical hub. Mathematica stands out from traditional computer languages by simultaneously supporting many programming paradigms, such as procedural, functional, rule-based, pattern-based, and more. In this video, Conrad Wolfram describes the advantages of having a system with a full programming language. One of the important features of Mathematica is that it can do symbolic, as well as numerical, calculations. This means it can handle algebraic formulas as well as numbers. In this video, Conrad Wolfram gives a brief overview of symbolic computation in Mathematica and explains its advantages. As an integrated all-in-one platform, Mathematica provides a smooth workflow from idea to deployment and allows users to explore ideas spanning different technical areas. In this video, Conrad Wolfram explains the advantages of building Mathematica as an all-in-one system. This video features John Kiehl, co-owner of Soundtrack Recording Studio, who shares an example of Mathematica using powerful set theory and pattern-matching capabilities to make and produce music. Includes Japanese audio.
Mathematics and Physics Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level. Volume 2 of Musimathics continues the story of music engineering begun in volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short-time Fourier transform, and the wavelet transform. "Mathematics can be as effortless as humming a tune, if you know the tune," writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music--a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science. The combination of two of the twentieth century's most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level. Robert Reitano's Introduction to Quantitative Finance This manual provides solutions to the Practice Exercises in the text. This text Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. real-world situations. A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.
the millions of students each year who struggle with the math portion of the GED, McGraw-Hill's Top 50 Math Skills for GED Success helps learners focus on the 50 key skills crucial for acing the test. From making an appropriate estimate and solving for volume, to interpreting a bar graph and identifying points on a linear equation, this distinctive workbook from the leader in GED study guides features step-by-step instructions; example questions and an explanatory answer key; short concise lessons presented on double-page spreads; an appealing, fully correlated pretest and computational review of basic skills; application, concept, and procedure problems; and more. {"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":13.08,"ASIN":"0071445226","isPreorder":0},{"}],"shippingId":"0071445226::7QvHWaBAVtaz0oJ8pdBS3YT7PM1%2FVbaYIAViBDiajaQ%2B%2F1pZLVGBCTUf8Gq7tURBYgmN0fC0mXq4YSOD5Kv%2FocDcWsLA5QO9Ew5O6xu86sk%3D,0071381791::XOMsw7%2Fct845Yqth3qfOk1ftYze%2F3Cz9bX%2B464XlI0BxkxBQ6GgJokDmMHzGH9TaeXfqxJ1gQaDav3NM8vMaQJWAe4w%2FoISV8wIXQybeTms%3D,1438071493::bw4%2BQK1gHgalpWaDR45q%2BKM%2BzuvF5JCsJ2fR0I06TX38ClemWIExXga777gFjacMooIHfGAu6nTSdwcKKGFUBXd0uj7UHLQgp3KYkFRwX6VT4Og8AIXasMath skills can often be the difference between passing the GED on your first try and disappointment. But it is often hard to pinpoint those areas that you still need to master. Let McGraw-Hill's Top 50 Math Skills for GED Success give you everything you need to ace the math questions on GED test day. Written by two experts who have years of experience with the GED, this easy-to-use book features: A pretest designed to identify your weaknesses in those math areas the GED traditionally focuses on Two-page lessons that increase your knowledge in 50 essential skills so that they become your strengths Detailed guidance on using a calculator and making estimations A full answer key with helpful explanations Don't take chances with the GED. Brush up on the knowledge you need to know now with McGraw-Hill's Top 50 Math Skills for GED Success. [BOX] How to use this book to quickly--and dramatically--improve your GED math skills: 1. Take the pretest to determine where you most need help. 2. Study the two-page lesson on each skill that gave you problems. 3. Take the posttest under timed, testlike conditions. 4. Do it again, focusing only on the areas still giving you trouble. 5. PASS THE GED! About the Author Robert Mitchell and Dolores Emery are experienced authors in the GED math field. Most Helpful Customer Reviews This is a great book for teachers, tutors and study groups. The book is obviously made up of fifty skills. Each skill is only a couple of pages long and offers practice with GED style questions. I like the book because the small bits of information make a quick review for students. A student can do one skill a day or a week and know exactly how much is left. I also like the book as an introduction to what students actually need. All too often students are overly concerned with fractions and not concerned enough about word problems and problem solving. The book keeps word problems and GED specific problem solving front and center in each skill. I had gotten "McGraw-Hill's GED" complete study book (that massive book that combines everything) and was impressed at how much it included. I did incredibly badly at Math, so I thought getting the "Top 50 Math Skills" would be better for me. I was disappointed first of all how thin this book is in comparison. I took the pretest and got a 92%. I seriously doubt I am that good at math. A lot of the hardest questions from the big book aren't in this book. Also, in the big book I got around 40% at the Pretest for my first attempt, and then a 60% after some studying. I believe those scores are more accurate. In conclusion, I suggest you buy the big book "McGraw-Hill's GED" because it covers a lot more and will be better at preparing you for difficult math. I bought this for my teen two years ago as he struggled with the math portion of the GED. He ended up scoring in the top 99% on that portion of the test; I am sure this book was at least 75% responsible for that. We approached his work in this book on a daily basis: one top skill a day for 50 days. Now, two years later, I've purchased a copy for my other teen. She's a wiz at math, but I want her to keep her math skills in check as she works more on the areas she is weaker in for the GED. (Incidentally, both my kids have opted out of high school, instead choosing to attend college at the ripe old age of 16. I've heard it's a trend in some school districts. With the number of calls I field from interested parents, it seems that it may become a trend here too.) This is a good math review book--but for my needs, it doesn't include enough of the very basic math skills that are a prerequisite to these lessons. I tutor students who are preparing for the GED and this book is great for an advanced student. This is a very good book. It's step by step and it just makes things simple. I've always had a problem with math, and this book really helped me through that. For the first time, I actually understood fractions! I'm taking my GED test soon, and I'm confident I'll do good thanks to this book!
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
Algebra Success in 20 Minutes a Day Book Description: Whether you're new to algebra or just looking for a refresher, Algebra Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with algebra essentials, this extensive guide covers all vital algebra skills, including combining like terms, solving quadratic equations, polynomials, and beyond. This proven study aid is completely revised with updated lessons and exercises that give students and workers alike the algebra skills they need to succeed. Algebra Success in 20 Minutes a Day also includes: Hundreds of practice exercises, including word problems Application of algebra skills to real-world (and real-work) problems A diagnostic pretest to help pinpoint strengths and weaknesses Targeted lessons with crucial, step-by-step practice in solving algebra problems A helpful posttest to measure progress after the lessons Glossary, additional resources, and tips for preparing for important standardized or certification tests
A First Course in Probability and Markov Chains Provides an introduction to basic structures of probability with a view towards applications in information technology A First Course in Probability and Markov Chains presents an introduction to the basic elements in probability and focuses on two main areas. The first part explores notions and structures in probability, including combinatorics, probability measures, probability distributions, conditional probability, inclusion-exclusion formulas, random variables, dispersion indexes, independent random variables as well as weak and strong laws of large numbers and central limit theorem. In the second part of the book, focus is given to Discrete Time Discrete Markov Chains which is addressed together with an introduction to Poisson processes and Continuous Time Discrete Markov Chains. This book also looks at making use of measure theory notations that unify all the presentation, in particular avoiding the separate treatment of continuous and discrete distributions. A First Course in Probability and Markov Chains: - Presents the basic elements of probability. - Explores elementary probability with combinatorics, uniform probability, the inclusion-exclusion principle, independence and convergence of random variables. - Features applications of Law of Large Numbers. - Introduces Bernoulli and Poisson processes as well as discrete and continuous time Markov Chains with discrete states. - Includes illustrations and examples throughout, along with solutions to problems featured in this book. The authors present a unified and comprehensive overview of probability and Markov Chains aimed at educating engineers working with probability and statistics as well as advanced undergraduate students in sciences and engineering with a basic background in mathematical analysis and linear algebra. SHOW LESS READ MORE > Preface xi 1 Combinatorics 1 1.1 Binomial coefficients 1 1.1.1 Pascal triangle 1 1.1.2 Some properties of binomial coefficients 2 1.1.3 Generalized binomial coefficients and binomial series 3 1.1.4 Inversion formulas 4 1.1.5 Exercises 6 1.2 Sets, permutations and functions 8 1.2.1 Sets 8 1.2.2 Permutations 8 1.2.3 Multisets 10 1.2.4 Lists and functions 11 1.2.5 Injective functions 12 1.2.6 Monotone increasing functions 12 1.2.7 Monotone nondecreasing functions 13 1.2.8 Surjective functions 14 1.2.9 Exercises 16 1.3 Drawings 16 1.3.1 Ordered drawings 16 1.3.2 Simple drawings 17 1.3.3 Multiplicative property of drawings 17 1.3.4 Exercises 18 1.4 Grouping 19 1.4.1 Collocations of pairwise different objects 19 1.4.2 Collocations of identical objects 22 1.4.3 Multiplicative property 23 1.4.4 Collocations in statistical physics 24 1.4.5 Exercises 24 2 Probability measures 27 2.1 Elementary probability 28 2.1.1 Exercises 29 2.2 Basic facts 33 2.2.1 Events 34 2.2.2 Probability measures 36 2.2.3 Continuity of measures 37 2.2.4 Integral with respect to a measure 39 2.2.5 Probabilities on finite and denumerable sets 40 2.2.6 Probabilities on denumerable sets 42 2.2.7 Probabilities on uncountable sets 44 2.2.8 Exercises 46 2.3 Conditional probability 51 2.3.1 Definition 51 2.3.2 Bayes formula 52 2.3.3 Exercises 54 2.4 Inclusion–exclusion principle 60 2.4.1 Exercises 63 3 Random variables 68 3.1 Random variables 68 3.1.1 Definitions 69 3.1.2 Expected value 75 3.1.3 Functions of random variables 77 3.1.4 Cavalieri formula 80 3.1.5 Variance 82 3.1.6 Markov and Chebyshev inequalities 82 3.1.7 Variational characterization of the median and of the expected value 83 3.1.8 Exercises 84 3.2 A few discrete distributions 91 3.2.1 Bernoulli distribution 91 3.2.2 Binomial distribution 91 3.2.3 Hypergeometric distribution 93 3.2.4 Negative binomial distribution 94 3.2.5 Poisson distribution 95 3.2.6 Geometric distribution 98 3.2.7 Exercises 101 3.3 Some absolutely continuous distributions 102 3.3.1 Uniform distribution 102 3.3.2 Normal distribution 104 3.3.3 Exponential distribution 106 3.3.4 Gamma distributions 108 3.3.5 Failure rate 110 3.3.6 Exercises 111 4 Vector valued random variables 113 4.1 Joint distribution 113 4.1.1 Joint and marginal distributions 114 4.1.2 Exercises 117 4.2 Covariance 120 4.2.1 Random variables with finite expected value and variance 120 4.2.2 Correlation coefficient 123 4.2.3 Exercises 123 4.3 Independent random variables 124 4.3.1 Independent events 124 4.3.2 Independent random variables 127 4.3.3 Independence of many random variables 128 4.3.4 Sum of independent random variables 130 4.3.5 Exercises 131 4.4 Sequences of independent random variables 140 4.4.1 Weak law of large numbers 140 4.4.2 Borel–Cantelli lemma 142 4.4.3 Convergences of random variables 143 4.4.4 Strong law of large numbers 146 4.4.5 A few applications of the law of large numbers 152 4.4.6 Central limit theorem 159 4.4.7 Exercises 163 5 Discrete time Markov chains 168 5.1 Stochastic matrices 168 5.1.1 Definitions 169 5.1.2 Oriented graphs 170 5.1.3 Exercises 172 5.2 Markov chains 173 5.2.1 Stochastic processes 173 5.2.2 Transition matrices 174 5.2.3 Homogeneous processes 174 5.2.4 Markov chains 174 5.2.5 Canonical Markov chains 178 5.2.6 Exercises 181 5.3 Some characteristic parameters 187 5.3.1 Steps for a first visit 187 5.3.2 Probability of (at least) r visits 189 5.3.3 Recurrent and transient states 191 5.3.4 Mean first passage time 193 5.3.5 Hitting time and hitting probabilities 195 5.3.6 Exercises 198 5.4 Finite stochastic matrices 201 5.4.1 Canonical representation 201 5.4.2 States classification 203 5.4.3 Exercises 205 5.5 Regular stochastic matrices 206 5.5.1 Iterated maps 206 5.5.2 Existence of fixed points 209 5.5.3 Regular stochastic matrices 210 5.5.4 Characteristic parameters 218 5.5.5 Exercises 220 5.6 Ergodic property 222 5.6.1 Number of steps between consecutive visits 222 5.6.2 Ergodic theorem 224 5.6.3 Powers of irreducible stochastic matrices 226 5.6.4 Markov chain Monte Carlo 228 5.7 Renewal theorem 233 5.7.1 Periodicity 233 5.7.2 Renewal theorem 234 5.7.3 Exercises 239 6 An introduction to continuous time Markov chains 241 6.1 Poisson process 241 6.2 Continuous time Markov chains 246 6.2.1 Definitions 246 6.2.2 Continuous semigroups of stochastic matrices 248 6.2.3 Examples of right-continuous Markov chains 256 6.2.4 Holding times 259 Appendix A Power series 261 A.1 Basic properties 261 A.2 Product of series 263 A.3 Banach space valued power series 264 A.3.2 Exercises 267 Appendix B Measure and integration 270 B.1 Measures 270 B.1.1 Basic properties 270 B.1.2 Construction of measures 272 B.1.3 Exercises 279 B.2 Measurable functions and integration 279 B.2.1 Measurable functions 280 B.2.2 The integral 283 B.2.3 Properties of the integral 284 B.2.4 Cavalieri formula 286 B.2.5 Markov inequality 287 B.2.6 Null sets and the integral 287 B.2.7 Push forward of a measure 289 B.2.8 Exercises 290 B.3 Product measures and iterated integrals 294 B.3.1 Product measures 294 B.3.2 Reduction formulas 296 B.3.3 Exercises 297 B.4 Convergence theorems 298 B.4.1 Almost everywhere convergence 298 B.4.2 Strong convergence 300 B.4.3 Fatou lemma 301 B.4.4 Dominated convergence theorem 302 B.4.5 Absolute continuity of integrals 305 B.4.6 Differentiation of the integral 305 B.4.7 Weak convergence of measures 308 B.4.8 Exercises 312 Appendix C Systems of linear ordinary differential equations 313 C.1 Cauchy problem 313 C.1.1 Uniqueness 313 C.1.2 Existence 315 C.2 Efficient computation of eQt 317 C.2.1 Similarity methods 317 C.2.2 Putzer method 319 C.3 Continuous semigroups 321 References 324 Index 327 "This is useful not only as review material to mathematics students, but also to students in the engineering and information sciences which may be curious about theoretically understanding the material presented before." (Zentralblatt MATH, 1 August 2013)
Buy PDF There is a national consensus that teachers who teach middle-grades and elementary mathematics need deeper and broader exposure to mathematics in both their undergraduate and in their graduate studies. The Mathematics Education of Teachers, published by The Conference Board on the Mathematical Sciences, recommends 21 semester hours of mathematics for prospective teachers of middle-grades mathematics. In several states pre-service teachers preparing to teach middle-grades mathematics and pre-service teachers preparing to teach elementary school must complete 6- 9 semester hours of mathematics content at the junior-senior level. Graduate schools across the nation have developed special programs for educators who specialize in teaching mathematics to elementary school children and to middle grades students. However, there is a paucity of text materials to support those efforts at junior-senior level and graduate level courses. Faculty members must choose to teach yet another course out of one of the "Mathematics for Teachers" texts that have formed the basis of the curriculum for the last two decades. These texts tend to treat a very limited set of topics on a somewhat superficial level. Alternatively, faculty members can use mathematics textbooks written primarily for students majoring in mathematics or the sciences. Neither the topic choice nor the pedagogical style of these texts is optimal for pre-service and in-service teachers of middle grades and elementary mathematics. Discrete Mathematics for Teachers is a text designed to fill this void. The topic is right. Discrete mathematics provides a rich and varied source of problems for exploration and communication, expands knowledge of mathematics in directions related to elementary and middle school curricula, and is easily presented using our best understanding of the ways that mathematics is learned and taught. The presentation is right. In the spirit of NCTM's Principles and Standards for School Mathematics, topics are presented with careful attention to the best traditions of problem solving, reasoning and proof, communication, connections with other disciplines and other areas of mathematics, and varied modes of representation.
You are here CALCULUS II Topics include techniques of integration, area computations, improper integrals, infinite series and various convergence tests, power series, Taylor's Formula, polar coordinates, and parametric curves. Prerequisite: MATH 151 with a minimum grade of "C-."
Mathematics Department Mathematics has been shown to be a most effective problem-solving tool; quantitative interpretations of the world are illuminating, and mathematical methods underlie scientific inquiry. Math Class Formats TMCC offers math classes in a variety of formats to accommodate varying student needs and preferences. Students should check with the Mathematics department when in doubt as to the format of a particular class. Lecture format. Class meets twice a week for one hour and fifteen minutes on one of the TMCC sites. Traditional and/or non-traditional learning/instruction methods may be used (lecture, group work, discovery modules, in-class exercises, question-and-answer sessions, etc.). A lecture math class may include an online component (for example, homework and quizzes). Computer-based format (Math 95 and 96). These classes meet in a classroom equipped with computers. Students work with interactive software, completing homework and assessments on the computer. Faculty instruct on an individual and/or small group basis. Access to a computer outside of class time is required in order to complete coursework. Online format. Syllabus, class notes, videos, homework, quizzes, practice tests, etc. are delivered online. Students interact with the instructor and with their classmates online. Students must come to the college to take their midterm and final exams (unless proctoring arrangements have been made with the instructor). Hybrid format. Online class, but meets on campus one day per week for discussion. Self-paced lab format. Class meets twice a week for one hour and fifteen minutes in a math lab. Students work individually and at their own pace. Homework isn't collected. Students take exams after studying the appropriate sections of the textbook. The instructor helps students on an individual and/or small group basis. Registration for online developmental math classes is by departmental permission and limited to students who meet the following three requirements: The student has not dropped or failed the class before, or the student has a minimum GPA of 3.0. The student has a grade of A or B in the prerequisite class, or a qualifying Accuplacer math, ACT math or SAT math score, taken within the past two years. The student has a minimum Accuplacer Reading score of 86 and a minimum Accuplacer Essay Sample score of 5 (or a minimum score of 440 on both the SAT Reading and Writing tests, or a minimum score of 18 on both the ACT Reading and Writing tests), or a C of higher in English 98R, taken within the past two years.
All algebraic processes widely explained in a step by step reasoning method. I highly recommend it for anyone who wants to learn algebra, or reinforce their knowledge in the subject. One thing for the information of the reviewer on top of the list, and everyone else: Aurelio Baldor is actually a Cuban professor of mathematics, and absolutely not an Indian mathematician. It is advisable to do some research before writing a review. Ignore the picture and proceed to the book, besides Baldor was a genius Indian mathematician not Arab but that's besides the point. This book is outstanding, I remember working with this book back in my younger years, I have a degree in computer science. This book was the foundation to overcome all my Math classes through college. I got so good in Algebra when I was a teenager that even the girls wanted to sit with me in class. If you understand this well illustrated Algebra book no math class will be impossible to understand. However it's you that can make it happen, as you need to dedicate your time and effort to master it. In other words turn your TV off, enjoy it. ... With plenty of detailed examples and tons of exercises, you do learn and understand Algebra with this book. Provides the best foundation for Trigonometry and Calculus. You WILL use it for reference and/or to refresh your memory when your children start studying Algebra. Guaranteed !! I really remember having to go through math and trigonometry under tutors that kept on pounding on your head that math was a neccesary nuisance, until I came across this remarkable book, I can tell you that it so clear and impressive that anyone, with or without mathematical background will be able to understand it. Remember that math is the universal language and for this book the piece by piece attack on the theme is more than enough to understand it, spanish is advisable though not essential, this book teaches you to love math and makes it fun, open and easy, it can be applied on your everyday life. It takes you by the hand step by step from two variable equations to full scale three dimensional matrix series, giving it sense to a whole new world of mathematical thinking, right now I am going through a proccess to start my Masters by Research on Australia (On Biomedical Sciences), and to begin with I needed to refresh my memory on some algebra and trigonometry, I took some steps towards books like the Tippler and Shaums, and though they claim the easiness of use of its contents, to my surprise more that 80% percent of my answers were coming from the Baldor series. Sometimes is easy to under estimate a book that comes from a neighboring country that is say "underdeveloped" but I think it is about high time that we might start to share some common knowledge that would enrich our mutual knowledege. By now I haven't found any book that comes closer to the comprehention that this book opens to the novele and experienced mathematician, I sincerely recomend this text to anyone that might be submerged into mathematic themes from shallow to deep, belive me it will not disappoint anyone, or at least it hasn't done so, I know more than a 100 people between students and serious proffessionals and investigators that have used it and are still using it. It has run water under the bridge since I used it and it is still brilliant and robust. This book it's been on Mexican Schools for many many years and people who used it will always remember because it was too good or they hate it because algebra it's tough. Love it or Hate it most of the people know this is DA BOOK!!!!!. ... An excellent book, although the illustration on the cover may raise suspicion about those who carry it. Specially after September 11, 2001. Is it him ??? -- Un libro excelente, a pesar de que la ilustracion de la portada podria levantar sospechas de quienes lo usan. Especialmente despues del 11 de Septiembre del 2001. Sera el ???
Modify Your Results An ideal program for struggling students "Glencoe Algebra: Concepts and Applications" covers all the Algebra 1 concepts. This program is designed for students who are challenged by high school mathematics. Glencoe Algebra: Concepts and Applications includes lessons that will help students prepare for the Texas Essential Knowledge and Skills assessed on the Texas state test. This textbook contains a special section of practice problems specifically for the Texas state test. Algebra: Concepts & Applications, is a comprehensive Algebra 1 program that is available in full and two-volume editions. Algebra: Concepts & Applications uses a clean lesson design with many detailed examples and straightforward narration that make Algebra 1 topics inviting and Algebra 1 content understandable. Volume 1 contains Chapters 1-8 of Algebra: Concepts & Applications plus an initial section called Chapter A. Chapter A includes a pretest, lessons on prerequisite concepts, and a post test. Designed for students who are challenged by high school mathematics, the 2006 edition has many new features and support components.<P> Advisory: It has been reported to us that this book contains mathematical problems that have been rendered by the publisher as images without image descriptions. Algebra: Concepts & Applications, is a comprehensive Algebra 1 program that is available in full and two-volume editions. Algebra: Concepts & Applicationsuses a clean lesson design with many detailed examples and straightforward narration that make Algebra 1 topics inviting and Algebra 1 content understandable. Volume 1 contains Chapters 1-8 ofAlgebra: Concepts & Applicationsplus an initial section called Chapter A. Chapter A includes a pretest, lessonson prerequisite concepts, and a posttest. Designed for students who are challenged by high school mathematics, the 2007 edition has many new features and support components. The book's design is up-to-date as it underlines the real-world applications of Maths as well as its connections to other subjects like science, history and music. The Chapter Projects, Hands-On Labs, and Interdisciplinary Investigations makes the book very useful and interesting to the students. To help chart their journeys, wise travelers consult a map before they begin. Just as maps lead travelers to their destinations, the script on the next five pages points out the ways that you use the mathematics in this text in you daily lives. This textbook of Glencoe Mathematics Course 1 has unit lessons on Number, Operations, and Statistics, Number and Operations: Decimals and Fractions, Patterns, Relationships, and Algebraic Thinking, Measurement and Geometry, Number, Operations, and Algebraic Thinking. This book is talked about The Texas Prairies and Lakes region offers a wide range of attractions. Among them is the States Fair of Texas. Located in Dallas, it boasts the 212-foot Texas Star-the tallest Ferris wheel in North America. As with all circles, the ratio of the circumference of the Texas Star to its diameter is a constant, π. You'll learn more about ratios in Chapter 7 and circumference in Chapter 12
The goal of this session, as well as many that follow, is to immerse ourselves in mathematics that illustrates two components of algebraic thinking: mathematical thinking tools (problem solving, representation, and reasoning skills) and algebraic ideas (functions, patterns, variables, generalized arithmetic, and symbolic manipulation). Groups: Discuss how these two components relate to the current debate in mathematics reform. Then, divide into small groups to answer Problems A1 and A2. When finished, everyone should share their answers with the whole group. At this point, the idea of what algebraic thinking is may not be clear. The purpose here is not to construct a precise definition, but to consider initial ideas without judgment as a way of beginning a longer conversation. In fact, in Session 9 we will consider the same questions again, in order to evaluate whether our conception of algebraic thinking has broadened and strengthened.
Elementary Linear Algebra 9780132296540 ISBN: 0132296543 Edition: 9 Pub Date: 2007 Publisher: Prentice Hall Summary: This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof. Kolman, Bernard is the author of Elementary Linear Algebra, published 2007 under ISBN 9780132296540 and 0132296543. Five hundred three Elementary Linear Algebra text...books are available for sale on ValoreBooks.com, one hundred twenty four used from the cheapest price of $57.75, or buy new starting at $95.612296543 BRAND NEW. PLASTIC WRAPPED. We are a tested and proven company with over 900, 000 satisfied customers since 1997. Choose expedited shipping (if available) for much [more] 0132296543 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less]
This course uses an F1 wheel as an example project, but the techniques can be applied to any other automotive or consumer productbook description: Provides a concise journey through the subject of calculus Emphasises the relationship between calculus and geometry, relevant to the computer graphics, animation and games communities Chapters are self-contained, allowing readers singular sources of reference for all aspects of calculus Students studying computer animation and computer games have to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces, and as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems. The author draws upon his experience in teaching mathematics to undergraduates to make calculus appear no more challenging than any other branch of mathematics. He introduces the subject by examining how functions depend upon their independent variables, and then derives the appropriate mathematical underpinning and definitions. This gives rise to a function's derivative and its antiderivative, or integral. Using the idea of limits, the reader is introduced to derivatives and integrals of many common functions. Other chapters address higher-order derivatives, partial derivatives, Jacobians, vector-based functions, single, double and triple integrals, with numerous worked examples, and over a hundred illustrations. Calculus for Computer Graphics complements the author's other books on mathematics for computer graphics, and assumes that the reader is familiar with everyday algebra, trigonometry, vectors and determinants. After studying this book, the reader should understand calculus and its application within the world of computer games and animation. book description: This book brings together several advanced topics in computer graphics that are important in the areas of game development, three-dimensional animation and real-time rendering. The book is designed for final-year undergraduate or first-year graduate students, who are already familiar with the basic concepts in computer graphics and programming. It aims to provide a good foundation of advanced methods such as skeletal animation, quaternions, mesh processing and collision detection. These and other methods covered in the book are fundamental to the development of algorithms used in commercial applications as well as research. book description: Computer graphics systems are capable of generating stunningly realistic images of objects that have never physically existed. In order for computers to create these accurately detailed images, digital models of appearance must include robust data to give viewers a credible visual impression of the depicted materials. In particular, digital models demonstrating the nuances of how materials interact with light are essential to this capability. This is the first comprehensive work on the digital modeling of material appearance: it explains how models from physics and engineering are combined with keen observation skills for use in computer graphics rendering. Written by the foremost experts in appearance modeling and rendering, this book is for practitioners who want a general framework for understanding material modeling tools, and also for researchers pursuing the development of new modeling techniques. The text is not a "how to" guide for a particular software system. Instead, it provides a thorough discussion of foundations and detailed coverage of key advances. Practitioners and researchers in applications such as architecture, theater, product development, cultural heritage documentation, visual simulation and training, as well as traditional digital application areas such as feature film, television, and computer games, will benefit from this much needed resource.
Main menu Study Tools math.com: has good overview explanations for pre-algebra through calculus concepts and terms. It also has a section that gives study advice as well as strategies to overcome test anxiety. However, there is no step by step help available on this site. math.stackexchange: this is a question/answer web site for anything math related. No adds and it's totally FREE. mathway.com: is easily navigated and has several options for what a student might be looking for from a given equation (solve for x, solve for y, find the 0, etc). The site costs $19.99/month. For no fee, it does show the answer to a given equation and it can also generate sample worksheets for any subject type (like arithmetic operations). varsitytutors.com: free math practice tests and assessments; professionally created math problems in a variety of formats including comprehensive diagnostics, short concept-oriented practice tests, and concept-oriented flashcards. All of the content is FREE. They also have support for standardized tests such as the Accuplacer, ACT, LSAT, CLEP, GRE, GED, etc. Mesa Community College provides outstanding transfer and career and technical programs, workforce development, and life-long learning opportunities to residents of the East Valley area of Phoenix, Arizona.
Algebra - Wikipedia, the free encyclopedia Algebra (from Arabic al-jebr meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. As such ... Pinellas ninth-graders might get summer help with algebra Tbo.com While Summer Bridge is meant to help students who are falling behind grade level, the new Algebra Boot Camp specifically targets incoming ninth-graders who have not taken an Algebra 1 course. During the six-week course, students will learn the skills ... Algebra Nation To Add Teacher Training T.H.E. Journal A "design and build" shop for education at the University of Florida just received a $250,000 grant to build a teacher network to go along with a new tool introduced in 2013 to help students with algebra. The Lastinger Center for Learning, which ... and more » Algebra II Again In the Spotlight WOAI.com A State Senate Committee today is again examining a very emotional issue---whether to mandate that all students pass Algebra II as a requirement for graduation, or whether that time could be better taken on vocational courses, 1200 WOAI news reports. Make Algebra II standard requirement mySanAntonio.com The San Antonio Hispanic Chamber of Commerce stands alongside many educators, business leaders and parents, urging all school districts throughout Texas to ensure that Algebra II is included in all endorsement tracks for high school education across ... The Spectator: Algebra II vs. Citizenship I Eastern Arizona Courier The Spectator: Algebra II vs. Citizenship I By John Young Copper Era columnist Eastern Arizona Courier \| 0 comments. What would you say if someone told you that your state's emphasis on algebra was undermining math instruction? What would you say if ... and more »
Book Review: The Princeton Companion to Mathematics, Timothy Gowers, ed Review by Tom Siegfried Math is everywhere, from the gas station and grocery store to the stock market and science magazines. And it shows up, of course, in schools at all levels. But the educational system doesn't provide enough math for most people to appreciate its scope, or understand its intrinsic powers or practical applications. For those with a deep interest in understanding such things, this book provides a reasonably accessible, technically precise and thorough account of all of math's major aspects—from the basics of algebra, geometry, algorithms and proofs to the essential features of Hilbert spaces and Hamiltonians. Much is understandable to anyone with a good high school math background; sometimes more advanced education is better. Added attractions include biographical sketches of close to 100 famous mathematicians, a comprehensive chronology of mathematical events throughout history and engaging discussions of math's influence. This book covers such diverse areas as communications, chemistry, biology, economics, image compression, the flow of "traffic" in all sorts of networks (including transportation), music and medical statistics. Students of math will find this book a helpful reference for understanding their classes; students of everything else will find helpful guides to understanding how math describes it all. PrincetonUniv. Press, 2008, 1,034 p., $99
Lesson 8.1ExploringExponentialModels Mrs. Snow, Instructor Exponential functions are similar in looks to our other functions involving exponents, but there is a big difference. The variable is now the power, rather than the base. Title: ExploringExponential Growth and Decay Functions Brief Overview: ... 1Answers will vary, but to insure accurate ... Which models of cars are more/less likely to become antiques? When is that likely to happen? Understand and use basic exponential functions as models of real phenomena. f ... reviewed and students practice working with rational exponents. ... where a is a non-zero real number and b is a positive real number other than 1. An exponential growth function has a value of b that is greater ... [SAS 3, question 1] Exploring "Geometric sequences and series" ... What is the constant multiplier of the exponential function that models this situation? ... Have them practice writing the sum in sigma notation. [SAS 3, question 4] Describe the scenario from page 1 of the Exploring "Geometric sequences and series." ... What is the constant multiplier of the exponential function that models this situation? What is its domain? ... More practice, pages 6-8 Student Activity Sheet 3, question 6. linear and exponentialmodels. ... Common Core State Standards for Mathematical Practice1. Make sense of problems and persevere in solving them. ... When making statistical models, technology is valuable for varying assumptions, exploring ... quadratic, and exponential through graph models and algebraic models. ... answers by using "benchmarks" to estimate measures and other strategies to approximate a ... Thinking With Mathematical Models (Inv. 1, 2) 8.SP.4 The Mathematical Practice Standards apply throughout each course and, ... (1) Exploring Data: observing patterns and departures from patterns (2) ... be able to explain their answers using arguments, graphs, and statistical skills that they will learn in the
Integrated Physics and Calculus - Volume 2 - 00 edition Summary: This groundbreaking text combines the second and third semesters of calculus with the first and second semesters of calculus-based physics. Used successfully at the authors' school in a two-semester course, the text provides full integration of the math and physics. Through text and problems, the authors carefully develop the calculus so that it can be used in many physical applications. In turn, the physics provides examples for the development of the calculus conce...show morepts. As a result, students gain a full understanding of calculus and its relevance to physics. Features Using applications and examples, the text integrates physics and calculus wherever possible to help students make the complex but necessary connections between the two subjects. Throughout the text, worked examples in both physics and calculus clarify the topics. Numerous problems allow students to practice applying concepts and theories. Historical developments in both physics and calculus are discussed whenever appropriate to give students a context for learning the material. The text is ideal for schools at which physics and calculus are closely coordinated
Synopses & Reviews Publisher Comments: The famous problems of squaring the circle, doubling the cube, and trisecting the angle have captured the imagination of both professional and amateur mathematician for over two thousand years. These problems, however, have not yielded to purely geometrical methods. It was only the development of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. This text aims to develop the abstract algebra. Book News Annotation: Develops the abstract algebra necessary to prove the impossibility of constructions to square the circle, double the cube, trisect the angle by geometrical means. Assumes linear algebra
BJU Press Math "Every subject is taught from a thoroughly biblical viewpoint, naturally and logically. BJUP materials help students not only to read, multiply fractions, and recognize grammar principles but also to understand and evaluate what they read, solve problems, and write with conviction and clarity. The teacher is more important than the textbook. BJUP texts offer multiple approaches and activities in every lesson, allowing each teacher to address unique needs. Customize without losing continuity. A student who loves to learn will be a student his whole life. Why just read about science when you can do science? Why just memorize dates when history can be experienced? School can be an adventure! Math 1 Student Worktext The full-color Student Worktext presents activities around a theme involving Digit the Clown and Cecilia, a seal. Student will do problems for practice, solve word problems to develop problem-solving skills, and maintain skills with review activities. Math 3 Student Worktext The full color worktext provides activities with Hal, a photographer, and Horatio, a squirrel, as part of a national park theme. Students will do problems for practice, solve word problems to develop problem-solving skills, and maintain skills with review problems. Fundamentals of Math Student Text Presents concepts in numerous examples worked out with clear step-by-step explanations. Includes systematic, cumulative review. Algebra 1 Student Text Includes scriptural principles woven throughout but also an "Algebra and Scripture" spread in each chapter. Concepts are presented with examples and explanations. Other features include "Algebra Around Us" and sections on "Probability and Statistics." Homework sections are on three levels. Cumulative Review questions are located at the end of every section." Reviews of BJU Press math curriculum Time 10 years Your situation: Homeschooling Alg 1, Pre-Alg, 5th grade Why you liked/didn't like the book: I've used BJU since the start and have always found it to be a good, solid program. In the younger years I skipped the "stories" and focused only on the math concepts because of the amount of prep time. I also skip much of the presentation and teach the lesson my own way due to time constraints. I think it has been a solid program and with anything I've had to modify it to fit. As in anything, I have found a few mistakes in the answer keys in every book. In Algebra 1 however, I had a very difficult time teaching the lessons. I didn't think there was enough explanation and since I didn't remember enough of my HS math it was difficult for me to explain to my son the concepts. Also, he often wanted to know the "why" and I couldn't tell him. It wasn't covered in the text. I am considering a different program for Geom. and will have to choose something else for Algebra 2. It is about in the middle in regard to difficulty level. Any other helpful hints: I modified it to fit our needs. You need to add in more drill work. My kids are behind in that aspect. It is a great, colorful, friendly approach. Shelly Goff Review left June 17, 2010 Grade level: Bob Jones DVD Time 2 years Your situation: Homeschooling for the last six years. Bob Jones DVD's helps me out a lot, especially when things goes a bit hectic and I do not have the time to explain each lesson. I do keep an eye on each lesson and will give some added practice if necessary. We also make use of Singapore math and try to incorporate BJones into our classical approach to homeschooling. Why you liked/didn't like the book: We just love the Science and Language Arts programme. The Science and English lessons Grade 6 is especially of a high quality. My son marvels about his grade 6 Science and repeats the lesson in detail afterwards. We did find the Grade 4 Math tedious with lots of confusion. At some point we skipped Maths and did Singapore Math instead. The Language Arts programmes are of outstanding quality and one will have to look far and wide to get a better lesson every day which contain a load of energy, field trips and a various appropriate activities to explain concepts. Any other helpful hints: Stay on top of what each lesson offers, some extra conversation afterwards helps to bring proper clarity. Marika du Preez Review left November 5, 2009 Grade level: ? Time 5 years Your situation: We just finished our 7th year of homeschooling. I had 4 students this past year, in grades K5-5th. One of the main reasons I like BJU's math is because it is very "why"-based. It doesn't focus on the rules or rote memorization until after the child has been taught the WHY behind the rules. The main goal is for the student to understand what is going on "behind the scenes" rather than just accepting the rules and memorizing facts. He learns WHY 2+ 2 = 4. He learns WHY you have to rename in the ones column when the problem is 25 + 37. Etc. It utilizes a lot of manipulatives, which is great for kids who have to see and touch things in order to learn them. They are easy to leave off if the child doesn't need them to grasp the concept. There is built-in review in nearly every lesson. At the beginning of the lesson there is a review time, and on the worktext pages there are sometimes some review problems. There is also an optional review worktext. The teacher's guide is easy to understand. It is scripted, which can be a big help to a new homeschool teacher. The ONLY thing I do not like about BJU's math is that it is very teacher-intensive (at least in the grades I used it for...I'm not sure about 6th and up). It doesn't have the teacher just show the child how to do something, it involves lots of examples, manipulatives, explanations, etc. The worktext doesn't explain things directly to the student very much - the main teaching must come from the teacher. So for someone who is homeschooling several different children, this can be a problem. Any other helpful hints: The curriculum calls for Unifix cubes, but Lego bricks work just as well. We have TONS of Lego bricks in our home, so I was able to save money by using them instead. Kirstin Reeder Review left August 14, 2008 Grade level: Algebra 1 Time 1 year I'm homeschooling my 13 year old daughter. I LOVED this text. Each concept was broken down into smaller parts that even I could teach. (It's been 25 years since I got my "C" in Algebra!) I was very worried about homeschooling upper math, but this was a breeze. Each new skill was EASY to understand through the examples, as the examples listed each step and clearly identified the step and explained it again within the example. Every chapter has 7 to 10 sections, and each section has a Cummulative Review that provides an opportunity for past skills to be revisited. Odd numbered homework answers are in the back. That made it nice to give odd homework for concepts taught that day, and the next day to give evens for the day before's concept and odd, again, for that day's. I LOVE how this text adds an "Algebra and Science," or "Algebra Through History," or "Algebra and Applied Skills," etc. in each chapter. They teach how someone in history used algebra in their lives for something important, or how algebra applies today. I believe as a result of these add-ins, my teen has never asked the age-old question, "What in the world will I ever USE this stuff for!" It tells you right there in black and white! And of course, the Algebra and Scripture add-in at the end of each chapter is absolutely wonderful. It uses scripture and Bible study to demonstrate a God-view of math, numbers, algebraic concepts, and asks the student to apply that view to their lives. It's really great. My favorite? The algebraic concept: using the substitution method to solve systems of inequalities used II Corinthians 5:21 to demonstrate God's principle of substitution. Then went on to say, "Let's be sure to apply the principle of substitution in our Christian lives. Replace bad habits with good ones. Put off the old man... put on the new." And the Probabilities and Statistics add-in in each chapter is awesome! I never took Probs&Stats, and learned things in Algebra 1 that I never got out of any of the higher math I took up to Calculus. Any other helpful hints: I started out teaching a section in a day, giving odd homework, and the next day teaching a new section, giving the yesterday even and the today's odd. That didn't work out best for us. Since the problems get harder as they go along, instead, I taught 3 or 4 sections in one day... gave 1-15ish odds for each section, and the next day, class would be a review of all the homework, and 2-16ish evens, then 17ish- 25ish odds for each, etc for a few days. That allowed her to integrate the information more completely, for me to check her understanding as she went, for her to fine-tune, and for me to have class time to spend on the add-ins. I thought about not getting the teacher's addition, and boy oh boy am I glad I DID get it! I didn't use any of the lesson openers, but I did use the "Common Student Error" information all the day, as well as the Additional Problems. It also offers Assignment suggestions, Objectives, and the main points in a Vocabulary list. Also, in each section of the teachers text, it has a "Reading and Writing Mathematics" which suggests a writing assigment... ie: "Read the Algebra Around Us section in this chapter. Do some internet research about quality control, especially noting any information of a mathematical nature. Write a paragraph about your findings." Aun Review left June 30, 2008 Time: 2007-2008 school year I have three children and chose BJU satellite this year. I thought having all their classes on DVD would really free me up to do the renovations on our house. NOT. However, BJU does a beautiful job with the classes and I love the Christian perspective on everything. Why you liked/didn't like the book: I think the method of teaching on a topic for a week or so and then dropping it to go on to something completely different is frustrating. My 5th grader went over comparing fractions earlier in the year and 3 months later can't remember how to do it. BJU math classes are very good at explaining how and why. Any other helpful hints: I've been told the BJU math teaches children for higher level math. If you have the time to make daily worksheets to give, in addition to daily class, that would give your child a sample problem from all the other topics covered I'd say this would be a great program. Melissa Review left April 14, 2008 Time 5 months Your situation: Been homeschooling for only 5 months. Why you liked/didn't like the book: Don't like that it is really designed for a classroom, not a single student. Several of the great ideas for teaching new concepts are for multiple students. Also there is a lot of prep work. It is not inexpensive either. It would be great for multiple students. Cheryl Time 6 yrs Your situation: Using Bob Jones satellite because of multiple children and I did not have time to teach each one every subject. But I am afraid of changing curriculums and getting all messed up. I needed the videos for high school. My 3 graduated students did Saxon but in h.s. had tutoring for algebra and up. Any suggestions? I was thinking of rod and staff for the yonger kids. Then what for the upper grades? Why you liked/didn't like the book: I get bogged down with the estimating that is done all the time and they do not focus on mastering anything. They also in the upper grades do estimating and then front end estimating and my daughter has been doing this from 3rd to 8th gr and still can't remember how to do it. Susan Jude Grade levels used: BJU Math 1 & 2 Time 1 1/2 years I have been using BJU Math for 1st and 2nd grade with my daughter. Overall, I would have to say this curriculum is great. I am finding that my daughter is having trouble currently with doing her math, but I don't believe its a BJU issue. I think with the holidays she just doesn't want to do school. Why you liked/didn't like the book: I like the curriculum because of these reasons: 1) it's colorful and keeps my daughters attention 2) it goes through math step by step to make sure the child understands the concept 3) If your child has trouble catching on, you can always supplement with other workbooks from BJU (such as Spread your Wings) which will help reinforce these concept some more 4) The curriculum makes good use of manipulatives but you don't have to purchase a ton of them to use this curriculum. Every day items also work (like beans or candy for instance) What I don't like about the curriculum: 1) It's expensive 2) Sometimes it takes a long time to organize the lesson for the day and a long time to teach it (this isn't every lesson, but probably about 20% of the lessons take me awhile to organize and then about 1 hour to teach. I think that is too long) 3) The tests are not colored which is a pain when you are trying to test your child on things like money. It is very hard to actually see what coins they are trying to ask about. 4) The teacher and student materials often times take a long time to prepare. Cutting out 20 circles and coloring them takes alot of time. The bottom line is that BJU Math is an overall good curriculum. I just wish you didn't have to spend so much time trying to teach basic concepts or atleast I wish that more of the stuff that is included with the curriculum was more prepared. Other than that, using this curriculum has improved my daughters math skills and its right on target with her course of study for the year. Any other helpful hints: I purchase this curriculum from yahoo groups that are dedicated to selling BJU curriculum. You can get on a HOMESAT group list which only sells current editions and pay alot less for the curriculum which is slightly used or in almost new condition. EBay no longer sells teacher editions. I have purchased all my 2nd grade materials through the loop and everyone I dealt with was honest and sent the stuff in a decent amount of time. Otherwise you will pay top dollar if you order through BJU or other resellers. Michelle Grade levels used: Algebra 1 Time 6 months Your situation: We'd been struggling for a year with Saxon's Algebra 1 and wanted to try something new. Saxon seemed to introduce things in complex ways. Why you liked/didn't like the book: Bob Jones was a welcome new start for us. The kids were vaguely familiar with the concepts, but hadn't mastered them. They are practicing one thing at a time (building on known concepts) and gaining confidence as they move through the book. We spent so much time struggling, it's refreshing to have a book that presents things clearly, rather than jumbling new concepts in the middle of complex problems. Any other helpful hints: I'd have math all five days of the week; the family I'm teaching for has school four days, but we could get a lot more done with the extra day. The three day weekend just seems to set them back and half of class on Monday ends up being review. Jessica Hobbs Grade levels used: 7 Edition: Fundamentals of Math Time 5 months Bob Jones has a strong multi-sensory approach in the early grades which is great. The teaching is also sound and gives glory to God. In the later grade, I am finding the pace is behind a public school student I am tutoring. My dilemma is whether to use this book at a faster pace or choose a different curriculum. Many plusses other than the pace of the program.
Thirty Three Ways to Help with Numeracy equips teachers and teaching assistants with a wide range of practical resources to help children who are having difficulties learning the basic skills of numeracy.About the Book: This book `Advanced Mathematics` is primarily designed for B.Tech., IV Semester (EE and EC branch) students of Rajasthan Technical University. The subject matter is discussed in a lucid manner. The discussion is covered in five units: Unit I: deals with Numerical Analysis, Unit-II: gives different aspects of Numerical Analysis, Unit-III:... The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque,... more...
I just viewed the first lecture and have a lot of questions. Have been out of school for many years.Is it okay to view lectures again to understand concepts ? How helpful is the text ? one year ago one year ago View the lectures, try to solve the given problems and ask here if you have more specific questions. This is the way I recommend if you want learn calculus or refresh what you learned before. The texting is usefull as it contains many error corrections that the lecturer either didnn't notice when making them.
The wait is over! With great excitement, Alpha Omega Publications is pleased to announce the upcoming release of its new math course for homeschooling families, Horizons Pre-Algebra! Available in mid-February of 2011, Horizons Pre-Algebra is the highly anticipated, colorful continuation of the award-winning K-6 math series. Recommended for 7th or 8th grade students, this fun-filled course is packed with diverse, colorful lessons that prepare your child for upper-level math courses with a review of vital basic math concepts and a robust introduction to algebra, trigonometry, and geometry. What's Inside? Comprised of three perfect-bound components, the packaged set includes a colorful student workbook, a user-friendly teacher's guide, and handy tests and resources book. Student Book Similar in layout to Horizons' popular K-6 math courses, the consumable, full-color Horizons Pre-Algebra Student Book includes 160 daily lessons. Designed for completion in 45-60 minutes, each engaging lesson displays an illustrated teaching box that details the new concept being taught, along with a new class work section which reinforces the information with guided practice. Also part of each lesson's assignment is an activities section that contains problems for reviewing both the current lesson topic and previously taught concepts. What will your child learn? Horizons Pre-Algebra readies your child for more advanced mathematics by teaching several new areas of math concepts, including the following: Another new feature of the 360-page student book is a set of college test prep questions. Following each block of ten lessons, these challenging problems are designed to help students prepare for standardized math testing. Also included in the Horizons Pre-Algebra Student Book is a new collection of interviews with ordinary people who use math in their daily vocations. Setting the stage for each group of lessons, these thought-provoking, math-minute interviews bring math concepts to life by adding a human interest touch to word problems. Teacher's Guide The 400-page Horizons Pre-Algebra Teacher's Guide makes homeschooling easier with a variety of helpful resources, including daily lesson plans with clearly-defined objectives, practical teaching tips, and suggested materials lists; a math readiness test for evaluation; an in-depth scope and sequence; appearance of concepts charts; and solution keys that making grading a breeze as they mirror a reduced version of student worksheet pages for daily lessons, bi-weekly tests, and quarterly exams. Tests and Resources Book The Horizons Pre-Algebra Tests and Resources Book gives peace of mind that your student is comprehending concepts with easy-to-use, tear-out materials that include 80 review worksheets, 16 tests, and 4 exams. Each test conveniently follows every10 lessons, and each exam comes after every group of 40 lessons. Along with a detailed guide that indicates when and where to use each worksheet, test, and exam, this Horizons Tests and Resources Book also provides hands-on, cut-out supplements that assist both visual and kinesthetic learners in mastering algebraic concepts. Included are formula strips, full-color net diagrams of 3-D shapes, and color-coded algebra squares printed on cardstock. Always a best-seller, Horizons is well-known for its captivating content, appealing activities, and solid results. Wondering if your child is ready for AOP's new Horizons Pre-Algebra? Find out now by downloading the Horizon Pre-Algebra Readiness Test today! WE ARE SOOO EXCITED. WE ARE FINISHING UP HORIZONS 6. IT WAS SAD TO THINK THAT WAS IT. NOW WE CAN CONTINUE WITH WHAT MY KIDS SAY IS THE BEST MATH OUT THERE - HORIZONS. THANK YOU! Posted on: 02.10.11 \| Rating: 0 ELINE P Please, continue the serie. dc will never love math, I think, but after a few years in 4th grade she finally liked math. A great job. And please keep it spiral... Posted on: 08.19
Loading, please wait... Loading, please wait... Forms Manager Mathematics Course Proposal In order to omit errors, we strongly recommend you type your answers in MS Word and then cut & paste them into this form to avoid typos. When you click submit, a copy of your submission will be automatically emailed to you. Please include your full email address here:Date submitted: Is this proposal the result of program review? yes no If so, what year was the review completed? I. Basic course information 1. Department or Program: 2. Course Number: 3. MOST RECENT Official course description: the above course description is from catalog from class schedule 4. Semester and Year designation would begin: 5. Is this a NEW course? no yes If answered "yes" to question 5, please give date it was approved: 6. List all other designations applied for: received: 7. Instructor(s): 8. Are there any prerequisites for registering for this course? yes no if there are prerequisites for this course, please list here: How many credits is this course worth? General Course description for the Mathematics requirement in the common curriculum The course will address the contemporary role of mathematics. It will also stress mathematics as a conceptual discipline and will demonstrate to students the aesthetics and value of mathematics. The course will be structured so that students are actively involved in doing mathematics and demonstrating their understanding of concepts appropriate to that course in various ways. The specific content, the questions, and the examples used in the class should begin with ideas familiar to the students. The course will enable students to understand and use mathematical language and notation and to appreciate the need for that language and notation. It will also address the power and limitations of mathematical reasoning as a tool for solving problems from other disciplines and from everyday life. The course will focus on student involvement, understanding and appreciation for mathematics rather than on computational rigor. II. Question regarding Mathematics criteria Each of the following questions is designed to help the Committee understand how the Mathematics learning goals will be met in your course. Please be as specific as possible in your responses. Examples are especially helpful. 1. Which specific areas of mathematics will be targeted for problem solving, and what kinds of problem solving techniques will students apply? 2. Goal 2 states that "Students will demonstrate an understanding of the mathematical principles which underlie the techniques they use." Which mathematical principles will students be expected to understand? How will they demonstrate that understanding? 3. On which specific area of mathematics will this course focus, and which mathematical concepts in this area will the students be expected to understand? 4. In what ways will students be applying mathematical techniques to model problems in other disciplines or everyday life? Please give specific examples of the kinds of problems students will be expected to model.
Develop Algebraic Thinking 6-8 - MAT-926 ONLINE course will help teachers discover how to support deeper understanding of foundational algebraic concepts in grades 6-8. Teachers will explore growth patterns and functions, variables, linear relationships, and coordinate graphs. Based on the included text and research-based journal articles, teachers will design and implement a unit of grade-level appropriate algebraic thinking activities with their students. All of the readings and activities are built upon the Common Core standards
Excursions in Modern Mathematics: With Mini-Excursions For undergraduate courses in Liberal Arts Mathematics, Quantitative Literacy, and General Education. NEW: Now with "Mini-Excursions" Included! These ...Show synopsisFor undergraduate courses in Liberal Arts Mathematics, Quantitative Literacy, and General Education. NEW: Now with "Mini-Excursions" Included! These are enrichment topics that have been added at the end of each part and require an understanding of the core material covered in one or more of the chapters. Shorter than a full chapter but much more substantive than an appendix. Each mini-excursion includes its own exercise set. This very successful liberal arts mathematics textbook is a collection of "excursions" into the real-world applications of modern mathematics. The excursions are organized into four independent parts: 1) The Mathematics of Social Choice, 2) Management Science, 3) Growth and Symmetry, and 4) Statistics. Each part consists of four chapters plus a mini-excursion (new feature in 6/e). The book is written in an informal, very readable style, with pedagogical features that make the material both interesting and clear. The presentation is centered on an assortment of real-world examples and applications specifically chosen to illustrate the usefulness, relevance, and beauty of liberal arts mathematics.Hide synopsis Description:Good. Book is paper back but also binder ready. Cover has...Good. Book is paper back but also binder ready. Cover has minimal edge wear and corners lightly rubbed. Pages are clean and free of any noticeable marks or highlighting! ! FAST SHIPPING W/USPS TRACKING! ! !
Introductory mathematics written specifically for students new to engineering Now in its sixth edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide... more... A practical introduction to the core mathematics principles required at higher engineering level John Bird?s approach to mathematics, based on numerous worked examples and interactive problems, is ideal for vocational students that require an advanced textbook. Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills,... more... Unlike most engineering maths texts, this book does not assume a firm grasp of GCSE maths, and unlike low-level general maths texts, the content is tailored specifically for the needs of engineers. The result is a unique book written for engineering students, which takes a starting point below GCSE level. Basic Engineering Mathematics is therefore... more... John Bird?s approach, based on numerous worked examples and interactive problems, is ideal for students from a wide range of academic backgrounds, and can be worked through at the student?s own pace. Basic mathematical theories are explained in the simplest of terms, supported by practical engineering examples and applications from a wide variety of... more... In this book John Bird introduces engineering science through examples rather than theory - enabling students to develop a sound understanding of engineering systems in terms of the basic scientific laws and principles. The book includes 575 worked examples, 1200 problems, 440 multiple choice questions (answers provided), and the maths that students... more... Newnes Engineering Science Pocket Book is a uniquely versatile and practical tool for a wide range of engineers and students. All the fundamentals of electrical and mechanical engineering science and physics are covered, with an emphasis on concise descriptions, key methods, clear diagrams, formulae and how to use them. John Bird's presentations of... more... Newnes Engineering Mathematics Pocket Book is a uniquely versatile and practical tool for a wide range of engineers and students. All the essentials of engineering mathematics are covered, with clear explanations of key methods, and worked examples to illustrate them. Numerous tables and diagrams are provided, along with all the formulae you could... more... This textbook for courses in electrical principles, circuit theory, and electrical technology takes students from the fundamentals of the subject up to and including first degree level. The coverage is ideal for those studying engineering for the first time as part of BTEC National and other pre-degree vocational courses, especially where progression... more... Electrical Circuit Theory and Technology is a fully comprehensive text for courses in electrical and electronic principles, circuit theory and electrical technology. The coverage takes students from the fundamentals of the subject, to the completion of a first year degree level course. Thus, this book is ideal for students studying engineering for... more...
Book Description: It's no secret: The best way to ace the Regents exams is by practicing on real tests. This guide includes 12 actual full-length Sequential Math III Regents exams with answers and complete explanations, plus the January 1999 exam.Let the Regents experts at The Princeton Review teach you the simple test-taking techniques you'll need to know. We'll help you focus on the material that is most likely to show up on the sets. We'll teach you how to find the correct answers by eliminating the wrong ones. We even provide a "Target Practice" section so that you can quickly find sample problems for each math topic. This guide leads you step-by-step through each part of the test and helps you master the skills you'll need to crack the Regents exam.Learn the techniques in this book, practice them on the actual Sequential Math III Regents exams inside, and give yourself The Princeton Review advantage
Algebra for Dummies - 01 edition Summary: Algebra touches everyone's lives, from calculating mortgage interest to going Dutch at a restaurant -- not to mention the millions of high school students taking algebra classes. This friendly guide covers everything from fractions to quadratic equations. It includes real-world examples and story problems that will help even the most entrenched algebra-phobes approach the subject with ease. Mary Jane Sterling has been an educator since graduating from college. Teaching at the junior high, high school, and college levels, she has had the full span of experiences and opportunities while working in education. She has been teaching at Bradley University in Peoria, Illinois, for the past twenty years. View Table of Contents Introduction. About This Book. What Not to Read. Foolish Assumptions. How This Book Is Organized. Where to Go from Here. Part I: Starting Off with the Basics. Chapter 1: Assembling Your Tools. Beginning with the Basics: Numbers. Varying Variables. Speaking in Algebra. Taking Aim at Algebra Operations. Playing by the Rules. Chapter 2: Assigning Signs: Positive and Negative Numbers. Showing Some Signs. Going In for Operations. Operating with Signed Numbers. Working with Nothing: Zero and Signed Numbers. Associating and Commuting with Expressions. Chapter 3: Figuring Out Fractions and Dealing with Decimals. Pulling Numbers Apart and Piecing Them Back Together. Following the Sterling Low-Fraction Diet. Fitting Fractions Together. Putting Fractions to Task. Dealing with Decimals. Chapter 4: Exploring Exponents and Raising Radicals. Multiplying the Same Thing Over and Over and . . . . Exploring Exponential Expressions. Multiplying Exponents. Dividing and Conquering. Testing the Power of Zero. Working with Negative Exponents. Powers of Powers. Squaring Up to Square Roots. Squaring Up to Quadratics. Rooting Out Another Result from Quadratic Equations. Factoring for a Solution. Solving Quadratics with Three Terms. Applying Quadratic Solutions. Figuring Out the Quadratic Formula. Chapter 15: Distinguishing Equations with Distinctive Powers. Queuing Up to Cubic Equations. Working Quadratic-Like Equations. Rooting Out Radicals. Dividing Synthetically. Chapter 16: Fixing Inequalities. Operating on Inequalities. Solving Linear Inequalities. Working with More Than Two Expressions. Solving Quadratic Inequalities. Working with Absolute Value Inequalities. Part IV: Applying Algebra. Chapter 17: Making Formulas Behave. Measuring Up. Spreading Out: Area Formulas. Pumping Up with Volume Formulas. Going the Distance with Distance Formulas. Calculating Interest and Percent. Working Out the Combinations and Permutations. Formulating Your Own Formulas. Chapter 18: Sorting Out Story Problems. Getting Up to Solve Story Problems. Working Around Perimeter, Area, and Volume. Making Up Mixtures. Going the Distance. Righting Right Triangles. Going 'Round in Circles. Missing Middle Term. Distributing. Breaking Up Fractions. Breaking Up Radicals. Order of Operations. Fractional Exponents. Multiplying Bases Together. A Power to a Power. Reducing. Negative Exponents. Chapter 21: Ten Ways to Factor a Polynomial. Two Terms with a GCF. The Difference of Two Squares. The Difference of Two Cubes. The Sum of Two Cubes. Three Terms with a GCF. Three Terms with unFOIL. Changing to Quadratic-Like. Four or More Terms with a GCF. Four or More Terms with Equal Grouping. Four or More Terms with Unequal Grouping. Chapter 22: Ten Divisibility Rules. Divisibility by 2. Divisibility by 3. Divisibility by 4. Divisibility by 5. Divisibility by 6. Divisibility by 8. Divisibility by 9. Divisibility by 10. Divisibility by 11. Divisibility by 12. Chapter 23: Ten Tips for Dealing with Story Problems. Draw a Picture. Make a List. Assign Variables to Represent Numbers. Translate Conjunctions and Verbs. Look at the Last Sentence. Find a Formula. Simplify by Substituting. Solve an Equation. Check for Sense. Check for Accuracy. Glossary. Index. Book Registration InformationAwesomeBooksUSA Valley Cottage, NY 29/09/2001 Paperback Used-Good Book in good or better condition. Dispatched same day from US or UK warehouse
This brand-new manual provides high school students throughout the state of Virginia with in-depth preparation for the required Algebra I exam. The authors present an overview of the test, provide a calculator tutorial, and introduce algebraic expressions and operations. Following chapters offer review and practice in equations and inequalities, relations and functions, and statistics and data analysis. Also included are three full-length practice exams with all questions answered and explained.
this text integrates the discussion of graphs and digraphs and has new material on graph algorithms and their applications. This book should be of interest to undergraduate and graduate students taking courses in graph theory.
Fundamental Laws of Algebra Advertisement Learners review the fundamental laws of algebra including the commutative law of addition, the commutative law of multiplication, the associative law of addition, the associative law of multiplication, and the distributive law. Examples are given. Author(s): Douglas Jensen Allen Reed
Basic Technical Mathematics - 8th edition ISBN13:978-0321284433 ISBN10: 0321284437 This edition has also been released as: ISBN13: 978-0321131935 ISBN10: 0321131932 Summary: This tried-and-true text from the pioneer of the basic technical mathematics course now has Addison-Wesley's amazing math technologies MyMathLab and MathXL helping students to develop and maintain the math skills they will need in their technical careers. Technical mathematics is a course pioneered by Allyn Washington, and the eighth edition of this text preserves the author's highly regarded approach to technical math, while enhancing the integration of te...show morechnology in the text. The book is intended for a two- or three-semester course and is taught primarily to students who plan to pursue technical fields. The primary strength of the text is the heavy integration of technical applications, which aids the student in pursuit of a technical career by showing the importance of a strong foundation in algebraic and trigonometric math. Allyn Washington defined the technical math market when he wrote the first edition of Basic Technical Mathematics over forty years ago. His continued vision is to provide highly accurate mathematical concepts based on technical applications. The course is designed to allow the student to be simultaneously enrolled in allied technical areas, such as physics or electronics. The material in the text can be easily rearranged to fit the needs of both instructor and students. Above all, the author's vision of this book is to continue to show today's students that an understanding of elementary math is critical in many aspects of life. ...show less Introduction to Functions. More About Functions. Rectangular Coordinates. The Graph of a Function. Graphs on the Graphing Calculator. Graphs of Functions Defined by Tables of Data. 4. The Trigonometric Functions. Angles. Defining the Trigonometric Functions. Values of the Trigonometric Functions. The Right Triangle. Applications of Right Triangles. 5. Systems of Linear Equations; Determinants. Linear Equations. Graphs of Linear Functions. Solving Systems of Two Linear Equations in Two Unknowns Graphically. Solving Systems of Two Linear Equations in Two Unknowns Algebraically. Solving Systems of Two Linear Equations in Two Unknowns by Determinants. Solving Systems of Three Linear Equations in Three Unknowns Algebraically. Solving Systems of Three Linear Equations in Three Unknowns by Determinants. 6. Factoring and Fractions. Special Products. Factoring: Common Factor and Difference of Squares. Factoring Trinomials. The Sum and Differences of Cubes. Equivalent Fractions. Multiplication and Division of Fractions. Addition and Subtraction of Fractions. Equations Involving Fractions. 7. Quadratic Equations. Quadratic Equations; Solution by Factoring. Completing the Square. The Quadratic Formula. The Graph of the Quadratic Function. 8. Trigonometric Functions of Any Angle. Signs of the Trigonometric Functions. Trigonometric Functions of Any Angle. Radians. Applications of Radian Measure. 9. Vectors and Oblique Triangles. Introduction to Vectors. Components of Vectors. Vector Addition by Components. Applications of Vectors. Oblique Triangles, the Law of Sines. The Law of Cosines. Book shows a small amount of wear to cover and binding. Some pages show signs of use.Sail the Seas of Value $14.13 +$3.99 s/h VeryGood Books-FYI ky cadiz, KY 2005 Unknown Binding Very good Ships out next day, click expedited for faster shipping. $15.8015.809898
Software Review: Destination Math Mastering Skills & Concepts V: Pre-Algebra from River Deep For Grades 6-8 Content Area: Math Reviewed on: Pentium4 GHz 2.66 with 768MB and 48X DVD/CD Reviewed with: The evaluation form demonstrated on the Superkids website: Description from Manufacturer: A comprehensive approach to teaching pre-algebra. In preparation for high school mathematics, students explore ratios, proportions, and irrational numbers. They also begin a study of the fundamental skills and concepts of algebra, statistics, geometry, and probability. Unit topics cover the following content strands:  Essentials of Algebra: algebra fundamentals, evaluating algebraic expression, simple equations, variable on both sides of the equation, solving literal equations  Fundamentals of Geometry: geometry fundamentals, triangles, volume and surface areas  Radicals and Exponents: introduction of radicals and Pythagorean Theorem, scientific notation  Ratio and Proportion: ratio, proportion, direct and inverse variation, similar polygons  Statistics: interpreting and constructing graphs, mean median and mode, frequency distribution, and histograms  Probability: simple probability, probability of combined events Educational Value This program is very well designed and laid out. It works like an outline, with clear topics and subtopics to choose from, depending what area you need to concentrate on. The program clearly covers all of the content strands listed above. It provides a choice of a tutorial to teach the concept or workouts to practice the concepts with problems. The language and terms are easy to understand and follow. There is a glossary of terms available if you need it. The initial interface is visually engaging and looks slightly futuristic, which would appeal to youth. There is a male cartoon character, a space alien, which provides the tutorials, alternating with a female voice to provide clarification and additional instructions. The learning curve is very short, because the design is so simple to navigate. The challenge I see immediately is that students may not complete the tutorials before trying the workout problems. Kid Appeal From a student point of view, Destination Math Mastering Skills & Concepts V: Pre-Algebra is probably too juvenile and "cutesy" for many students because of its character design. I believe the teaching methods and navigation are age appropriate, but the cartoon character that guides the program is inappropriate to grades 6-8, the target audience, particularly in an urban setting like Springfield. I think student reviewers would be turned off almost immediately by the main character and it would have been better to design the character as someone reflecting the students more closely. The character could be "tweaked" to represent an avatar or an anime character, for example. The program has won several awards, including the 2006 iParenting Best Products of 2006, so clearly it has appeal in other markets and/or to other age groups. Best for... / Bottom-Line Destination Math Mastering Skills & Concepts V: Pre-Algebra is appropriate for students studying pre- algebra that can work with its cartoon interface. It is easy to learn, easy to follow and provides clear instructions, practice and interactive learning. I would suggest this product for younger students. System Requirements Stand-alone System Requirements Free hard CD Title Platform / OS Processor Available RAM disk Display Required / Other ROM space 800x600, Hi Color 16-bit, Win 98, ME, 64MB/128MB SoundBlaster 16 or 2000 SP2, NT Pentium II (128MB for 2000 150MB 16X compatible with 4.0 SP 6, XP 200 MHz or XP) headphones, Acrobat Destination Home, XP Pro Reader 5+ Math 800x600 High Color 16- Mac OS 8.6+, G3 128MB (Virtual bit, standard Macintosh OS 10.2.x- 150MB 16X processor Memory On) sound with headphones, 10.4.x (Native) Acrobat Reader 5+ Technical Support Online technical support is available here: It provides a range of online support, updates, program guides and manuals, enhancements and related tools. 4.5 3.0 4.5 MA State Curriculum Frameworks Aligned to the Software Content: Math Strands Note: These were provided by the program's description pages on the Riverdeep website under the correlations for Massachusetts. Number Sense and Operations Grade 7 7.N.2 Use ratios and proportions in the solution of problems involving unit rates, scale drawings, and reading of maps. Patterns, Relations and Algebra Grade 7 7.P.1 Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding. This standard is intentionally the same as standard 8.P.1. 7.P.2 Evaluate simple algebraic expressions for given variable values, e.g., 3a2 – b for a = 3 and b = 7. This standard is intentionally the same as standard 8.P.2. Geometry Grade 7 7.G.1 Analyze, apply, and explain the relationship between the number of sides and the sums of the interior angle measures of polygons. 7.G.2 Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems. This standard is intentionally the same as standard 8.G.2. Measurement Grade 6 6.M.3 Solve problems involving proportional relationships and units of measurement, e.g., same system unit conversions, scale models, maps, and speed. l 6.M.4 Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same area. Develop strategies to find the area of more complex shapes. l 6.M.5 Identify, measure, and describe circles and the relationships of the radius, diameter, circumference, and area (e.g., d = 2r, p = C/d), and use the concepts to solve problems. l 6.M.6 Find volumes and surface areas of rectangular prisms. l 6.M.7 Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles. l Grade 7 7.M.3 Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms and cylinders. Use technology as appropriate. Grade 8 8.M.3 Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/ circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate. Data Analysis, Statistics and Probability Grade 6 6.D.1 Describe and compare data sets using the concepts of median, mean, mode, maximum and minimum, and range. l 6.D.2 Construct and interpret stem-and-leaf plots, line plots, and circle graphs.l 6.D.3 Use tree diagrams and other models (e.g., lists and tables) to represent possible or actual outcomes of trials. Analyze the outcomes. n 6.D.4 Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions. Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event. n Grade 7 7.D.3 Use tree diagrams, tables, organized lists, and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of number cubes. Grade 7-8 8.D.2 Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, boxand- whisker plots, histograms, tables, and charts. Differentiate between continuous and discrete data and ways to represent them. 8.D.3 Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data. 8.D.4 Use tree diagrams, tables, organized lists, basic combinatorics ("fundamental counting principle"), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice
Math Trek 04/01/05 The NECTAR Foundation's new Math Trek suite of products ( uses curriculum-based programs that cover the foundations of math for grades 1-12. These engaging programs feature sound, graphics, animation and music clips through interactive tutorials, problem-solving activities, assessment components and student tracking. The Macintosh- and Windows-compatible learning aids include a comprehensive teacher resource document with print support materials, as well as individual, group and culminating performance tasks that incorporate many skills into a meaningful context. The NECTAR Foundation also offers specialized programs for algebra I, calculus and trigonometry
More About This Textbook Overview "102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics. Editorial Reviews From the Publisher From the reviews: "Andreescu's 51 'introductory problems' and 51 'advanced problems,' all novel, would nicely supplement any university course in combinatorics or discrete mathematics. This volume contains detailed solutions, sometimes multiple solutions, for all the problems, and some solutions offer additional twists for further thought . . . " —CHOICE "Another excellent effort towards building combinatorial skills especially for students engaged in mathematical competitions is presented in this book through 102 selected Combinatorial problems." —ZENTRALBLATT MATH "Each solution is given in full, and often with alternative versions as well. Some solutions introduce standard combinatorial tools like inclusion-exclusion, generating functions, and graphs. Others stray into probability, number theory, complex numbers, inequalities and functional equations. The book will be useful for teachers looking for challenging problems for able students and for those preparing for Olympiads." —The MATHEMATICAL GAZETTE "This book contains 102 highly selected combinatorial problems used in the training and testing of the USA International Mathematical Olympiad team. Half of the problems are introductory, while the rest are more difficult. All problems have complete solutions. . . It is not a collection of very difficult, impenetrable questions. Instead, the book gradually builds students' combinatorial skills and techniques. It aims to broaden a student's view of mathematics in perparation for possible participation in mathematical competitions." —IASI POLYTECHNIC MAGAZINE "Both of the two authors serves as a coach of the USA International Mathematical Olympiad (IMO) Team for several years. … the book gradually builds students' combinatorial skills and techniques. It aims to broaden a student's view of mathematics in preparation for possible participation in mathematical competitions. … this is a book for problem-solvers. … The present collection of problems and the presented solutions are carefully designed to develop the readers' problem-solving abilities. … Have fun working on them!" (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol. 69
1576851680 9781576851685 Basic Skills for Homeschooling:This essential guide for the homeschooling parent provides practice exercises correlated to standard language arts and math curricula, from reading comprehension to essay writing, fractions to algebra, and every requirement in between--designed to supplement traditional teaching materials and challenge your child as you make your way through the middle school years. Back to top Rent Basic Skills for Homeschooling 1st edition today, or search our site for Lee textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by LearningExpress LLC.
dear sir/madam can you please send me the discount prise of the following books 1.differential calculus 2.integral calculus 3. matrices all the above books are of Rajhans publication and written by P.N. Chatterji please send the details to my mail as quick as possible.. thanks
Francis Borceux With this volume, the author completes his trilogy of books covering the broad sweep and many facets of geometry. The first in the series (An Axiomatic Approach to Geometry) looked at geometry from a synthetic viewpoint, starting from its pre-Greek origins and working forward in time through the development of non-Euclidean geometry, finally culminating in a chapter giving a precise axiomatic development of the subject. The second (An Algebraic Approach to Geometry) used the methods of abstract and linear algebra to define and explore affine, Euclidean and projective geometry, and also provided an introduction to the theory of algebraic curves. In this book, the focus is on how calculus can be used to develop geometric ideas. Like the other books in this trilogy, this one relies heavily on history as a motivational tool. The first chapter, in fact, constitutes a look at the evolution of definitions of things like curves and tangent lines; various definitions are proposed and examined, with problems inherent in them discussed. Eventually the author settles on definitions, and the work of studying (classical) differential geometry begins with chapter 2. Since chapter 1 uses history for motivational purposes, the rest of the book is essentially independent of it, and a course based on this book could certainly begin with chapter 2. Curves are the subject of chapters 2 through 4. Plane curves are discussed in chapter 2 and space (or "skew", as the author calls them) curves are the subject of chapter 4. These two chapters bookend a chapter devoted entirely to an examination of detailed examples — the deltoid, cissoid, tractrix, catenary, and more than a dozen others. Although the titles of these three chapters do not distinguish between the "local" and "global" theory, both aspects of the theory are discussed in them; for example, the Four-Vertex theorem, a global result, is proved. And of course the traditional topics of the local theory (e.g., the Frenet apparatus) are covered as well. The remaining three chapters of the book deal with surfaces. Chapter 5, the first of them, discusses the classical local theory of surfaces in three-space. Topics include the definition of a surface, and the basic facts connected with them, including a heavy emphasis on curvature. In the next chapter, the notion of a surface is looked at from a different point of view (emphasizing its status as an entity in its own right rather than as a subset of three-space) to discuss its intrinsic properties, giving the author an opportunity to introduce the basic terminology and notions of Riemannian geometry in a nice concrete setting. (As a person who loathes the Einstein summation convention, I appreciated the fact that although the author mentioned it (albeit without using the name "Einstein"), he deliberately chose not to use it in this chapter). Some ideas of non-Euclidean geometry (the Poincare half-plane) are discussed here, and the idea of a Riemann surface is introduced. The remaining chapter addresses the global theory of surfaces, the highlight of which is perhaps the statement and proof of the Gauss-Bonnet theorem. The chapter ends with a brief foray into algebraic topology, via the Euler-Poincaré characteristic. Two multi-section appendices, one on basic topology and the other on differential equations, round out the text. The first of these appendices starts with the basic constructs of topology in Euclidean spaces (open and closed sets, connectedness, compactness, etc.) and then generalizes them to arbitrary topological spaces. Full proofs are generally given, even of some deep results like the Heine-Borel theorem. The second appendix, on differential equations, is much shorter and generally devoid of proofs; it simply states some results on both ordinary and partial differential equations that were used in the text. American undergraduate mathematics majors don't generally get to take courses in this material much anymore, so, even though this book comes equipped with exercises, it probably won't find much use as an undergraduate text; Springer doesn't seem to even be marketing it as one, since the webpage for the book does not list it under "textbooks" and lists the level as "graduate". This is probably appropriate — Professor Borceux teaches in Europe (in Belgium) and this book was undoubtedly written for European undergraduates. While it is clearly written, it is fairly dense and requires some degree of mathematical maturity. The fact that this may not be used much as a textbook, however, does not detract from its quality. This trilogy is, in fact, a remarkable accomplishment; Borceux obviously cares a lot about geometry, and these books are a real labor of love. I'm glad that they are on my shelves; if you have any interest in geometry, they should be on yours as well. One final comment, unrelated to the quality of this particular book, concerns Springer's production practices. I recently had to return a Springer book that I purchased on amazon because my copy had about 50 blank pages in it, including one streak of 17 consecutive blank pages; a colleague I emailed reported similar printing problems with other books. In this volume, none of the pages were blank, but one did fall out of the book as I opened it for the first time.
clear, time-tested problem sets in ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, CLASSIC EDITION, 12E, will prepare you for success in future math classes. Swokowski and Cole carefully explain each concept and include step-by-step comments in the solutions. Many examples are accompanied by graphs, figures, charts, or tables to help you interpret graphical data. Packaged with each book, the Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction, featuring a 10-question Web quiz per section, a test for each chapter, with answers, and MathCue tutorial and quizzing software. The accompanying online tutorials give you the practice you need to improve your grade in the course44.49 from$44.49 Save up to $253.46! Rent thru 06/22/14 for $44.49 $44.49 Save $253.46! Rent thru 07/22/14 for $44.49 $44.49 Save $253.46! Rent thru 08/31/14 for $44.49 $44.49 Save $253.46! Rent thru 01/18/15 for $50.49 $50.49 Save $247.46! Rent thru 10/15/15 for $56.49 $56.49 Save $241 your 04/18/15 for $73.99 $73.99 Save $223
Numerical Linear Algebra Book Description: This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra. Contents: Preface; Acknowledgments; Part I: Fundamentals. Lecture 1: Matrix-Vector Multiplication; Lecture 2: Orthogonal Vectors and Matrices; Lecture 3: Norms; Lecture 4: The Singular Value Decomposition; Lecture 5: More on the SVD; Part II: QR Factorization and Least Squares. Lecture 6: Projectors; Lecture 7: QR Factorization; Lecture 8: Gram-Schmidt Orthogonalization; Lecture 9: MATLAB; Lecture 10: Householder Triangularization; Lecture 11: Least Squares Problems; Part III: Conditioning and Stability. Lecture 12: Conditioning and Condition Numbers; Lecture 13: Floating Point Arithmetic; Lecture 14: Stability; Lecture 15: More on Stability; Lecture 16: Stability of Householder Triangularization; Lecture 17: Stability of Back Substitution; Lecture 18: Conditioning of Least Squares Problems; Lecture 19: Stability of Least Squares Algorithms; Part IV: Systems of Equations. Lecture 20: Gaussian Elimination; Lecture 21: Pivoting; Lecture 22: Stability of Gaussian Elimination; Lecture 23: Cholesky Factorization; Part V: Eigenvalues. Lecture 24: Eigenvalue Problems; Lecture 25: Overview of Eigenvalue Algorithms; Lecture 26: Reduction to Hessenberg or Tridiagonal Form; Lecture 27: Rayleigh Quotient, Inverse Iteration; Lecture 28: QR Algorithm without Shifts; Lecture 29: QR Algorithm with Shifts; Lecture 30: Other Eigenvalue Algorithms; Lecture 31: Computing the SVD; Part VI: Iterative Methods. Lecture 32: Overview of Iterative Methods; Lecture 33: The Arnoldi Iteration; Lecture 34: How Arnoldi Locates Eigenvalues; Lecture 35: GMRES; Lecture 36: The Lanczos Iteration; Lecture 37: From Lanczos to Gauss Quadrature; Lecture 38: Conjugate Gradients; Lecture 39: Biorthogonalization Methods; Lecture 40: Preconditioning; Appendix: The Definition of Numerical Analysis; Notes; Bibliography; Index. Audience: Written on the graduate or advanced undergraduate level, this book can be used widely for teaching. Professors looking for an elegant presentation of the topic will find it an excellent teaching tool for a one-semester graduate or advanced undergraduate course. A major contribution to the applied mathematics literature, most researchers in the field will consider it a necessary addition to their personal collections
Drawing on the authors' more than six years of R&D in location-based information systems (LBIS) as well as their participation in defining the Java ME Location API 2.0, Location-Based Information Systems: Developing Real-Time Tracking Applications provides information and examples for creating real-time LBIS based on GPS-enabled cellular phones. Each chapter presents a general real-time tracking system example that can be easily adapted to target any application domain and that can incorporate other sensor data to make the system "participatory sensing" or "human-centric sensing." This text, which grew out of a NSF grant, takes a fresh approach with a focus on the underlying concepts of precalculus, rather than sheer algebraic manipulation. It effectively prepares students for a new generation of calculus courses and allows instructors to become actively involved in the teaching process. The authors make extensive use of real world applications, showing students how mathematics relates to their field of study, as well as including a thorough integration of technology. Additionally, the authors have incorporated a number of learning features designed to ready students for a more positive calculus experience.
Pedricktown Precalculus all the skills learned in Algebra 1&2 to a much deeper level, while at the same time advances several concepts begun in Geometry. The goal of Precalculus is to prepare students for Calculus by exposing them to a variety of graphs and functions which will be used or seen in higher level math. It is a great deal of fun, especially if you like puzzles
3.3: Multiplication with Decimals; Circumference and Areas of a Circle (28) 3.4: Division with Decimals (29) 3.5: Fractions and Decimals, and the Volume of a Sphere (28) Chapter 4: Ratio and Proportion 4.1: Ratios (23) 4.2: Rates and Unit Pricing (23) 4.3: Solving Equations by Division (19) 4.4: Proportions (24) 4.5: Applications of Proportions (23) 4.6: Similar Figures (22) Chapter 5: Percent 5.1: Percents, Decimals, and Fractions (21) 5.2: Basic Percent Problems (23) 5.3: General Applications of Percent (24) 5.4: Sales Tax and Commission (24) 5.5: Percent Increase or Decrease and Discount (25) 5.6: Interest (24) Chapter 6: Descriptive Statistics 6.1: Mean, Median, and Mode (26) 6.2: Displaying Information (22) 6.3: Pie Charts (10) 6.4: Introduction to Probability (16) Chapter 7: Measurement 7.1: Unit Analysis I: Length (29) 7.2: Unit Analysis II: Area and Volume (34) 7.3: Unit Analysis III: Weight (28) 7.4: Converting Between the U.S. and Metric Systems and Temperature (29) 7.5: Operations with Time and Mixed Units (26) Chapter 8: Geometry 8.1: Perimeter and Circumference (16) 8.2: Area (16) 8.3: Surface Area (21) 8.4: Volume (19) 8.5: Square Roots and the Pythagorean Theorem (29) Chapter 9: Introduction to Algebra 9.1: Positive and Negative Numbers (29) 9.2: Addition with Negative Numbers (25) 9.3: Subtraction with Negative Numbers (26) 9.4: Multiplication with Negative Numbers (26) 9.5: Division with Negative Numbers (28) 9.6: Simplifying Algebraic Expressions (30) Chapter 10: Solving Equations 10.1: The Distributive Property and Algebraic Expressions (31) 10.2: The Addition Property of Equality (25) 10.3: The Multiplication Property of Equality (30) 10.4: Linear Equations in One Variable (28) 10.5: Applications (25) 10.6: Evaluating Formulas (35) 10.7: Paired Data and the Rectangular Coordinate System (22) Questions Available within WebAssign Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.
"This self-contained text offers an elementary introduction to partial differential equations (pdes), primarily focusing on linear equations, but also providing some perspective on nonlinear equations. The classical treatment is mathematically rigorous with a generally theoretical layout, though indications to some of the physical origins of pdes are made throughout in references to potential theory, similarity solutions for the porous medium equation, generalized Riemann problems, and others. The material begins with a focus on the Cauchy-Kowalewski theorem, discussing the notion of characteristic surfaces to classify pdes. Next, the Laplace equation and connected elliptic theory are treated, as well as integral equations and solutions to eigenvalue problems. The heat equation and related parabolic theory are then presented, followed by the wave equation in its basic aspects. An introduction to conservation laws, the uniqueness theorem, viscosity solutions, ill-posed problems, and nonlinear equations of first order round out the key subject matter. Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct errors, and improve clarity. Most of the necessary background material has been incorporated into the complements and certain nonessential topics have been given reduced attention (noticeably, numerical methods) to improve the flow of presentation. The exposition is replete with examples, problems and solutions that complement the material to enhance understanding and solidify comprehension. The only prerequisites are advanced differential calculus and some basic Lp theory. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists."--Publisher's description.
You are here Algebra and Tiling Sherman Stein and Sándor Szabó Read what reviewers had to say about this excellent monograph: Algebra and Tilingis perfect for bringing alive an abstract algebra course. Intuitive but difficult problems of geometry are translated into algebraic problems more amenable to solution.… Full of surprises, the book is a pleasure to read. Essential for collections that serve undergraduates. — Choice The authors have arranged the text so that exercises are stated frequently throughout the chapters, rather than at the end, and they have presented as problems some questions that have not yet been answered. Historical background relating to tiling problems helps focus the reader on the mathematical discussions. The student or mathematician whose area of interest is algebra should enjoy this text. —The Mathematics Teacher There are many questions about tilings which lend themselves nicely to the tools of modern algebra. This book is about several such questions. Each chapter is an independent instance of turning a tiling problem into a problem in algebra. … This book is almost self-contained; a lot of time is spent describing carefully the relevant algebra. —Zentralblatt für Mathematik Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper division algebra courses, but teachers, researchers, and professional mathematicians will find the book equally appealing. Beginners will find the exercises and the appendices especially useful. The unsolved problems will challenge both beginners and experts. The book could serve as the basis of an undergraduate or graduate seminar or a source of applications to enrich an algebra or geometry course. Print-on-Demand (POD) books are not returnable because they are printed at your request. Damaged books will, of course, be replaced (customer support information is on your receipt). Please note that all Print-on-Demand books are paperbound.
Calculus Course Assistant Description This app covers the following topics applicable to Calculus, AP Calculus AB, AP Calculus BC, Calculus I, and Calculus II: - Evaluate any numeric expression or substitute a value for a variable. - Plot basic, parametric, or polar plots of the function(s) of your choice. - Determine the limit of a function as it approaches a specific value. - Differentiate any function or implicit function. - Find the critical points and inflection points of a function. - Identify the local and absolute extrema of a function. - Integrate a function, with or without limits. - Sum a function given a lower and upper bound. -Users Also Installed Algebra Course Assistant Wolfram Alpha, LLC 81 ratingsMathStudio Pomegranate Apps 289 ratings MathStudio is the most comprehensive math app available for Android phones and tablets. Whether you need a simple calculator to do your finances or a replacement for your TI graphing calculator, MathStudio is the most powerful and versatile...
Students who take SAT subject tests apply to the most selective colleges in the country. These are high-aptitude kids with overbooked schedules-finally, there's a series that refuses to waste their time. The revolutionary MyMaxScore prep series now covers SAT subject tests. Each chapter begins with 5 to 10 test questions to diagnose what students... more... Whether you are returning to school, studying for an adult numeracy test, helping your kids with homework, or seeking the confidence that a firm maths foundation provides in everyday encounters, Basic Maths For Dummies, UK Edition, provides the content you need to improve your basic maths skills. Based upon the Adult Numeracy Core Curriculum,... more... This proceedings is a collection of articles by front-line researchers in Mathematical Analysis, giving the reader a wide perspective of the current research in several areas like Functional Analysis, Complex Analysis and Measure Theory. The works are a fundamental source for current and future developments in these research fields. The articles and... more... Lately there is an increasing interest in partial difference equations demonstrated by the enormous amount of research papers devoted to them. The initial reason for this increasing interest was the development of computers and the area of numerical analysis, where partial difference equations arise naturally when discretizing a partial differential... more... Discrete Hilbert-type inequalities including Hilbert's inequality are important in mathematical analysis and its applications. In 1998, the author presented an extension of Hilbert's integral inequality with an independent parameter. In 2004, some new extensions of Hilbert's inequality were presented by introducing two pairs of conjugate... more... Most people don?t think about numbers, or take them for granted. For the average person numbers are looked upon as cold, clinical, inanimate objects. Math ideas are viewed as something to get a job done or a problem solved. Get ready for a big surprise with Numbers and Other Math Ideas Come Alive . Pappas explores mathematical ideas by looking behind... more... Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable... more... This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay... more...
Mathematics (MATH) Basic Skills Courses All courses at this level are offered for college credit. Credit for these courses will not apply toward the associate degree but will count toward the determination of a student's workload and eligibility for financial aid. 15A Prealgebra Refresher - 3 hours lab, 1 unit (Pass/No Pass Only) This course is intended for students who have completed the math assessment with a level of M20 (prealgebra) and wish to improve their placement level; students who have successfully completed Prealgebra but need more review; or students who unsuccessfully attempted Beginning Algebra and need review of Prealgebra skills. The course consists of personalized computer assisted instruction to refresh those concepts identified as needed for each student. Successful completion of this course may serve as a basis for a petition to challenge a Prealgebra prerequisite. This course will not replace a failing grade in Prealgebra. Not Applicable to Associate Degree. This course is intended for those students who have completed the math assessment with a level of M30 (beginning algebra and geometry) and wish to improve their placement level; students who have successfully completed Beginning Algebra but need more review; or students who unsuccessfully attempted Intermediate Algebra and need review of Beginning Algebra and Geometry skills. The course consists of personalized computer assisted instruction to refresh those concepts identified as needed for each student. Successful completion of this course may serve as a basis for a petition to challenge a Beginning Algebra prerequisite. This course will not replace a failing grade in Beginning Algebra. Not Applicable to Associate Degree. This course is intended for those students who have completed the math assessment with a level of M40 (intermediate algebra and geometry) and wish to improve their placement level; students who have successfully completed Intermediate Algebra but need more review; or students who unsuccessfully attempted a transfer level math class and need review of Intermediate Algebra and Geometry skills. The course consists of personalized computer assisted instruction to refresh those concepts identified as needed for each student. Successful completion of this course may serve as a basis for a petition to challenge an Intermediate Algebra prerequisite. This course will not replace a failing grade in Intermediate Algebra. Not Applicable to Associate Degree. 15D Geometry Refresher - 3 hours lab, 1 unit (Pass/No Pass Only) This course is intended for those students who have completed a high school geometry course or for those students who have completed Intermediate Algebra and Geometry and need to review geometric principles prior to taking Math for Elementary Teachers or Trigonometry. The course consists of personalized computer assisted instruction to refresh those concepts identified as needed for each student. (FT) Not Applicable to Associate Degree. 15E Trigonometry Refresher - 3 hours lab, 1 unit (Pass/No Pass Only) This course is intended for those students who have completed the math assessment with a level of M50 who need to review their Trigonometry knowledge prior to taking Precalculus or Calculus. Students begin at the level of their original placement and, working at their own pace, may improve their placement up to M60 (precalculus level). The course consists of personalized computer assisted instruction to refresh those concepts identified as needed for each student. (FT) Not applicable to the Associate Degree. This course is intended for those students who have completed the math assessment with a level of M50 and need to review their College Algebra skills prior to taking a Calculus sequence. The course consists of personalized computer assisted instruction to refresh those concepts identified as needed for each student. Successful completion of this course may serve as a basis for a petition to challenge a College Algebra prerequisite. Students wishing to challenge Pre-calculus must also show competence in Trigonometry. (FT) Not applicable to the Associate Degree. (Formerly Mathematics 32) Advisory: English 42 or English for Speakers of Other Languages 31, with a grade of "C" or better, or equivalent, or Assessment Skill Levels R4 or L40. Limitation on Enrollment: This course is not open to students with previous credit for Mathematics 32. This course is an introduction to fundamental concepts of arithmetic. Emphasis is placed on par addition, subtraction, multiplication, division and exponentiation on whole numbers, fractions, and decimals. Topics also include simple percents and ratios, systems of measurement, and applications of these topics. Students learn basic study skills necessary for success in mathematics courses. This course is intended for students preparing for Prealgebra. (FT) Not applicable to the Associate Degree. (Formerly Mathematics 35) Advisory: English 42 or English for Speakers of Other Languages 31 and Mathematics 34A, with a grade of "C" or better, or equivalent, or Assessment Skill Levels R4 or L40 and M20. Limitation on Enrollment: This course is not open to students with previous credit for Mathematics 35. This course is a study of the fundamentals of arithmetic operations with signed numbers, including fractions and decimals as well as an introduction to some elementary topics in beginning algebra. Topics also include ratios and proportions, perfect squares and their square roots, elementary topics in geometry, systems of measurement, and monomial arithmetic. Students learn basic study skills necessary for success in mathematics courses. This course is intended for students preparing for Beginning Algebra. (FT) Not applicable to the Associate Degree. Limitation on Enrollment: This course is not open to students with previous credit for Mathematics 54, 90, 91 or 95. This course is intended for students who have not passed the California State University Entry-Level Mathematics Examination (ELM). This course reviews arithmetic and geometric concepts, and covers topics in elementary algebra including operations with polynomials, factoring, rational expressions, expressions involving radicals, solving non-linear equations, graphing linear equations, and solving linear systems of equations in two variables. Not Applicable to Associate Degree, pre-collegiate basic skills - reading, writing, computation. Advisory: Mathematics 42 with a grade of "C" or better, or equivalent. Limitation on Enrollment: This course is not open to students with previous credit for Mathematics 96, 100 or 91. This course is a continuation of Mathematics 042 and is intended for those students who have not passed the California State University Entry-Level Mathematics Examination (ELM). This course is designed to prepare students for college algebra and consists of a review of intermediate algebra concepts. Topics for the class include set and function notation, simplifications and solutions to equations involving rational and radical expressions, quadratic equations and functions, complex numbers, exponential and logarithmic functions and applications. Not Applicable to Associate Degree, pre-collegiate basic skills - reading, writing, computation. (Formerly Mathematics 95) Prerequisite: Prerequisite: Mathematics 38 with a grade of "C" or better, or equivalent, or Assessment Skill Level M30. Advisory: Completion of or concurrent enrollment in: English 43 and English 48, each with a grade of "C" or better, or equivalent, or Assessment Skill Levels W4 and R5. Limitation on Enrollment: This course is not open to students with previous credit for Mathematics 95 with a grade of "C" or better. Elementary algebra and geometry serves as the foundation for the other math courses and is the first of a two-course integrated sequence in algebra and geometry intended to prepare students for transfer level mathematics. This course covers the real number system; writing, simplifying, solving and graphing of linear equations in one variable; solving linear inequalities in one variable; solving systems of linear equations in two variables; algebraic operations with polynomial expressions and factoring; functions; operations involving rational expressions and related equations; and geometric properties of lines, angles, and triangles. This course is intended for students preparing for higher-level geometry and algebra courses. (FT) Not Applicable to Associate Degree, basic skills. Associate Degree Credit Courses Prerequisite: Mathematics 46 with a grade of "C" or better, or equivalent, or Assessment Skill Level M40. Advisory: English 43 with a grade of "C" or better, or equivalent, or Assessment Skill Level W4. This course is a study of the practical applications of linear, quadratic and exponential growth models. Topics also include statistical methods, geometry, right triangle trigonometry and finance math. This course will develop math literacy through the use of current events and real life applications. This course is designed for students who are earning an associate's degree and who are not planning to transfer to a four-year institution. (FT) AA/AS. Prerequisite: Mathematics 46 with a grade of "C" or better, or equivalent, or Assessment Skill Level M40. Advisory: English 43 and English 48, each with a grade of "C" or better, or equivalent, or Assessment Skill Levels R5 and W4. Intermediate algebra and geometry is the second of a two-course integrated sequence in algebra and geometry. This course covers systems of equations and inequalities, radical and quadratic equations, quadratic functions and their graphs, complex numbers, nonlinear inequalities, exponential and logarithmic functions, conic sections, sequences and series, and solid geometry. The course also includes application problems involving these topics. This course is intended for students preparing for transfer-level mathematics courses. (FT) AA/AS. Prerequisite: Mathematics 46 with a grade of "C" or better, or equivalent or Assessment Skill Level M40. Advisory: English 48 and English 49, each with a grade of "C" or better, or equivalent or Assessment Skill Levels R5 and W5. This course introduces an applied technology approach to problem solving in Intermediate Algebra and Geometry, and it is intended to support the curriculum required in the Engineering and applied technologies majors. Students are expected to apply problem solving techniques to technology-based situations in their technical physics and applied technology courses. Topics include scientific notation, algebra of functions, linear systems of equations, graphing using log and semi-log paper, technology applications of quadratic, exponential and logarithmic functions, right triangle trigonometry, applications in electronics of vectors and phasors. Special emphasis will be placed on the use of the graphing calculator and mathematical software packages to solve application problems. (FT) AA/AS. Statistical Pathway Math 47A, and Math 115 are a two-course sequence of courses that take a student with a Math skill level of 30 or placement into Math 46, from Beginning Algebra through a transfer level statistics course. Math 47A is a basic skills class, while Math 115 is a transfer level class that focus on statistics, data analysis, and quantitative reasoning. These are mathematics skills that are essential for a growing number of occupations and professions. This is the math that will help students understand the world around them and it is math you can use immediately. This path of courses is referred to as Statistics Pathway, (or Statway for short), and is designed for liberal arts, non-STEM social science majors (STEM= Science, Technology, Engineering and Mathematics). This pathway of courses will not satisfy any requirements for students that are planning on studying science or science related fields. Student need to make an appointment with their counselors to determine if this sequence is appropriate for them. Prerequisite: Mathematics 38 with a grade of "C" or better, or equivalent or Assessment Skill Level M30. Advisory: Completion of or concurrent enrollment in English 43 and English 48 each with a grade of "C" or better, or equivalent or Assessment Skill Levels W4 and R5. This course is the first of a two course sequence in the study of statistical methods integrated with algebraic tools to prepare students to analyze processes encountered in society and the workplace. The course covers an introduction to algebra and descriptive statistics in an integrated approach. Topics include data collection, organizing and interpreting data graphically, qualitative and quantitative data sets, measures of central tendency and measures of dispersion, bivariate data and scatter plots, linear functions and their graphs, nonlinear functions and their graphs, and applying technology to calculate various types of regressions. Students are expected to implement technology to perform calculations to organize data in order to make statistical conclusions. This sequence of courses is intended for students that are not planning on majoring in a science, technology, engineering, or mathematics related disciplines. This course is only basic skills/remedial. (FT) Not applicable to the Associate Degree. Prerequisite: Mathematics 47A with a grade of "C" or better, or equivalent Statway I. Advisory: Completion of or concurrent enrollment in English 43 and English 48, each with a grade of "C" or better, or equivalent or Assessment Skill Levels W4 and R5. This course is a second in the study of statistical methods integrated with algebraic tools to prepare students to analyze these processes encountered in society and the workplace. The course covers a review of functions, their geometric properties, counting principles and probability rules, probability distribution functions, sampling, and inferential statistics of one and two variable data sets. Students are expected to implement technology to perform calculations to analyze data and make statistical conclusions. This sequence of courses is intended for students that are not planning on majoring in a science, technology, engineering or mathematics related discipline. (FT) AA/AS; CSU. Transfer Level Courses Prerequisite: Mathematics 96 with a grade of "C" or better, or equivalent, or Assessment Skill Level M50. This course is a study of the numerical, analytical, and geometric properties of right and oblique triangles, of trigonometric and inverse trigonometric functions, and their applications. The course content includes right angle trigonometry, radian measure, circular functions, graphs of circular functions and their inverses, trigonometric identities, equations involving trigonometric and inverse trigonometric functions, an introduction of the complex plane, vectors and their operations, and the trigonometric form of complex numbers. This course is designed as a preparation for calculus and it is intended for the transfer student planning to major in mathematics, engineering, economics, or disciplines included in the physical or life sciences. This course meets CSU general education requirements. (FT) AA/AS; CSU. Prerequisite: Mathematics 96 with a grade of "C" or better, or equivalent, or Assessment Skill Level M50. Corequisite: Mathematics 107L. Advisory: English 48 with a grade of "C" or better, or equivalent, or Assessment Skill Level R5. This course is an introduction to mathematical and scientific problem-solving on a computer; focusing on designing algorithms of a high level programming language. Extensive programming is required. Students are expected to plan and write programming projects with documentation. This course is recommended for students transferring to majors in Computer Science and/or mathematics. (FT) AA/AS; CSU; UC. Corequisite: Mathematics 107. This is a lab course to be taken concurrently with Mathematics 107. Extensive programming is required. Students are expected to plan and write programming projects with documentation. This course is recommended for students transferring to majors in Computer Science and/or mathematics. (FT) AA/AS; CSU. Prerequisite: Mathematics 96 with a grade of "C" or better, or equivalent, or Assessment Skill Level M50. This course is designed to strengthen the algebra skills of students seeking Business or Natural Science degrees who are required to take an applied calculus course. Topics in the course include the theory of functions; graphing functions; exponential and logarithmic functions; solving equations involving algebraic, exponential and logarithmic functions; solving systems of linear equations; matrix algebra; linear programming; modeling; and applications problems. Analytical reading and problem solving skills are required for success in this course. (FT) AA/AS; CSU; UC Transfer Limitation: Mathematics (MATH) 116 and 141 combined: maximum credit, one course. Prerequisite: Mathematics 96 with a grade of "C" or better, or equivalent, or Assessment Skill Level M50. Advisory: English 101 with a grade of "C" or better, or equivalent, or Assessment Skill Levels R6 and W6. This course covers topics in probability, statistics, logical reasoning, quantitative literacy, the history of mathematics, and applications of mathematics to the real world. This course is designed for students who do not intend to prepare for a career/ major in science, business, math, technology, and engineering. Analytical reading and problem solving are required for success in this course. (FT) AA/AS; CSU. Prerequisite: Mathematics 116 with a grade of "C" or better, or equivalent. This course examines the study of calculus using numerical, graphical, and analytical methods to analyze calculus problems encountered in real-world applications in business, natural/life sciences, and social sciences. Topics include limits, derivatives, and integrals of algebraic, exponential, and logarithmic functions, curve sketching, optimization, and areas under and between curves and partial derivatives and optimization of multivariable functions. This is the first course in a sequence of mathematics courses for students intending to major in business, economics, or natural and social sciences. This course does not fulfill a mathematics requirement for mathematics, chemistry, physics, or engineering majors at most universities. (FT) AA/AS; CSU; UC Transfer Limitation: Mathematics (MATH) 121 and 150 combined: maximum credit, one course. Prerequisite: Mathematics 121 with a grade of "C" or better, or equivalent. This second course in a math sequence covers methods of integration, multivariable functions and optimization problems, differential equations, Taylor series development and application, derivatives and integrals of trigonometric functions, and their usage in solving problems encountered in real-world applications in business, life and social sciences and economics. It is intended for students majoring in business, natural science, social science and economics. AA/AS; CSU; UC Transfer Limitation: Mathematics (MATH) 122 and 151 combined: maximum credit, one course. Prerequisite: Mathematics 104 with a grade of "C" or better, or equivalent. This course is a study of numerical, analytical, and graphical properties of functions. The course content includes polynomial, rational, irrational, exponential, logarithmic, and trigonometric functions. Additional topics include: inverse functions, complex numbers, polar coordinates, matrices, conic sections, sequences, series and the binomial theorem. This course is designed as a preparation for calculus and is intended for the transfer student planning to major in mathematics, engineering, economics, or disciplines included in the physical or life sciences. (FT) AA/AS; CSU; UC Transfer Limitation: Mathematics (MATH) 116 and 141 combined: maximum credit, one course. Prerequisite: Mathematics 141 with a grade of "C" or better, or equivalent. This course is an introduction to universitylevel calculus requiring a strong background in algebra and trigonometry. The topics of study include analytic geometry, limits, differentiation and integration of algebraic and transcendental functions, and applications of derivatives and integrals. Emphasis is placed on calculus applications involving motion, optimization, graphing, and applications in the physical and life sciences. This course incorporates the use of technology. Analytical reading and problem solving are strongly emphasized in this course. This course is intended for students majoring in mathematics, computer science, physics, chemistry, engineering, or economics. AA/AS; CSU; UC Transfer Limitation; Mathematics (MATH) 121 and 150 combined: maximum credit, one course. Prerequisite: Mathematics 141 with a grade of "C" or better, or equivalent. Corequisite: Mathematics 150. This course is a workshop, project-oriented course dealing with exploration and development of the calculus topics introduced in Calculus and Analytic Geometry I. This course directly supports the calculus lectures by having hands-on, collaborative assignments where technology is strongly incorporated throughout all the in-class assignments. Students work individually and in small groups on explorations and applications thus extending the material presented in Mathematics 150. Topics including geometric, analytic and numeric applications of limits, derivatives and integrals as well as calculus applications found in the physical and life sciences. This course is intended for all students currently enrolled in Mathematics 150. Instructor monitors and facilitates group and individual presentations and projects. (FT) AA/AS; CSU; UC. Prerequisite: Mathematics 150 with a grade of "C" or better, or equivalent. This is the second course in the calculus and analytic geometry sequence. This course covers more advanced topics in analytic geometry, differentiation and integration of algebraic and transcendental functions, infinite series, Taylor series, and parametric equations. This course also covers a general introduction to the theory and applications of power series, techniques of integration, and functions in polar coordinates, as it serves as a basis for multivariable calculus and differential equations, as well as most upper division courses in mathematics and engineering. This course is intended for the transfer student planning to major in mathematics, computer science, physics, chemistry, engineering or economics. (FT) AA/AS; CSU; UC Transfer Limitation: Mathematics (MATH) 122 and 151 combined: maximum credit, one course. Prerequisite: Mathematics 96 with a grade of "C" or better, or equivalent, or Assessment Skill Level M50. Advisory: This course is intended for students enrolled in the first semester Engineering Technology/ Mecomtronics program. This course is the first semester of a four-semester sequence in applied college algebra and trigonometry, and applied technical calculus. Students are expected to apply the mathematical problem solving techniques developed in this course in the real world situations presented and discussed in the program's technology and science courses. Topics include the algebra of functions, graphing algebraic functions, exponential and logarithmic functions, linear systems of equations, matrices and matrix operations, trigonometric functions and their graphs, trigonometric identities, complex numbers, vector algebra, descriptive statistics, an introduction to series and summation notation, an introduction to Boolean algebra and symbolic logic, and the use of the graphing calculator to solve application problems. (FT) AA/AS; CSU. Prerequisite: Mathematics 181 with a grade of "C" or better, or equivalent. Advisory: This course is intended for students enrolled in the second semester Engineering Technology/ Mecomtronics program. This course is the second semester of a four semester sequence in applied college algebra and trigonometry, and applied technical calculus. Students are expected to implement the mathematical problem solving techniques developed in this course in the real world situations presented and discussed in the Mecomtronics technology and science courses. Topics covered are a continuation of those introduced in Mathematics 181. Topics include applications of exponential and logarithmic functions, graphs of trigonometric functions, inverse trigonometric functions, Riemann sums, polynomial approximations of special transcendental functions, vector algebra, spherical and cylindrical coordinates, conic sections, the binomial theorem, an introduction to Boolean algebra and symbolic logic, and the use of the graphing calculator to solve application problems. (FT) AA/AS; CSU. 183 Mecomtronics Calculus I - 3 hours lecture, 3 units (Grade Only) Prerequisite: Mathematics 182 with a grade of "C" or better, or equivalent. Advisory: This course is intended for students enrolled in the third semester Engineering Technology/ Mecomtronics program. This course is the third semester of a four-semester sequence in applied college algebra and trigonometry, and applied technical calculus. Students are expected to implement the mathematical problem solving techniques developed in this course in the real world situations presented and discussed in the Engineering Technology/ Mecomtronics program's technology and science courses. Topics include limits, continuity, differentiation of algebraic and transcendental functions, an introduction to multivariable functions and their partial derivatives, Riemann sums, integration by substitution and by parts, separable and linear first order differential equations, applications in technology and physics, and the use of the graphing calculator to solve application problems. (FT) AA/AS; CSU. Prerequisite: Mathematics 96 with a grade of "C" or better, or equivalent, or Assessment Skill Level M50. Advisory: English 101 with a grade of "C" or better, or equivalent, or Assessment Skill Levels W6 and R6; or English 105 with a grade of "C" or better, or equivalent. This course is a study of the mathematical concepts needed for teaching elementary school mathematics with emphasis on number and function. This course promotes an appreciation of the importance of logical thinking and applications of mathematics in problem solving and critical thinking. It studies the basic computational skills, but also requires the understanding and explanation of the basic mathematical concepts and the connections between them. It is designed especially for students preparing for credentials in elementary education. Analytical reading and problem solving are required for success in this course. (FT) Associate Degree Credit & transfer to CSU and/or private colleges and universities. UC Transfer Limitation: Mathematics (MATH) 210A and 210B combined: maximum credit, one course. Prerequisite: Mathematics 210A with a grade of "C" or better, or equivalent. Advisory: English 101 with a grade of "C" or better, or equivalent, or Assessment Skill Level R6/W6 or English 105 with a grade of "C" or better, or equivalent. This course is the second course in a one-year sequence in the study of the mathematical concepts needed for teaching elementary school mathematics with emphasis on geometry, transformational geometry, and measurement. This course also promotes an appreciation of the importance of logical thinking and applications of mathematics in problem solving and critical thinking. It studies the understanding and explanation of the basic mathematical concepts and the connections between them. It is designed especially for students preparing for credentials in elementary education. Analytical reading and problem solving are required for success in this course. (FT) AA/AS; CSU; UC Transfer Limitation: Mathematics (MATH) 210A and 210B combined: maximum credit, one course. Corequisite: Completion of or concurrent enrollment in: Mathematics 210A with a grade of "C" or better, or equivalent.. Advisory: English 101 or English 105, with a grade of "C" or better, or equivalent, or Assessment Skill Levels W6 and R6. This course focuses on children's mathematical thinking and includes an in-depth study of placevalue, fractions and how children solve mathematical problems. Students observe children and evaluate the problem strategies that are used. This course is intended for students pursuing a Multiple Subject Credential. (FT) AA/AS; CSU. Prerequisite: Mathematics 122 or Mathematics 151, each with a grade of "C" or better, or equivalent. Advisory: English 101 with a grade of "C" or better, or equivalent, or Assessment Skill Level W6 and R6. This course is an introduction to the theory of discrete mathematics and introduces elementary concepts in logic, set theory, number theory, and combinatorics. The topics covered include prepositional and predicate logic, methods of proof, set theory, Boolean algebra, number theory, equivalence and order relations, counting techniques, and recursion. This course forms a basis for upper division courses in mathematics and computer science and it is intended for the transfer student planning to major in these disciplines. (FT) AA/AS; CSU; UC. Prerequisite: Mathematics 151 with a grade of "C" or better, or equivalent. The content of this course includes the algebra and geometry of 2 and 3 dimensional Euclidean vectors, limits, continuity, partial differentiation, extremes of vector-valued and multivariable functions, higher order derivatives, the chain rule, Lagrange's theorem, multiple integrals, integrals over paths and surfaces, and integral theorems of vector analysis. This course is intended as a general introduction to the theory and applications of multivariable calculus. It is essential for most upper division courses in mathematics and forms part of the foundation for engineering and physics. It is intended for the transfer student planning to major in mathematics, physics, engineering, computer science, physical chemistry, operational research, or economics. (FT) AA/AS; CSU; UC. Prerequisite: Mathematics 151 with a grade of "C" or better, or equivalent. This course serves as an introduction to the theory and applications of elementary linear algebra, and is the basis for most upper division courses in mathematics. The topics covered in this course include matrix algebra, Gaussian Elimination, systems of equations, determinants, Euclidean and general vector spaces, linear transformations, orthogonality and inner product spaces, bases of vector spaces, the change of basis theorem, eigenvalues and eigenvectors, the rank and nullity of matrices and of linear transformations. This course is intended for the transfer student planning to major in mathematics, physics, engineering, computer science, operational research, economics, or other sciences. AA/AS; CSU; UC. 255 Differential Equations - 3 hours lecture, 3 units (Grade Only) Prerequisite: Mathematics 252 and Mathematics 254, each with a grade of "C" or better, or equivalent. Limitation on Enrollment: This course is not open to students with credit for Mathematics 253. This course covers first order and higher order equations and their applications. Topics include linear first order and higher order equations, homogeneous and nonhomogeneous equations with constant or variable coefficients, and systems of ordinary differential equations. Methods used to solve equations include substitution methods, integrating factors, reduction of order, variation of parameters, power series solutions, and Laplace Transforms. This course is intended as an introduction to the theory and applications of differential equations and is the basis for many upper division courses in engineering, physics, and mathematics. It is intended for the transfer student planning to major in mathematics, engineering, operational research, physics, or other physical science. (FT) AA/AS; CSU; UC. Limitation on Enrollment: Must obtain an Add Code from instructor for registration. This course is for advanced students who wish to pursue special investigations
Study guide for Differentiation Kia ora, welcome This module is about differential calculus. It will help you revise your knowledge of introductory calculus, learn some new techniques of differentiation, and use derivatives to solve a variety of problems. Read right through this study guide to ensure you know everything you need to do to prepare for different unit and achievement standards. What is in this pack? This pack has this study guide and three booklets: MX704 Learning about differentiation MX705 Developing skills in differentiation MX707 Solving problems using differentiation. How can I learn best? Read through the lessons carefully for understanding and try the steps in the examples yourself to make sure you follow the reasoning. You can help your own learning by self-marking each set of exercises. These are designed to develop your understanding of the key learning concepts and full answers are provided. Have the Formulae and tables booklet you received in the first posting readily available. If you mislay this, contact your teacher. Work through and answer as many questions at a time as you can manage. If you are unsure on the topic, or if the question has a long answer, it is useful to check the first question or two to make sure you are on the right track. There is no point in copying the answers without trying the questions, but if you find you have made an error, correct it and continue the work from that point. MXPDF The Correspondence School 1 A good way to improve your learning, if you have gone astray, is to attempt a question again to make sure that you understand the main points. There are summary points and a review exercise at the end of each booklet. These can help you revise before attempting the assignment or the unit standard assessment task. Because the unit standard task is open book, before starting it is worthwhile to look at the questions and go back through the relevant learning. What if I get stuck? Sometimes reading through the lesson again, or working through a solution in the answer guide is enough, but if you need further help you can  Contact the maths help-desk, week days, 9 am to 4 pm Phone: 0800 835 2788 Fax: 0800 329 2788 Email: maths.helpdesk@tcs.ac.nz  Contact your maths teacher by phone, email or letter. Want to access differentiation online? If you have online access, check out The Correspondence School maths website on differentiation to look at what is recommended for this topic. Links to past examination questions with answers and help with the graphics calculator can be found here, too. There is reference to specific sites in this study guide. The Maths Department website is at Click on School Websites Click on Maths Click on Online courses and support Click on Mathematics with calculus Click on Differentiation The log-in name is parklands and the password is cspark1 (both lowercase) 2 The Correspondence School MXPDF What standards can I gain? You may gain Unit Standard 5265, Differentiate functions and use calculus to solve problems, worth six credits at Level 3. This module will also help you prepare for the external Achievement Standard 90635 (C3.1), Find and use derivatives to solve problems, worth six credits at Level 3. If you gain both of these, they will both appear on your record of learning. However, you will be able to count the credits for only one of these on your NCEA certificate. Preparing for Unit Standard 5265 Ideally, you should complete all the work in this pack. Then you should do the unit standard assessment task in MX707 and send it to your teacher. However, if you are not considering entry for the external achievement standard on differentiation, and you are under time pressure, you can omit any or all of the following: - MX705 lesson 6, review question 9, assignment questions 5, 6 - MX707 lesson 8 and assessment question 8 - the work on graphs of derived functions in this study guide. Preparing for Achievement Standard 90635 Full details of Achievement Standard 90635 from NZQA are given later in this study guide. There is an internal examination at the end of August or the beginning of September that will help you prepare for this standard. Ideally, you should complete all the work in this pack. However, you may be under time pressure or just wanting a taste of the topic. You may be happy to achieve the standard without a merit or excellence grade. To achieve the standard you need to be able to differentiate simple functions including use of the chain rule, product rule and quotient rules and be able to solve straightforward problems using differentiation. This learning is covered in: MX704, MX705 and in MX707 lessons 2 to 7. (For achieved only, you can omit learning to do with points of inflection). Then, practise using review questions 1 to 4 and assignment questions 1, 2, 3, 5, 6 and 7. For achieved with merit, you also need to work with parameters and parametric equations, be able to differentiate implicitly, be able to differentiate functions from first principles, solve more challenging optimisation problems, solve problems involving related rates of change, identify features of graphs, sketch graphs of polynomials and sketch graphs of derived functions. You should do all the work in MXPDF The Correspondence School 3 this pack, as well as the work on sketching graphs of derived functions in this study guide. For achieved with excellence, problems could include among other things, a proof, establishing a model before solving a problem and related rates of change involving more than two related rates. Refer to the standard description attached. How will I be assessed? You can assess your own progress by doing the activities and reviews and marking them yourself. You can achieve the unit standard by doing the unit standard assessment task in MX707. Your teacher will assess this. If you don't achieve it on the first attempt, your teacher will provide you with a further assessment opportunity to do so. Your teacher will also mark the assignment at the end of each booklet. If you are going to sit the external achievement standard at the end of the year, this will help you identify areas in which you need to do extra work. National Qualifications Authority Entry If you are not already enrolled in a secondary school, in July, you will be sent an entry form for national qualifications. If you wish to have the internally or externally assessed standards you achieve recognised on your Record of Learning you will need to enter and pay the entry fee. You will also need to state what externally assessed standards you want to sit examinations in. 90635 Calculus is one of these. Can I use a graphics calculator? Yes you can. The manual that came with your calculator will help you become familiar with its use. If you have a Casio graphics calculator CFX-9750 PLUS let your teacher know as you can be sent help directly relevant to this topic. The same help is on the Mathematics with Calculus website – see above. You must still show the derivatives needed to solve differentiation problems. Graphs of derived functions and on-line learning Find these after the information on the external achievement standard that follows. 4 The Correspondence School MXPDF Subject Reference Calculus 3.1 (90635 Version 2) Title Differentiate functions and use derivatives to solve problems Level 3 Credits 6 Assessment External Subfield Mathematics Domain Calculus Registration date 16 November 2005 Date version published 16 November 2005 This achievement standard involves differentiating functions and using derivatives to solve problems. Achievement Criteria Explanatory Notes  Differentiate functions  Types of functions will be selected from: and use derivatives to  power solve problems.  exponential (base e only)  logarithmic (base e only)  trigonometric (including reciprocal functions).  Differentiation of functions may include the use of the chain rule and product and quotient rules for expanded polynomials: - chain rule with polynomials in expanded form such as i ( x 2  5 x) 7 ii 3 2x  3 Achievement iii 7e 2 x iv ln( 2 x  7) v sin 5x - product and quotient rules for combinations of straightforward functions, at least one of which is in expanded polynomial form, such as i x 2 sin x ii (2 x 3  4)e x 2x iii x3  Problems may include:  optimisation of a given function  rates of change which may involve kinematics  finding equations of normals and tangents  locating maxima and minima of polynomial functions. MXPDF The Correspondence School 5 Achievement Criteria Explanatory Notes  Demonstrate knowledge  Knowledge, concepts and techniques of differentiation of advanced concepts and will be selected from the following types: techniques of  differentiation from first principles of polynomial differentiation and solve functions of degree 3 differentiation problems.  sketching the graph of a derived function from a given graph  differentiation of combinations of functions including: i products, such as (3 x 2  7) 3 (4 x  8) or x 2 sin x x ii quotients, such as 1 x2 Achievement with Merit iii implicit differentiation such as x 2  3 y 2  15 iv parametric differentiation for first derivative only  identifying features of given graphs involving a selection from: i limits ii differentiability iii discontinuity iv gradients v concavity vi turning points vii points of inflection  sketching graphs to demonstrate knowledge of the above features.  Problems may involve:  interpretation of features of graph  modelling of a situation  optimisation  related rates of change, involving two directly related rates.  Solve more complex  Problems may involve: differentiation problem(s).  establishing a model Achievement with  a proof Excellence  testing the nature of turning points and verifying points of inflection  related rates of change involving more that two related rates, eg dh/dt = dh/dθ.dθ/dv.dv/dt  the use of higher derivatives including parametric and implicit differentiation techniques. 6 The Correspondence School MXPDF General explanatory notes 1 This achievement standard is derived from Mathematics in the New Zealand Curriculum, Learning Media, Ministry of Education, 1992:  achievement objectives p. 86  suggested learning experiences pp. 25, 27, 29, 87  sample assessment activities pp. 88–89  mathematical processes pp. 24, 26, 28. 2 The use of appropriate technology is expected but candidates must be able to demonstrate the skill of differentiation. Quality Assurance 1 Providers and Industry Training Organisations must be accredited by the Qualifications Authority before they can register credits from assessment against achievement standards. 2 Accredited providers and Industry Training Organisations assessing against achievement standards must engage with the moderation system that applies to those achievement standards. Accreditation and Moderation Action Plan (AMAP) reference 0226 MXPDF The Correspondence School 7 Online learning activities If you have access to the Internet completing these short activities as you go along will enhance your learning. Answers to activities 1, 2 and 3 are on the next page. Answers to the work on graphs of derived functions are at the end of the study guide. Activity 1 When to do this: Before MX704 on page 12 on finding the gradient of a tangent to y  x2 . What to do:  Select Differentiation – Limits and curves, select the function y  x 2 , (x ^ 2), and arrange the screen so you can see the box beneath the graph.  Move the point Q as far as you can from P and see what happens to the gradient of PQ (the secant) as it gets closer and closer to P from either direction. Questions to answer:  Why is the gradient of the secant undefined when it becomes a tangent at P?  Is the gradient of the tangent at P, given as 12, what you would have expected from what you observed as Q approaches P from above and below? Activity 2 When to do this: Before MX704 lesson 3 on finding a formula for gradients of tangents. What to do:  Select Differentiation – Differentiation from first principles. When you get to this interactive activity, use the "helping hand" to explain what you need to do to complete the activity. Questions to answer:  What is the gradient of the tangent to y  x 2 where x = 1?  What is the gradient of the tangent to y  x 2 where x = 2?  Write down a formula for finding the gradient of a tangent to a curve from first principles. 8 The Correspondence School MXPDF Activity 3 When to do this: After MX704 Exercise 5A on a quicker way of finding f (x) . If you are already proficient at techniques of differentiation from your work in year 12, you can omit this. What to do:  Select Differentiation – Leibnitz notation and polynomial differentiation. There are two click and drag activities to help with differentiating expressions with negative powers and other expressions. Questions to answer: 1  If f ( x)  , what is f (x) ? x  If f ( x)  ( x  3)(x  2) , what is f (x) ? Answers to Activities 1, 2 and 3 Activity 1  The gradient of the secant given on the graph when it becomes a tangent at P is undefined because the denominator of the fraction that the gradient of the secant is being calculated from is zero at P. y  y1 m 2 is undefined when the denominator is zero. x 2  x1  The closer Q gets to P, the closer the gradient of the secant is to 12. So even though the gradient of the secant is undefined at P, it is expected that the gradient of the tangent at P is 12. Activity 2  The gradient of the tangent to y  x 2 when x = 1 is 2  The gradient of the tangent to y  x 2 when x = 2 is 4  A formula for finding the gradient of a tangent to a curve from first principles is on page 18 of MX704. Return to MX704 page 16 to practice using the formula. Activity 3 f ( x)  1x 2 f ( x)  2 x  1 … (expand brackets before differentiating) MXPDF The Correspondence School 9 Sketching graphs of derived functions Complete this work at any time after completing MX707 if you are entering for the external standard 90635 Calculus. This work is now a requirement of the standard for Merit. Activity 4 If you have access to the Internet, go to Differentiation – The meaning of the derivative and work through this 'click and drag' activity that explains how the graph of the derived function of y  x 2 is obtained. Then go to question 1 below. Activity 5 Look at the graphs of y  x 2 and its derived function drawn below each other. Using these graphs and your knowledge of differentiating functions, which of the following statements do you think are correct?  The derived function of a parabola is a line.  Stationary points on f (x) (maximum or minimum) become x intercepts on10 The Correspondence School MXPDF Activity 5 Go to Differentiation – Graphs and derivatives and watch the short slide show that shows what happens to points at maximum and minimum values of a function when the gradient function is drawn. Then go to Question 2 below. Activity 7 Above is part of a cubic curve with its derived function (the parabola) drawn as a dy dotted line on the same axes. (For this, the vertical axis is the axis). Using these graphs and dx your knowledge of differentiating functions, which of the following statements do you think are correct?MXPDF The Correspondence School 11 In questions 1 and 2 all of the bullet points are correct. The information about graphs of derived functions is summarised below. There are several bullet points added for the sake of completion. You will be able to verify these for yourself as you complete the following activities. Features of graphs of derived functions Stationary points of inflection on f (x) become turning points on the x-axis Points of inflection on f (x) become turning points of f (x) .  If there is a discontinuity or spike or abrupt change in slope on f (x) , f (x) is undefined.  Vertical asymptotes on f (x) stay vertical asymptotes on f (x) .  Horizontal asymptotes on f (x) stay horizontal asymptotes on . f (x)  At a spike, an abrupt change in slope or a discontinuity, f (x) is undefined. A summary of graph shapes will help, too. Graph of f (x) Graph of f (x) quartic cubic cubic parabola parabola line Line gradient m Horizontal line through m More detail about graph shapes, extrapolating from the bullets above – Graph of f (x) Graph of f (x) Quartic going up first Cubic going down first Quartic going down first Cubic going up first Cubic going up first Parabola going down first Cubic going down first Parabola going up first Parabola going up first (inverted) Line going down (negative gradient) Parabola going down first (cup shaped) Line going up (positive gradient) Line with gradient m Horizontal line through m Line with gradient 0 Line along the x axis 12 The Correspondence School MXPDF Activity 8 Go to Differentiation – Practice sketching derived functions. There is a lot of 'click and drag' practice here where you will choose pairs of graphs and their derived functions. Practise until you feel familiar with most of the features summarised. Remember that you may be asked to draw the graph of a derived function from a given graph and not just select an appropriate function from a list, so do try to do this as well and use the click and drag function to check your answers. Question 1 For each of the following, sketch the graphs of the derived functions. It is best to sketch the derived functions below the graph of their functions as in question 1 above. The answers have them on the same axes, however, as in question 2 above. (a) (b) (c) (d) MXPDF The Correspondence School 13 (e) (f) (g) (h) (i) (j) (k) 14 The Correspondence School MXPDF Answers to Question 1 dy The derived functions are dotted on each graph and for these the vertical axis label is . dx (a) (b) (c) (d) MXPDF The Correspondence School 15 (e) (f) (g) (h) (i) dy The graph of  e x is the dx same as the graph of y  e x . (j) (k) 16 The Correspondence School MXPDF MXPDF The Correspondence School
CASE STUDY #4 Quantitative Education for Biologists University of Tennessee This course sequence provides an introduction to a variety of mathematical topics of use in analyzing problems arising in the biological sciences. It is designed for students in biology, agriculture, forestry, wildlife, and premedicine and other prehealth professions. The general aim of the sequence is to show how mathematical and analytical tools may be used to explore and explain a wide variety of biological phenomena that are not easily understood with verbal reasoning alone. Prerequisites are two years of high school algebra, one year of geometry, and half a year of trigonometry. The goals of the course are to develop the students' ability to quantitatively analyze problems arising in their own work in biology, to illustrate the great utility of mathematical models to provide answers to key biological problems, and to provide experience using computer software to analyze data and investigate mathematical models. This is accomplished by encouraging hypothesis formulation and testing and the investigation of real-world biological problems through the use of data. Another goal is to reduce rote memorization of mathematical formulae and rules through the use of software including Matlab and MicroCalc. Students can be encouraged to investigate biological areas of particular interest to them using a variety of quantitative software from a diversity of biological specialties. In many respects, this course is more difficult than the university's science/engineering calculus sequence (Math 141-142) since it covers a wider variety of mathematical topics, is coupled to real data, and involves the use of the computer. Although the course is challenging, it has been designed specifically for life science students, and includes many more biological examples than other mathematics courses. It, therefore, introduces the students to quantitative concepts not covered in these other math courses that they should find useful in their biology courses. The main text is Mathematics for the Biosciences by Michael Cullen, which is extensively supplemented by material provided in class. Each class session begins with the students generating one or more hypotheses regarding a biological or mathematical topic germane to that day's material. For example, students go outdoors to collect leaf size data. They are then asked: Are leaf width and length related? Is the relationship the same for all tree species? What affects leaf sizes? Why do some trees have larger leaves
With more and more physicists and physics students exploring the possibility of utilizing their advanced math skills for a career in the finance industry, this much-needed book quickly introduces them to fundamental and advanced finance principles and methods. Quantitative Finance for Physicists provides a short, straightforward introduction for... more... Talks about the provision of workplace learning and about employing learning as a critical weapon in the fight for an organisation's success. This book explores the arguments necessary to implement a learning architecture, and the competencies and responsibilities required of the 'learning architect' to create this environment. more... Incorporates the many tools needed for modeling and pricing in finance and insurance Introductory Stochastic Analysis for Finance and Insurance introduces readers to the topics needed to master and use basic stochastic analysis techniques for mathematical finance. The author presents the theories of stochastic processes and stochastic calculus and... more... Your guide to a higher score on the Florida Real Estate Sales Associate Exam * Why CliffsTestPrep Guides? * Go with the name you know and trust * Get the information you need--fast! * Written by test-prep specialists About the contents: * Introduction * How to use this book to hone your test-taking skills * Tactics for answering math questions... more... IF YOU WANT: a. Fast, more efficient prep for the new GMAT b. Secret strategies of test-prep professionals c. Ways to score in the high 600s or better d. Addmission to a top-ranked business school e. All of the above THEN YOU NEED: McGRAW-HILL'S GMAT* Before you apply to today's top business schools, you need to develop... more... STUDENTS:. This book is packed with exclusive rankings of America's top undergrad business programs. It tells you what's up, who's down, and which schools are best for you. PARENTS:. This book tells you how much it costs-and if it's all worth it. Based on BusinessWeek 's famous rating system, this at-a-glance guide will save you... more... Want to get an MBA? The Complete MBA For Dummies, 2 nd Edition, is the practical, plain-English guide that covers all the basics of a top-notch MBA program, helping you to navigate today's most innovative business strategies. From management to entrepreneurship to strategic planning, you'll understand the hottest trends and get the... more... MBA IN A BOOK offers the kind of information graduates of MBA programs ought to have, but usually gain only after years of hard-won experience. This volume contains essential advice about the fundamentals of business, sales, and leadership from some of history's most influential thinkers and doers: entepreneurs, executives, scholars, statesmen, and... more...
Most of the available literature in wireless networking and mobile computing concentrates on the physical aspect of the subject, such as spectrum management and cell re-use. In most cases, a description of fundamental distributed algorithms that support mobile hosts in a wireless environment is either not included or is only briefly discussed. Handbook... more... Technological improvements continue to push back the frontier of processor speed in modern computers. Unfortunately, the computational intensity demanded by modern research problems grows even faster. Parallel computing has emerged as the most successful bridge to this computational gap, and many popular solutions have emerged based on its concepts,... more... A feature of modern advanced computing is the functional approach to programming. In this book, the authors present an introduction to the mathematics which underline functional programming, emphasizing the understanding of definition and specification--a prerequisite of good programming and problem solving with a computer. The book is self-contained,... more... The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners. * Focuses on the most often used features of... more... Mathematica by Example, 4e is designed to introduce the Mathematica programming language to a wide audience. This is the ideal text for all scientific students, researchers, and programmers wishing to learn or deepen their understanding of Mathematica. The program is used to help professionals, researchers, scientists, students and instructors solve... more... ... more... It is an appropriate reference for the newly released Maple 9.5, however the book is backwards compatible for all previous versions. It is particularly useful for beginning users like students, instructors, engineers, and other professionals. The book introduces the very basic commands and includes typical examples of applications. In addition, the... more... Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical... more... Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. All disc-based content... more... This work reports critical analyses on complexity issues in the continuum setting and on generalization to new examples, which are two basic milestones in learning from examples in connectionist models. It also covers up-to-date developments in computational mathematics. more...
This is an excellent, complete K-12 curriculum for every home school. The only addition needed is Saxon math books. Saxon books are available to RC users at a 20% discount through the Oregon Institute of Science and Medicine, publisher of this curriculum. Everything else comes in the case of 22 CDs. The delivered price of $195 is astonishingly low. Although the curriculum is usable on the computer screen, it is better for the student for the materials to be printed out with the printing software provided with the curriculum. Use of this curriculum has expanded to about 60,000 children, largely through word-of-mouth recommendations from users because it produces such great results, even though parent involvement is minimal. Developed by a scientist and his six children and their scientist friends and coworkers, the first beneficiaries of this curriculum were the Robinson children themselves. Two of these have finished college, three are in college, and one is still at home. The records of the two who have finished college, so far, are remarkable. Both Zachary and Noah Robinson completed university BS degrees in chemistry in only two years and then went on to postgraduate school. Zachary then earned a MS degree in chemistry and a doctorate in veterinary medicine at Iowa State University. His younger brother Noah, completed a doctorate in chemistry at the California Institute of Technology in only three years. Both of these young men used solely the Robinson Curriculum for their home educations and both helped to develop it. In this curriculum, mathematics is taught by a special self-teaching method developed for the curriculum. The method utilizes Saxon math books, but can be adapted to other math books if desired. Students begin self-taught math in the second year. This method is so effective, that students who follow it correctly often finish math through calculus between ages 14 and 16. As the student learns sufficient math skills, science is introduced. Robinson curriculum science is based upon chemistry and physics books provided on the CDs. These books were developed for freshman students at Caltech and written by Caltech professors. Once the basics of chemistry and physics are mastered, the lesser sciences are easy. Biology is not formally studied because modern biology is primarily just a special branch of chemistry. Some biology is covered in the chemistry book. Zachary and Noah, for example, obtained advanced placement in university biology by simply reading a biology book before the Advanced Placement exam. With a sound foundation in physics and chemistry, the biology was simple to master. The math and science program, with its included special learning methods, is a very effective means of teaching analytical thinking skills. Students using this method are found to perform much better in many other mental activities. An emphasis on thorough mastery of basic skills is the hallmark of this curriculum. The Robinson curriculum only requires about 4 to 5 hours per day of study. Those hours are packed with basic knowledge. The remaining hours of the day are free for less basic activities, hobbies, and recreation. There is no "pretend" to this curriculum. Science is taught only when the students have the necessary basic math skills. Prior to that, the students carry out science-type activities in their recreational time. Reading is taught by phonics, for which basic phonogram flash cards and appropriate beginning books are included. After that, the student reads a carefully designed progression of books throughout the 12 years. Each book introduces new vocabulary. Reading each book and using vocabulary flash cards keyed to that book teaches this vocabulary. The student also works special vocabulary exercises keyed to each book. The vocabulary system includes 6,400 words that should be actively used by all well-educated adults. Again, there is no pretend teaching. Most students, even very brilliant ones, require the full 12 years to master reading, writing, vocabulary, and spelling of the English language. The Robinson curriculum provides a wealth of tools for this purpose in a carefully structured program. The learning of languages other than English is left for extracurricular time. Most students can master English skills by reading and writing, which are heavily emphasized in this curriculum. They learn, by example, the skills of the great authors they are reading. Some students, however, need more. For these students, the Robinson curriculum contains outstanding grammar and spelling books written exclusively for the curriculum by Dr. Jane Orient. Her grammar and spelling books are so good that students who do not need this special help may still enjoy reading them. History is emphasized in the reading program, with special emphasis on the autobiographies of great historical figures. Other books, especially the works of G. A. Henty, augment these. All of G. A. Henty's 99 remarkable historical novels are available on CD or in soft cover or hardcover versions as additions to the curriculum. These books and CDs have been published by the Oregon Institute of Science and Medicine. As a Robinson student makes his way around the world as a vicarious participant in world historical events as seen through the eyes of those who made those events or the eyes of a Henty hero, he learns geography, social customs, and the ways of life of people throughout the world and throughout history. Learned in this way, the historical events and their settings become fixed in the student's mind so that he remembers and benefits from them. This is far superior to the usual dry factual teaching methods. The literature program in the Robinson curriculum is unequalled by any other curriculum source. It is based entirely upon reading and study of the best books in the English language. Even though this curriculum has been available for many years and does not have the luster of a "new" product, the readers of Practical Homeschooling magazine recently rated the Robinson curriculum First Place in literature for 2004. Overly politically correct critics demand that some of the world's greatest authors be censored because they express views or use terms that these critics oppose. The Robinson curriculum does not do this. For example, some critics demand that Mark Twain's Huckleberry Finn be banned, even though this is considered to be the greatest novel ever written by an American. They claim it contains racist material. In fact, Huckleberry Finn is one of the most brilliant condemnations of racism ever written. The Robinson curriculum includes Huckleberry Finn. In its study of history, too, the Robinson curriculum uses the best sources. Reading the autobiographies of U. S. Grant and W. T Sherman and the writings of President Lincoln on the Union side and the autobiographies of J. Davis and A. Stevens, the president and vice president of the confederacy on the Confederate side covers the American civil war. These men led the fighting of this war. Their writings are far superior to ordinary history books. Additional books about this conflict are also included. Robinson students write every day, after the age of 10 years. Writing can be introduced earlier, but most students are not ready to routinely organize their thoughts in written words before age 10. Writing is preceded by exercises that teach printing and cursive writing skills. At age 10, the student writes one page each day and proceeds from there. The writing lessons are the only part of this program that is not self-taught. Parents must read the student's writing each day and mark any errors in spelling, grammar, and punctuation. It is a well-established fact that children who learn to think and master the basic skills of reading, writing, and mathematics and science perform well in other undertakings such as art and music. Many great scientists, for example, have been excellent musicians. A student who follows the Robinson curriculum is more thoughtful and more skilled in his extracurricular activities. All six of the Robinson children, for example, play the piano and two have gone on to become excellent organists, even though they initially showed no special music skills. This curriculum emphasizes reading, writing, and arithmetic, and it also includes an outstanding education in science, literature, history, and the English language. It is being used successfully by tens of thousands of children. Users of the curriculum are 99% complimentary and delighted with its results. The occasional exception usually involves a student or parent who does not actually follow the curriculum course of study. The Robinson curriculum does have critics. These include primarily people who sell competing products and people with other educational philosophies who have never used the Robinson curriculum. The home school market contains a great many fine products that are making the home school revolution in America possible. The Robinson curriculum is an outstanding example.
This book aims to give a thorough grounding in the mathematical tools necessary for research in acoustics. Twelve authors, all highly-respected researchers in the field of acoustics, provide a comprehensive introduction to mathematical analysis and its applications in acoustics, through material developed for a summer school in mathematics for acoustics
More About This Textbook Overview A classic book is back in print! It can be used as a supplement in a Calculus course, or a History of Mathematics course. The first half of Calculus Gems entitles, Brief Lives is a biographical history of mathematics from the earliest times to the late nineteenth century. The author shows that Science-and mathematics in particular-is something that people do, and not merely a mass of observed data and abstract theory. He demonstrates the profound connections that join mathematics to the history of philosophy and also to the broader intellectual and social history of Western civilization. The second half of the book contains nuggets that Simmons has collected from number theory, geometry, science, etc., which he has used in his mathematics classes. G.H. Hardy once said, "A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." This part of the book contains a wide variety of these patterns, arranged in an order roughly corresponding to the order of the ideas in most calculus courses. Some of the sections even have a few problems. Professor Simmons tells us in the Preface of Calculus Gems: "I hold the naïve but logically impeccable view that there are only two kinds of students in our colleges and universities, those who are attracted to mathematics; and those who are not yet attracted, but might be. My intended audience embraces both types. The overall aim of the book is to answer the question, "What is mathematics for? and with its inevitable answer, To delight the mind and help us understand the world." Product Details Related Subjects Read an Excerpt On coming to the end of my work on this book and thinking again about its nature and purpose, I am reminded of W.H. Fowler's Preface to his great Modern English Usage: "I think of it as it should have been, with its prolixities docked, and its dullnesses enlivened, its fads eliminated, its truths multiplied." And also of W.H. Auden's rueful admission: "A poem is never finished, only abandoned." Some readers will recognize that this book had been reconstructed out of two massive appendices in my 1985 calculus book, with many additions, rearrangements and minor adjustments. Its direct practical purpose is to provide auxiliary material for students taking calculus courses, or perhaps courses on the history of mathematics. There have been a number of requests that this material be made separately available, and I have been happy to take advantage of this occasion to fill in some gaps and reconsider my opinions. I had a friend who said to me once, "I should probably spend about an hour a week revising my opinions." I treasure the remark and value the opportunity to act upon it. My overall aims are bound up with the question, "What is mathematics for?" and with its inevitable answer, "To delight the mind and help us understand the world." I hold the naïve but logically impeccable view that there are only two kinds of students in our colleges and universities: those who are attracted to mathematics; and those who are not yet attracted, but might be. My intended audience embraces both types. Part A. This half of the book, entitled Brief Lives, amounts to a biographical history of mathematics from the earliest times to the late nineteenth century. It has two main purposes. First, I hope in this way to "humanize" the subject, to make it transparently clear that great human beings created it by great efforts of genius, and thereby to increase students' interest in what they are studying. Science-and in particular mathematics-is something that men and women do, and not merely a mass of observed data and abstract theory. The minds of most people turn away from problems-veer off, draw back, avoid contact, change the subject, think of something else at all costs. The people-the great majority of the human race-find solace and comfort in the known and the familiar, and avoid the unknown and unfamiliar as they would deserts and jungles. It is hard for them to think steadily about a difficult problem as it is to hold together the north poles of two strong magnets. In contrast to this, a tiny minority of men and women are drawn irresistibly to problems: their minds embrace them lovably and wrestle with them tirelessly until they yield their secrets. It is those who have taught the rest of us most of what we know and can do, from the wheel and the lever to metallurgy and the theory of relativity. I have written about some of these people from our past in the hope of encouraging a few in the next generation. My second purpose is connected with the fact that many students from the humanities and social sciences are compelled against their will to study calculus as a means of satisfying academic requirements. The profound connections that join mathematics to the history of philosophy, and also to the broader intellectual and social history of Western civilization, are often capable of arousing the passionate interest of these otherwise indifferent students. Part B. In teaching calculus over a period of many years, I have collected a considerable number of miscellaneous topics from number theory, geometry, science, etc., which I have used for the purpose of opening doors and forging links with other subjects - and also for breaking the routing and lifting the spirits. Many of my students have found these "nuggets" interesting and eye-opening. I have collected most of these topics in this part in the hope of making a few more converts to the view that mathematics, while sometimes rather dull and routine, can often be supremely interesting. The English mathematician G.H. Hardy said, "A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.: Part B of this book contains a wide variety of these patterns, arranged in an order roughly corresponding to the order of the ideas in most calculus courses. Some of the sections even have a few problems, to give additional focus to the efforts of students who may read them: Sections A.14., B.1., B.2, B.16, B.21, B.25. I repeat the fervent hope I have expressed in other books, that any readers who detect flaws or errors of fact or judgment will do me the great kindness of letting me know so that repairs can be
9780131107342Math for Merchandising: A Step-by-Step Approach (3rd Edition) This book takes users step by step through the concepts of merchandising math. It is organized so that the chapters parallel a career path in the merchandising industry. The book begins with coverage of fundamental math concepts used in merchandising and progresses through the forms and math skills needed to buy, price, and re-price merchandise. Next readers learn the basics of creating and analyzing six-month plans. The final section of the book introduces math and merchandising concepts that are typically used at the corporate level. For individuals pursuing a career in merchandising.
integralCALCCourse Description Need some tips for Calculus 1A? Or maybe you're madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way. Lessons in this Course 1. Functions vs. Equations 5:22 2. How to Use the Vertical Line Test 2:58 3. Limits and Continuity 6:26 4. Prove the Limit Doesn't Exist \| Example 5:37 5. Precise Definition of a Limit \| Example 9:19 6. Derivatives 6:53 7. Definition of the Derivative \| Example 3:43 8. Equation of the Tangent Line \| Example 16:49 9. Implicit Differentiation \| Example 9:35 10. Optimization 8:55 11. Related Rates 8:16 What is included in the course? All of the video-based lessons listed on the Course Description tab, including interactive exercises and attached files you can use along with the lesson. You also can ask the teacher (and other students) questions, and submit a video or photo of your work to get direct feedback from the teacher. What is Curious.com? Curious.com is a site that enables teachers like integralCALC to make money by teaching online to students around the world. Where does my money go? Most of the money goes directly to the teacher. The rest goes to Curious for the hardware and software and human support required to make the delivery of this awesome course possible. How do I access the course when I want to learn? You can access the course, and any other Curious lessons you have enrolled in, by logging into on your computer or tablet. You will be prompted to create an account when you purchase the course if you don't have one already. How long do I have access to the course? For life. Really. What if I don't learn, or don't like it? We are confident you will love this course--like literally thousands of others before you--but if you don't for any reason we will be happy to refund your money and disable your access to it. Jordyn T comment: When I simplify 10=4pi(7.5)^2(dr/dt) I get 10/225pi = (dr/dt), not 10/217pi = (dr/dt). What have I done wrong? Jordyn T comment: It's okay! Keep at it. I look forward to future lessons, if they're in the works. integralCALC comment: they are! :) if you ever need more videos, i have hundreds on my website: integralCALC.com. :) Jordyn T comment: Oh, thanks. I'm ashamed to say I wasn't aware that you did things outside of this website. I just stumbled across your YouTube. Combined with Khan Academy, I should be a calc genius in no time! integralCALC comment: Yup I have a bunch more on YouTube and my website integralcalc.com. :) Glad I can help! integralCALC comment: You haven't! You're right, it should be 225, not 217. Sorry about that, and good catch!! :D Students in this lesson (92) About the TeacherTable of Contents 1. Lesson Intro 0:36 2. Implicit Differentiation 1:21 3. Example: Implicit Differentiation 1:19 4. Related Rates 0:34 5. Related Rates Example: Spherical Balloon 2:08 6. Related Rates Example: Leaning Ladder 1:57 7. Wrapping Up 0:19 Lesson Description One of the most difficult and most common applications of derivatives is the related rates problem. But related rates don't have to be hard! In this lesson from integralCALC, Krista gives you the tools to conquer these problems. Implicit differentiation is the key to learning how to deal with an equation when there is no clean separation of the unknown variables—once you've got that down, you'll be able to solve any related rates problem in just four easy steps.
Product Synopsis This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject
has been widely adopted for its comprehensive coverage, exceptionally clear explanations of difficult material, and avoidance of nonessential math. The text bridges the gap between the theory and practice of derivatives and helps readers develop a working knowledge of how derivatives can be analyzed.
Cliffs Quick Review for Geometry - 01 edition Summary: When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core geometry concepts -- from perimeter, area, and similarity to parallel lines, geometric solids, and coordinate geometry -- and get the best possible grade. At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented wri...show moreters who know how to cut to the chase -- and zero in on the essential information you need to succeed. ...show less Ed Kohn, MS is an outstanding educator and author with over 33 years experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at Sherman Oaks Center for Enriched Studies.Shopbookaholic Wichita, KS 2001 ship ped the same day or the next day. This is a used book, in good condition, that ma...show morey show some signs of use or wear. ...show less $2.00 +$3.99 s/h Good AGood_Book TX Waco, TX 2001 Paperback Good May have slight wear to covers, spine, and/or cover is slightly creased. There is no underlining/highlighting of text or notations
This collection is included inLens:Connexions Featured Content By: Connexions Comments: "This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in Function Game: Introduction Summary: This module provides an introduction and explanation of the function game. Each group has three people. Designate one person as the "Leader" and one person as the "Recorder." (These roles will rotate through all three people.) At any given time, the Leader is looking at a sheet with a list of "functions," or formulas; the Recorder is looking at the answer sheet. Here's how it works. One of the two players who is not the Leader says a number. The Leader does the formula (silently), comes up with another number, and says it. The Recorder writes down both numbers, in parentheses, separated by a comma. (Like a point.) The Recorder now writes down the formula—not in words, but as an algebraic function. Then, move on to the next function. Sound confusing? It's actually pretty easy. Suppose the first formula was "Add five." One player says "4" and the Leader says "9". One player says "-2" and the Leader says "3". One player says "0" and the Leader says "5". One player says "You're adding five" and the Leader says "Correct." At this point, the Recorder has written down the following: Sometimes there is no possible answer for a particular number. For instance, your function is "take the square root" and someone gives you "–4." Well, you can't take the square root of a negative number: –4 is not in your domain, meaning the set of numbers you are allowed to work on. So you respond that "–4 is not in my domain." Leader, do not ever give away the answer!!! But everyone, feel free to ask the teacher if you need help
Computational Geometry Mathematica's strengths in algebraic computation and graphics as well as numerics combine to bring unprecedented flexibility and power to geometric computation. Making extensive use of original algorithms developed at Wolfram Research, Mathematica's ability to represent and manipulate geometry symbolically allows it for the first time to fully integrate generation, analysis, and rendering of geometrical structures.
. Abstract: Features an explanation of modern graph theory. This title presents graph theory from an algorithmic point of view, allowing for a variety of technical applications. It includes useful programming techniques to solve graph theory problems, and applicable data structures to show how algorithms can be programmed.Read more... Reviews Editorial reviews Publisher Synopsis "The book is written in an easygoing style, and the proofs are concisely presented and easy to follow. [This book] would serve as a fine textbook for an undergraduate graph theory course for math majors. [I]t is well-written, the proofs are easy to follow, the figures complement the text, and the exercises are helpful to student understanding" - MAA Online "A valuable resource for mathematics and computer science students and professionalscontains a wealth of information on algorithms and the data structures needed to program them efficientlythe graph theory presented is rigorous, but the style is informal." - L'Enseignement MathimatiqueRead more... ""."

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.