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Math Lab What is the Math Lab? The purpose of the Math lab is to aid students in developing their mathematical abilities. The lab is staffed by a director and several student tutors who are available to help students in their calculus and statistic courses. Instruction in the Math Lab is very informal. Students are welcome to come to the lab with questions whenever they need help in understanding math course work. The lab has a Hewlett Packard workstation which students may use. Our goal in the lab is to increase each student's understanding of her or his course material. This takes time and active participation on the student's part. Please do not expect the lab to provide quick answers for the purpose of completing homework assignments. This does you a disservice. If we can help you understand the material so you can complete your assignment, we will be glad to do so. Many of the math professors are now assigning special problem sets from The Real Calculus Problems. Since these problems are graded by the professors and count substantially in a student's final grade, the lab does not routinely give assistance on these problems. Instead we have set up special problem-solving sessions with tutors who have been trained by the professors to give appropriate help on these special problem sets. Director Jim Lawrence is Director of the Math Lab. He sees students by appointment. If you would like an appointment or if you have other questions, stop in the lab or call x3060.
Hi, This morning I started working on my math assignment on the topic Intermediate algebra. I am currently not able to finish the same because I am not familiar with the basics of factoring polynomials, trigonometric functions and long division. Would it be possible for anyone to aid me with this? How about some more details about your trouble with tips on college algebra? I might be able to give some leads. If you are not able to get a good help or some one to sit and sort out your problem or if it is not affordable, then there might be another solution to your problem. There are some good math software that you can check out. I tried them out myself. It came across to me as good as any tutor can be. I would select Algebra Buster for the kind of solutions that you are in the hunt for. What is smart about it is that it takes you step by step to the solutions rather than simply providing the answer. Why not try it out? It would really be nice if you could let us know about a tool that can provide both. If you could get us a home tutoring software that would offer a step-by-step solution to our assignment, it would really be great. Please let us know the authentic websites from where we can get the tool. I remember having often faced difficulties with parallel lines, difference of squares and algebraic signs. A truly great piece of math program is Algebra Buster software. By simply typing in a problem homework a step by step solution would appear by a click on Solve. I have used it through many algebra classes – Pre Algebra, College Algebra and Algebra 1. I greatly recommend the program.
feedback. Prerequisites: High school calculus
Rent Textbook Buy New Textbook Used Textbook We're Sorry Sold Out eTextbook We're Sorry Not Available More New and Used from Private Sellers Starting at $18917Videos on DVD with Optional Captioning for Prealgebra and Introductory Algebra Worksheets for Classroom or Lab Practice for Prealgebra and Introductory Algebra Summary The Lial Serieshas helped thousands of students succeed in developmental mathematics by providing the best learning and teaching support to students and instructors. Author Biography Marge Lial became interested in math at an early age–it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology; trips to various digs and ruin sites produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. We dedicate the new editions of the paperback developmental math series to Marge in honor of her contributions to the field in which she helped thousands of students succeed. Stan Salzman is a long time resident of Sacramento, California. Stan has taught at American River College for many years, where he was a member of the business department. He is the author of Business Math and Essential Math, published by Pearson Education, Inc., and is coauthor of Basic Math. Diana Hestwood lives in Minnesota and has taught at Metropolitan Community College in Minneapolis for two decades. She has done research on the student brain and is an expert on study skills. She is the author of Lial/Hestwood's Prealgebra and coauthor of Lial/Salzman/Hestwood's Basic Math and Lial/Hestwood/Hornsby/McGinnis's Prealgebra and Introductory Algebra.
MATH 1271 Liberal Education: This course fulfills the Mathematical Thinking component of the Liberal Education requirements at the University of Minnesota. An important part of any liberal education is learning to use abstract thinking and symbolic language to solve practical problems. Calculus is one of the pillars of modern mathematical thought, and has diverse applications essential to our complex world. In this course, students will be exposed to theoretical concepts at the heart of calculus and to numerous examples of real-world applications. This message is mandated by your friendly administration bureaucracy. Go Gophers
MAA Review [Reviewed by Robert Talbert, on 05/21/2008] Out of all the topics treated by an introductory abstract algebra course, it is the subject of fields — especially finite fields — that enjoys perhaps the brightest spotlight in terms of real-world applications, as well as some of the most interesting theory. This book is an ingenious treatment of finite fields in which both the theory and three general areas of application are presented both with appropriate depth and intriguing breadth, with a commendable amount of interconnections between them and all contained in a very compact volume. The first chapter of the book is an extensive treatment of the theory of finite fields and polynomials over finite fields. The first half of the chapter studies the structure of finite fields, focusing on finite fields as vector spaces and bases for those vector spaces. The second half of the chapter deals with polynomials over finite fields and gives many interesting results that one does not normally find in the typical undergraduate algebra text. Chapter 1 assumes that the reader has experience with groups, rings, and fields equivalent to what one might obtain in a two-semester, or thorough one-semester, course in abstract algebra. Since not all interested readers have that background, the book contains an appendix that serves as a crash course in abstract algebra. This appendix is quite amazing in the way it develops just enough algebra — no more, no less — to learn from the rest of the book. Most readers of this book would do well to start with this appendix, regardless of their background. Following the introductory chapter, the book proceeds through three main areas of application: combinatorics, algebraic coding theory, and cryptography. The combinatorics chapter centers around the study of Latin squares, a concept familiar with anybody who has ever done a Sudoku puzzle and which has a number of real-world applications. The coding theory chapter develops all the concepts using the material in Chapter 1 and ending with a nice connection between codes and Latin squares. Finally, the cryptography chapter, after motivating the ideas behind basic cryptographic primitives, gives examples of cryptosystems which use finite fields. The treatment includes an overview of the AES cryptosystem, an interesting system based on mutually orthogonal Latin squares (again, making a nice connection between the applications in the book), a public-key system based on quadratic polynomials over a finite field, and ending with a brief treatment of key-exchange protocols, the discrete logarithm, and elliptic curve cryptography. I enjoyed the way in which this book manages both breadth and depth in a relatively small amount of pages. It is amazing how far one can go with finite fields, in both theory and applications, if one knows just the basics of abstract algebra. And all the algebra basics are contained in the book in a highly streamlined way (the proof of Lagrange's Theorem, for example, does not invoke cosets or quotient groups at all). I think this book would make an excellent sourcebook for either a second-semester course in algebra or an independent study for students who have completed a one-semester course in algebra. I appreciated, too, the ways in which the authors weave the applications together, using Latin squares not only as a subject of study unto itself but also as a recurring example in both coding theory and cryptography. Another strength of this book is the relative independence of the three application chapters. So, for example, a reader wanting to undertake a study of coding theory can cover the appendix, parts of chapter 1, and then the coding theory chapter without needing the other two chapters — but proceeding to the other two chapters if the connections provided by the authors prove intriguing enough. Indeed, I can see the book being used primarily in this way, covering the theory and then studying one or two of the applications. However, perhaps the main weakness of this book is that the theory in Chapter 1 goes deep — very deep — but the full depth is not always necessary for subsequent chapters, and it is not made clear to the reader just how much theory from Chapter 1 is really necessary for subsequent topics. Indeed, it seemed to me that some of the application chapters only use a fraction of the material in Chapter 1, although a reader would think she would have to get through it all in order to make it to Chapter 2. I worry that an an inexperienced reader would get bogged down in Chapter 1 and lose interest before making it to the applications. In future editions, my hope is that Chapter 1 might be split into two or three separate chapters of increasing theoretical depth and that there be some kind of chart indicating how much theory is needed to undertake an application. Professors using this book for an undergraduate course might need to do this themselves for now. The text tends to be somewhat light on examples which can serve as touchstones for students who might struggle with the abstraction. The cryptography chapter, in particular, would benefit from a few worked-out examples of the cryptosystems in use; AES gets especially short shrift, as there are no meaningful specifics given about that important cryptosystem at all. The authors have done a commendable job of using a unifying concept — the Latin square — throughout the second half of the book to provide cohesion among the applications. The book would benefit just as much from having unifying examples of concepts throughout individual chapters to make things more concrete. Overall, with the caveats given above, this is a well-written and wide-ranging book on a subject that doesn't usually get the level of treatment it deserves in a typical undergraduate course. Advanced students, and even professional mathematicians, will find this book to be an engaging and full-bodied tour of finite fields. Other readers will also find it to be well-written, and should find the applications interesting and well-chosen, but should be advised that it is quite dense and will require some background work. But I believe the effort will pay off richly. Robert Talbert is Associate Professor of Mathematics and Computing Science at Franklin College. His interests include cryptography, ring theory, evangelism for the Mac OS X operating system, writing at his blog Casting Out Nines, and being at the beck and call of his wife and two daughters.
Courses: Non-FL Students Course Name: Algebra I Course Code: 1200310 Honors Course Code: 1200320 AP Course Code: Description: Algebra I is the foundation—the skills acquired in this course contain the basic knowledge needed for all future high school math courses. The material covered in this course is important, but everyone can do it. Everyone can have a good time solving the hundreds of real-world problems algebra can help answer. Each module in this course is presented in a step-by-step way right on the computer screen. Hands-on labs make the numbers, graphs, and equations more real. The content in this course is tied to real-world applications like sports, travel, business, and health. This course is designed to give students the skills and strategies to solve all kinds of mathematical problems. Students will also acquire the confidence needed to handle everything high school math has in store for them Quadratic Equations: Solving Quadratic Equations by Factoring and Using the Quadratic Formula  Graphical Parts of Quadratics Honors Only  Solving Real-World Problems Involving Quadratics  Using Graphing Technology Radical Expressions  Simplifying Algebraic Ratios and Proportions  Simplifying Radical Expressions
Teacher makes maths-changing discovery – watch TVNZ Breakfast interview with author, Philip Lloyd – August 2010, click here The Calculus Workbook NCEA Level 3 offers students the tools they need for success in Calculus. In the first part there are exercises at Achieved, Merit and ExcellGrammar for Starters is an entertaining book that will have immediate appeal to students. It takes them on a Journey of discovery that will help them understand the nature of the language that they already use. It aims to stimulate curiosity about the way language works and encourage an interesting ...
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The last section of the chapter is on applications, but the only ones listed there are approximating non-rational ... (My actual question is at the very bottom of this posting.) Suppose you're teaching a course in mathematics-for-liberal-arts majors and it's the last math course they'll ever take. It has almost no ... For 6 months, I'll be organizing, as part as my volunteer work in an NGO, math classes with small groups (~10 students, aged 16 or 17). These classes are not compulsory, but students willing to stay ... I suppose everyone is familiar with the Mandelbrot set. I'm teaching a course right now in which I am trying to convey the beauty of some mathematical ideas to first year students. They basically know ... It is a common practice to have students of elementary algebra infer the domain of a function as an exercise. I believe this is contrary to the spirit of the definition of a function as a collection ... 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Algebra and TrAnyone trying to learn algebra and examples are also included that provide more detailed annotations using everyday language. Th... MOREis approach gives them the skills to understand and apply algebra and trigonometry.
College Algebra : Concepts And Contexts - 11 edition Summary: This book bridges the gap between traditional and reform approaches to algebra encouraging users to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling, and emphasizing the verbal, numerical, graphical and symbolic representations of mathematical concepts as well as connecting mathematics to real life situations drawn from the users' majors.44.67 +$3.99 s/h Good SellBackYourBook Aurora, IL 04953878
Being a tutor, this is a comment I usually hear from students. sequences from real life is not one of the most popular topics amongst kids. I never encourage my students to get ready made answers from the internet, however I do encourage them to use Algebra Buster. I have developed a liking for this tool over time. It helps the students learn math in a convenient way. It would really be great if you could tell us about a software that can offer both. If you could get us a resource that would give a step-by-step solution to our problem, it would really be good. Please let us know the genuine websites from where we can get the tool. I remember having problems with dividing fractions, difference of squares and algebra formulas. Algebra Buster is a truly great piece of algebra software. I have used it through several math classes - Pre Algebra, Intermediate algebra and College Algebra. I would simply type in the problem from a workbook and by clicking on Solve, step by step solution would appear. The program is highly recommended. Thanks for the details. I have purchased the Algebra Buster from and I happened to read through linear equations this evening. It is pretty cool and easily readable. I was attracted by the descriptive explanations offered on distance of points. Rather than being test preparation oriented, the Algebra Buster aims at educating you with the basic principles of Pre Algebra. The payment guarantee and the unimaginable discounts that they are currently giving makes the purchase particularly appealing
Detailed Description of this Course Algebra seems hard to many students simply because every topic builds upon one another. What usually happens is that the student will understand the first few topics in the course, then fall behind once variables are introduced. After this point many students don't really understand the purpose of variables in algebra but continue moving along in the course until a point is reached where it is impossible to understand further topics with out a solid grasp of the basics. The Algebra 1 Tutor series is designed assuming that you know absolutely nothing about Algebra. We begin at the very beginning of the sequence of topics with a review of fractions and exponents and gradually move through variables, expressions, and equations. What sets our tutorials apart is that every single topic is taught by showing fully worked example problems in a step-by-step fashion. This technique has proven to be extremely effective and has helped thousands of students from around the world learn Algebra with our video lessons. What you'll find is that once you begin to understand the topics, your confidence will improve in Algebra. Then, instead of fearing the subject you'll truly begin to see that it is very logical, approachable, and that you can check your work on virtually every single problem.
Precalculus posted on: 10 Dec, 2011 \| updated on: 29 Sep, 2012 Precalculus is a vast concept as it covers large number of topics and other concepts. Precalculus does not include topics from Calculus but it covers the topics and concepts which will be useful in calculus. Precalculus is studied from primary schools to research schools to help students in understanding important topics that will be used to solve problems in calculus. So we can say it teaches the basics of calculus. Some important concepts of precalculus are: • Curve – Plotting equations on a graph and the shape formed so is called the curve. • Polar coordinates – This is the system of coordinates in which coordinates ate defined with the help of angles. • Plane – Plane can be defined as a two dimensional surface which defines Linear Equations. • Tangents – Tangent is a line which touches the outer surface of the Circle or circular object at exactly one Point. • Complex Numbers – Complex numbers are the numbers which consist of two parts one is real part and other is imaginary part. • Conic sections – Conic sections are the curves which are generated when a plane intersects or cuts the parts of a cone. There are different types of conic sections like ellipse, hyperbola, and Parabola. • Logarithms – Logarithm can be defined as the power to which another number is raised to get another number. It contains base as 10. • Natural Logs – These are the logarithms which have base 'e'. • Functions – A function consists of variables with operations defined on them and these Functions depend on particular variables. • Vectors – Vectors can be defined as quantity which has both magnitude and direction. There are many other sub concepts of precalculus like Sets, real numbers, composite Functions etc.
MATH 111 – Mathematics for Educators I Description: This course teaches students to communicate and represent mathematical ideas, how to solve problems, and how to reason mathematically. Material covered includes operations and their properties, sets, counting, patterns, and algebra.
Learning Matlab - Essentials Skills (2012) - FREE SHIPMENT The advertisement posted in this page is already inactive and it is possible that the details here are already invalid. Content posted in this page is only provided for reference and does not constitute fact. Please be guided accordingly. In this video series 7 Hour, Jason Gibson Teaches you How to use this Software package with Step-by Step video tutorials. The lessons begin with Becoming familiar with the user interface and Understanding How to interact with Matlab. Then you'll learn about variables, Functions, and How to Perform Basic Calculations. Next, Jason Will guide you in Learning How to do Algebra, trigonometry, and Calculus computations Both numerically and symbolically. The course wraps up with basic plotting in Matlab. Take the mystery out of Matlab and improve your productivity with the software immediately! 1. Introduction Sect 1: Overview of the User Interface - Part 1 Sect 2: Overview of the User Interface - Part 2 Sect 3: Overview of the User Interface - Part 3 Sect 4: Using the Help Menus 2. Basic Calculations Sect 5: Basic Arithmetic and Order of Operations Sect 6: Exponents and Scientific Notation Sect 7: Working with Fractions and the Symbolic Math Toolbox - Part 1 Sect 8: Working with Fractions and the Symbolic Math Toolbox - Part 2
Number problems most often appear on tests in science, math, statistics, and some business courses. They require that the student know special symbols, formulas for solving problems, and the correct sequence of steps for solving problems. Practice Questions One of the best ways to prepare for number problems is to practice solving sample questions. Find out what types of problems will appear on the exam. Then look at old tests and student workbooks for those types of questions. Examine sample problems in the text book, and work through extra problems not covered in homework assignments. Change the numbers given in homework problems and rework them. Problems in the textbook and/or workbook are particularly useful because the answers are often provided, so one knows if the problem was solved correctly. If answers to problems are not available, ask a tutor or the instructor to check your work. Practice making and interpreting graphs and other visual aids as well. Review Procedural Steps Review the steps required to solve different problems, and be sure to understand how each step works. Sometimes it helps to list the steps for solving each type of problem, record the steps on paper or audio cassettes, review the steps, and then practice sample problems. Use mnemonics and try to identify a key word in each step that may act as a memory trigger. Use flow charts and other visual aids to remember the correct order of steps. Review Symbols, Formulas, and Equations Students should understand clearly the symbols used in all formulas and equations. Record symbols and formulas on flash cards or in lists for easy review. Memory Strategies The three things that must be remembered for most number problems are the steps for solving the problem, the formula(s) to be used, and the symbols in the formulas. Sequential steps are best remembered using strategies like mnemonics, peg words, and chaining. Formulas may be registered and recalled using rhymes or grouping strategies. Association strategies are useful in remembering symbols and their meanings. Formula Sheets If formula sheets are permitted on the exam, prepare them ahead of time. Make sure the information is organized, legible, and easy to find. Include what the symbols in the formulas mean as well as the formulas themselves. If calculators are permitted on the test, become familiar with the keys available and where they are, the order of operations for inputting data, scientific notation displays, and special function keys. This is especially true of borrowed calculators. Have an extra battery, and know how to change it if necessary. Attend to Mental and Physical Health Try to avoid negative feelings toward number problems and try to block out bad experiences from the past. Successful practicing should bolster confidence and mental attitudes. Get plenty of rest and eat well before the test. Open-Book Tests Even though books and/or notes may be used to answer questions, open-book tests require preparation. In fact, preparation may be the factor separating students who finish on time and those who don't, or students who do well and those who do poorly. The nature of preparation, however, will differ from that of objective and subjective in-class tests. Organize Information The best way to prepare for open-book tests is to organize information so that it is easily located. For the textbook, mark important pages with paper clips or labeled post-it notes. Learn how to use the index to find information. For the notes, logically organize them by topic or temporal sequence and then number the pages. Make up a personalized index, complete with page numbers for different topics, for the notes. Arrange the information in a three-ring notebook for easy access, incorporating class handouts and other materials as well as notes. Mark important pages with paper clips or labeled post-it notes. Make Summary Sheets Reduce the exam information to main ideas and supporting details, organize it logically, and record it on summary sheets. Paste the summary sheets in the book or notebook. This is especially helpful for tests with formulas, dates, and people. Develop an Appropriate Attitude Resist the temptation to "blow off" preparing for open-book tests. Some students think that, because they may use books or notes to answer questions, open-book tests are easier than closed-book exams. Not necessarily. Instructors often expect to see more details and more interpretation of concepts on this type of exam. There may be more questions to answer as well. Take open-book tests seriously.
5/10/04 REGISTRATION IS NOW CLOSED Have you ever struggled to come up with applications in a discrete mathematics course which demonstrate to your students the relevance of what seems like a rather disparate collection of topics to their study of material in computer science (and, yes, even excite them too!)? Then, this workshop is for you. The workshop will provide participants with an in-depth look at a number of problems and applications that arise in a typical discrete math course (sequence) which is designed to meet the needs of computer science majors. The problems and their solutions will be treated from both a mathematical and a computational perspective. Representative problems will be selected from the following domains: encryption algorithms, finite-state automata and Turing machines, analysis of algorithms, algorithm correctness, Boolean algebra and logic circuits, graph algorithms, data base systems, functional and logic programming, and computer graphics. As a pre-workshop activity, participants will be given a collection of possible problems to be discussed during the workshop, assigned some readings on each of the problems and asked to choose which ones they would like to see in more detail. At the workshop, for each of the applications chosen, the presenters will provide background information and the participants will work in teams to develop solutions to a carefully chosen set of exercises. Participants will return to their institutions prepared to implement the materials developed. As follow-up, participants will be asked to contribute their own examples and applications to an on-going, on-line repository developed by the workshop leaders.
The Mathematics Department at Saint Ignatius College Riverview have developed our teaching programs, pedagogy and assessment in terms of the content prescribed by the NSW Board of Studies. All students are required to complete a common Mathematics course in Years 5 to 8. While foundation classes are offered to those students with numeracy problems, classes are streamed so that the most gifted mathematics students are grouped into the same class. In Years 9 and 10 students are arranged into three distinct Mathematics courses Advanced (5.3), Intermediate (5.2) and Standard (5.1). These three courses cater for students of different mathematical abilities and prepare students to undertake the full range of courses in the senior school. At Saint Ignatius College Riverview more than 65% of each cohort attempt the Advanced(5.3) Mathematics course. In Years 11 and 12 students preparing to undertake Tertiary study in Mathematics for courses such as engineering and the physical sciences undertake the most rigorous Extension 1 and Extension 2 courses. For those students who want a sound understanding of Mathematics, especially introductory calculus, and need it as a pre-requisite for university courses such as commerce and life sciences the College offers Mathematics (2 unit). The final course offered does not require the students to study calculus but gives students a good foundation for further Mathematics is the General mathematics course. The Mathematics Department is proud of its impressive external examination results from both the HSC and the School Certificate. These results reflect the excellent standard of Mathematics achieved by students at the College. Mathematics Course Content The essential content for Mathematics in Years 5 10 is structured using one process strand - Working Mathematically and five content strands: Number Patterns and Algebra Data Measurement Space and Geometry. These strands contain the knowledge, skills and understanding for the study of mathematics in the compulsory years of schooling Strand Working Mathematically Students will develop knowledge, skills and understanding through inquiry, application of problem-solving strategies including the selection and use of appropriate technology, communication, reasoning and reflection. Number Students will develop knowledge, skills and understanding in mental and written computation and numerical reasoning. Patterns and Algebra Students will develop knowledge, skills and understanding in patterning, generalisation and algebraic reasoning. Data Students will develop knowledge, skills and understanding in collecting, representing, analysing and evaluating information. Measurement Students will develop knowledge, skills and understanding in identifying and quantifying the attributes of shapes and objects and applying measurement strategies. Space and Geometry Students will develop knowledge, skills and understanding in spatial visualisation and geometric reasoning. Topics studied - Kindergarten to Year 10 Years K- 6 7 - 8 Standard Intermediate Advanced Stage 5.3 Stage 5.2 Strand Early Stage 1 to Stage 3 Stage 4 Stage 5.1 Working Mathematically Five Interrelated Processes Questioning Applying Strategies Communicating Reasoning Reflecting Number Whole Numbers Addition and Subtraction Multiplication and Division Fractions and Decimals Chance
The only book of its kind available today, this popular handbook features comprehensive math review for the major graduate and business school exams. It helps sharpen the understanding of basic and complex math concepts to achieve high scores. [via]
Book Description: This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers students at both high school and college levels an excellent mathematics workbook. Filled with rigorous problems, it assists students in developing and cultivating their logic and probability skills. 1974 edition
Helpful Ways to Teach Geometry This video shows that visual aids such as pictures are helpful in teaching geometry. Dr. Stefan Forcey received his Ph.D. in mathematics from Virginia Tech University in 2004. He is currently teaching mathematics as an assistant professor at Tennessee State UniversityGraphing Linear Inequalities in Two Variables, Part III In this video, Sal Khan demonstrates how to graph a linear inequality. Mr. Khan uses the Paint Program (with different colors) to illustrate his points. Sal Khan is the recipient of the 2009 Microsoft Tech Award in Education. (03:20 Celebrates its First Raider Walk Come experience the thrill and excitement of Texas Tech Football's Raider Walk! Cheer on the coaches and meet your favorite players. Raider Walk starts 2 hours and 15 minutes before each home football game near Dan Law Field and continues to the southwest corner of Jones AT&T Stadium. Author(s): No creator set License information Related content No related items provided in this feed How to Avoid the Freshman 15 Jamie Cooper, assistant professor in the Texas Tech University Department of Nutrition, Hospitality and Retailing, recommends some easy alternatives for college students to keep in mind to avoid the dreaded "freshman 15". Author(s): No creator set outlinedVoice-leading analysis of music 2: the middleground This unit continues our examination of 'voice-leading' or 'Schenkerian' analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units ... Author(s): No creator set License information Related content Rights not set No related items provided in this feed Multivariable Calculus This is a textbook for a course in multivariable calculus that has been used for the past few years at Georgia Tech. Author(s): No creator set
I imagine any branch of physics will make heavy use of calculus and differential equations, and probably linear algebra. What kinds of mathematics you'll be utilizing depends on what you're studying, but the happy/sad news is that the more math you know the better. A few stats courses, like ones designed for science and engineering majors and/or some numerical methods courses (my math department splits them between math and stats pretty evenly, so I don't know where one would like to place it). However, as I said before the first list is likely the only required mathematics course work in physics, the rest are just good subjects to pick up on the way. What math classes are need for this... from my experience as an undergrad, it seems like you can get by at the undergraduate level with just your calc sequence, elementary differential equations, and linear algebra. taking courses on complex variables and numerical analysis might be a good idea, too. (some graduate level courses in physics seem to assume some experience with contour integrals--in the grad qm class i took last fall, we needed to either recall or look up the integral of sinx/x from -infinity to +infinity. the numerical analysis class i took didn't have useful material, per se, but it helped me solidify my scientific computing skills.)
Get to the Core: Modeling with Mathematics in the Algebra Classroom (Beginner Fathom) Description In this beginning Fathom webinar, we'll explore real-world data and illustrate how to address Common Core modeling standards from the conceptual categories of Algebra and Functions. We'll focus on mathematical models appropriate to Algebra 1 and Algebra 2 classes. In particular, we'll explore standards from the clusters of Creating Equations (A-CED), Building Functions (F-BF), and Linear, Quadratic, and Exponential Models (F-LE). No previous experience with Fathom is required. Presenter since 2004, first as an editor, and now as Mathematics Product Manager.
Mathematics/Applied Mathematics The Basis of Exact Science Mathematics is the language in which our era's technical and scientific knowledge is formulated. It is also an indispensable tool in computer science, insurance and the economy. However, its actual core is pure mathematics: the intensive study of abstract structures and geometrical objects, and the discovery and description of the laws that govern them. Educational objective: The principal aim of a degree in Mathematics is a broad education in the fundamentals of mathematics that allows graduates to independently acquire further knowledge for their future professional work. Career profile: Mathematicians work in many different fields. They conduct research and teach at universities, technical colleges and Gymnasien. They work for insurance companies and, increasingly, in banks, industry, software development, planning and business optimisation, or as statisticians in the public sector. A distinct talent for abstract thought is always essential for studying and working with Mathematics
Stremple, William (BJ) We begin the year with a review of the properties of algebra and the arithmetic of real numbers which include integers and fractions. We will discover how to solve one and two step equations. LInear functions will be explored and graphed on the coordinate plane. The course also includes introductory probability and geometry. This course does have an SOL test as well as a midterm and final.
Hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students. Written by two internationally renowned mathematicians, its accessible treatment requires no prev... read more Customers who bought this book also bought: Our Editors also recommend: Formal Knot Theory by Louis H. Kauffman The author draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in combinatorics. 51 illustrations. 1983 edition.Experiments in Topology by Stephen Barr Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit. Elementary Concepts of Topology by Paul Alexandroff Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures. General Topology by Waclaw Sierpinski Detailed theory of Fréchet (V) spaces and a comprehensive examination of their relevance to topological spaces, plus in-depth discussions of metric and complete spaces. For beginning students and mature mathematicians. Second edition. Product Description: Hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students. Written by two internationally renowned mathematicians, its accessible treatment requires no previous knowledge of algebraic topology. Starting with basic definitions of knots and knot types, the text proceeds to examinations of fundamental and free groups. A survey of the historic foundation for the notion of group presentation is followed by a careful proof of the theorem of Tietze and several examples of its use. Subsequent chapters explore the calculation of fundamental groups, the presentation of a knot group, the free calculus and the elementary ideals, and the knot polynomials and their characteristic properties. The text concludes with three helpful appendixes and a guide to the literature
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane. Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix. Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication. able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes
Course Number: MA.IMP2 Course Name: Interactive Math Program 2 Prerequisite: None Course Description: This course is part of an integrated, problem-centered mathematics program designed to meet the needs of all students. Algebra, geometry, trigonometry, probability and statistics are used together to emphasize logical analysis, inference and deduction rather than drill-skill memorization. Course Length: 2 semesters Period Length: 1 Grade Level: 9-12 grade(s) Credit Per Semester: 1.0 (Math requirement or Elective)
Speaker's Bureau Algebra: Hints and Helps Description: Hints for the Algebra classroom teacher that will make teaching algebra easier and more exciting. Open discussion to address particular problems you have when teaching Algebra. This workshop also gives helps for students who have difficulty with Algebra. Note: The speaker authored the BJU Press Algebra textbook.
This course is accessible by members of the "Center Grove" Institution Join This Course Announcements By Announcement Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '11.2 multiplying and dividing rational expressions...New Lesson Created With the Title '11.2 multiplying and dividing rational expressions'Read more about New Lesson.. 04/29/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '11.1 Simplifying Rational Expressions'New Lesson Created With the Title '11.1 Simplifying Rational Expressions' 04/27/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title 'Chapter 10 test'New Lesson Created With the Title 'Chapter 10 test' 04/20/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '10.5 Graphing Radical Functions'New Lesson Created With the Title '10.5 Graphing Radical Functions' 04/14/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '10.4 Solving Radical Equations'New Lesson Created With the Title '10.4 Solving Radical Equations' 04/11/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '10.1-10.3 Quiz'New Lesson Created With the Title '10.1-10.3 Quiz' 04/07/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title 'acuity testing'New Lesson Created With the Title 'acuity testing' 04/07/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '10.1 Pythagorean Theroem'New Lesson Created With the Title '10.1 Pythagorean Theroem' 03/24/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '10.3 Operations with Radical Expressions'New Lesson Created With the Title '10.3 Operations with Radical Expressions' 03/23/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '10.2 Simplifying Radicals'New Lesson Created With the Title '10.2 Simplifying Radicals' 03/18/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title 'TEST on Friday or Monday 3/11 or 3/14!!!!'New Lesson Created With the Title 'TEST on Friday or Monday 3/11 or 3/14!!!!' 03/09/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '9.7 Linear, Quadratic, and Exponential Models'New Lesson Created With the Title '9.7 Linear, Quadratic, and Exponential Models' 03/09/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '9.6 The Quadratic Formula'New Lesson Created With the Title '9.6 The Quadratic Formula' 03/03/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title '9.3 Solving Quadratic Functions by Graphing and Sq...New Lesson Created With the Title '9.3 Solving Quadratic Functions by Graphing and Square Roots'Read more about New Lesson.. 03/01/2011 Becki MeierInstructorcentergrove New Lesson Created New Lesson Created With the Title 'Graphing Quadratic Functions Day 2'New Lesson Created With the Title 'Graphing Quadratic Functions Day 2' 02/23/2011
Formats Trade in Mathematical Methods in the Physical Sciences for an Amazon.co.uk gift card of up to £21.00, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more Book Description Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference. Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference. I am a first year Physics undergraduate at Imperial College and this book covers all the major topics in a clear and concise way. To see a full list of everything covered go to the 'search inside this book' link below its image. The book starts each topic from the basics, so don't worry about being thrown in at the deep end having forgotten stuff. But also don't be put off thinking it wastes time on the basics, it doesn't. There are a lot of question and answers on all the topics as you go along so you can check your understanding, and worked examples too. I would say it is best for physics and I would double check with the course teacher/lecturer for biology or chemistry as it is not cheap. For me, it was the perfect choice! This was recommended to me by a physicist in the year above me at Oxford - have successfully used it for a year in Physics, and from next year's syllabus it should be fine for the second year too. It was set at the right level and does everything rigorously (for a non-mathematician), leaving no confusing contradictions when you learn more advanced topics. The explanations and questions are all well thought out for developing an understanding of the topics.
Grade 11 & 12 Math Plots your overall percentage so that you can track your progress throughout the year Moving up into Grade 11 Math can be a struggle, because the things you need to know are often not thoroughly learnt in Grade 10. Suddenly you have to look at things in a whole different way. AcademyOne Learning takes the mystery out of Math and helps prepares you for your final exams with confidence. Know your stuff! The way to succeed at Math is to ensure you have a full comprehension of what you are doing. With AcademyOne Learning you can rest assured that you are learning the things you need to know. Remember - even one extra mark can be enough to make sure that you make the grade for University. Testimonial "The program was a help because it allowed for the practice of coursework in a way that enabled the identification of weak areas of knowledge and the strengthening of those areas. It also gave another angle at which to view the information studied and hence improve explanations when answering questions" . Jenny, Medicine "I am most impressed that, using the Math Wiz program, the students have successfully learnt difficult concepts without the 'hard work' which is generally associated with learning mathematics through conventional methods".
An introduction to variables. The number-line is labeled and the different types of numbers are defined. Students manipulate simple equations, and practice constructing equations based on real world applications
Prealgebra - 11 edition ISBN13:978-0077349950 ISBN10: 0077349954 This edition has also been released as: ISBN13: 978-0073384313 ISBN10: 0073384313 Summary: Prealgebra, by definition is the transition from arithmetic to algebra. Miller/O'Neill/Hyde Prealgebra will introduce algebraic concepts early and repeat them as student would work through a Basic College Mathematics (or arithmetic) table of contents. Prealegbra is the ground work that's needed for developmental students to take the next step into a traditional algebra course.According to our market Julie and Molly's greatest strength is the ability to conceptualize algebraic concept...show mores. The goal of this textbook will be to help student conceptualize the mathematics and it's relevancy in everything from their daily errands to the workplace.Prealgebra can be considered a derivative ofBasic College Mathematics.One new chapter introducing the variable and equations is needed. Each subsequent chapter is basic mathematics/arithmetic content with additional sections containing algebra incorporated throughoutAll text is legible, may contain markings, cover wear, loose/torn pages or staining and much writing. SKU:9780077349950-5-0 $43.56 +$3.99 s/h VeryGood Collegebooksdirect Greenville, TX Very GoodI...show moreONS. ...show less $54.74 +$3.99 s/h Good Penntext Downingtown, PA May have minimal notes/highlighting, minimal wear/tear. Please contact us if you have any Questions. 007734995473.75 +$3.99 s/h Good Sandman Book Company Punta Gorda, FL 0077349954 Used, in good condition. Book only. May have interior marginalia or previous owner's name. $73.75 +$3.99 s/h Good Crashing Rocks Bookstore Punta Gorda, FL PAPERBACK Good 0077349954 Used, in good condition. Book only. May have interior marginalia or previous owner's name. $85
Afraid of math, finding difficulty in solving math problems, free online math help is available on Tutorcircle to help you out. Our online tutors will provide you math answers of difficult problems. ... In mathematics, the range of a function refers to either the codomain or the image of the function, depending upon usage. The codomain is a set containing the function's output, whereas the image is ...
Course Meeting Times Prerequisites Overview This course is an introduction to algebraic number theory. We will follow Samuel's book Algebraic Theory of Numbers to start with, and later will switch to Milne's notes on Class Field theory, and lecture notes for other topics. There will be assigned readings for every class. I will go through the proofs of the more important theorems in class, and maybe some extra material (for instance, proofs omitted in the book). Homework and Grading Scheme There will be weekly problem sets. If you are an undergraduate or a first-year graduate student, I will assign you a grade based on homework and exams. Even otherwise, I strongly recommend doing the homework, to learn the material. The breakdown of the grade is: Grading criteria. ACTIVITIES PERCENTAGES Homework 50% Midterm 20% Take-home final 30% As usual, you are encouraged to work on the homework in groups, but you must write up your own solutions, and I would like you to specify on your homework who was in your working group. On the take-home exam, you are to work on your own using only the specified resources (the book, your course notes, any book from the library, but not any human and not Google or Wikipedia
John Wiley and Sons Ltd, November 2011, Pages: 320 This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison. Professors can request a solutions manual by email: company website Preface xi Reading Guide xv 1. Introduction 1 2. A Quick Tour of Geometric Algebra 7 2.1 The Basic Rules of a Geometric Algebra 16 2.2 3D Geometric Algebra 17 2.3 Developing the Rules 19 2.3.1 General Rules 20 2.3.2 3D 21 2.3.3 The Geometric Interpretation of Inner and Outer Products 22 2.4 Comparison with Traditional 3D Tools 24 2.5 New Possibilities 24 2.6 Exercises 26 3. Applying the Abstraction 27 3.1 Space and Time 27 3.2 Electromagnetics 28 3.2.1 The Electromagnetic Field 28 3.2.2 Electric and Magnetic Dipoles 30 3.3 The Vector Derivative 32 3.4 The Integral Equations 34 3.5 The Role of the Dual 36 3.6 Exercises 37 4. Generalization 39 4.1 Homogeneous and Inhomogeneous Multivectors 40 4.2 Blades 40 4.3 Reversal 42 4.4 Maximum Grade 43 4.5 Inner and Outer Products Involving a Multivector 44 4.6 Inner and Outer Products between Higher Grades 48 4.7 Summary So Far 50 4.8 Exercises 51 5. (3+1)D Electromagnetics 55 5.1 The Lorentz Force 55 5.2 Maxwell's Equations in Free Space 56 5.3 Simplifi ed Equations 59 5.4 The Connection between the Electric and Magnetic Fields 60 5.5 Plane Electromagnetic Waves 64 5.6 Charge Conservation 68 5.7 Multivector Potential 69 5.7.1 The Potential of a Moving Charge 70 5.8 Energy and Momentum 76 5.9 Maxwell's Equations in Polarizable Media 78 5.9.1 Boundary Conditions at an Interface 84 5.10 Exercises 88 6. Review of (3+1)D 91 7. Introducing Spacetime 97 7.1 Background and Key Concepts 98 7.2 Time as a Vector 102 7.3 The Spacetime Basis Elements 104 7.3.1 Spatial and Temporal Vectors 106 7.4 Basic Operations 109 7.5 Velocity 111 7.6 Different Basis Vectors and Frames 112 7.7 Events and Histories 115 7.7.1 Events 115 7.7.2 Histories 115 7.7.3 Straight-Line Histories and Their Time Vectors 116 7.7.4 Arbitrary Histories 119 7.8 The Spacetime Form of ? 121 7.9 Working with Vector Differentiation 123 7.10 Working without Basis Vectors 124 7.11 Classifi cation of Spacetime Vectors and Bivectors 126 7.12 Exercises 127 8. Relating Spacetime to (3+1)D 129 8.1 The Correspondence between the Elements 129 8.1.1 The Even Elements of Spacetime 130 8.1.2 The Odd Elements of Spacetime 131 8.1.3 From (3+1)D to Spacetime 132 8.2 Translations in General 133 8.2.1 Vectors 133 8.2.2 Bivectors 135 8.2.3 Trivectors 136 8.3 Introduction to Spacetime Splits 137 8.4 Some Important Spacetime Splits 140 8.4.1 Time 140 8.4.2 Velocity 141 8.4.3 Vector Derivatives 142 8.4.4 Vector Derivatives of General Multivectors 144 8.5 What Next? 144 8.6 Exercises 145 9. Change of Basis Vectors 147 9.1 Linear Transformations 147 9.2 Relationship to Geometric Algebras 149 9.3 Implementing Spatial Rotations and the Lorentz Transformation 150 9.4 Lorentz Transformation of the Basis Vectors 153 9.5 Lorentz Transformation of the Basis Bivectors 155 9.6 Transformation of the Unit Scalar and Pseudoscalar 156 9.7 Reverse Lorentz Transformation 156 9.8 The Lorentz Transformation with Vectors in Component Form 158 9.8.1 Transformation of a Vector versus a Transformation of Basis 158 9.8.2 Transformation of Basis for Any Given Vector 162 9.9 Dilations 165 9.10 Exercises 166 10. Further Spacetime Concepts 169 10.1 Review of Frames and Time Vectors 169 10.2 Frames in General 171 10.3 Maps and Grids 173 10.4 Proper Time 175 10.5 Proper Velocity 176 10.6 Relative Vectors and Paravectors 178 10.6.1 Geometric Interpretation of the Spacetime Split 179 10.6.2 Relative Basis Vectors 183 10.6.3 Evaluating Relative Vectors 185 10.6.4 Relative Vectors Involving Parameters 188 10.6.5 Transforming Relative Vectors and Paravectors to a Different Frame 190 11.5.4 The Electromagnetic Field of a Plane Wave Under a Change of Frame 223 11.6 Lorentz Force 224 11.7 The Spacetime Approach to Electrodynamics 227 11.8 The Electromagnetic Field of a Moving Point Charge 232 11.8.1 General Spacetime Form of a Charge's Electromagnetic Potential 232 11.8.2 Electromagnetic Potential of a Point Charge in Uniform Motion 234 11.8.3 Electromagnetic Field of a Point Charge in Uniform Motion 237 11.9 Exercises 240 12. The Electromagnetic Field of a Point Charge Undergoing Acceleration 243 12.1 Working with Null Vectors 243 12.2 Finding F for a Moving Point Charge 248 12.3 Frad in the Charge's Rest Frame 252 12.4 Frad in the Observer's Rest Frame 254 12.5 Exercises 258 13. Conclusion 259 14. Appendices 265 14.1 Glossary 265 14.2 Axial versus True Vectors 273 14.3 Complex Numbers and the 2D Geometric Algebra 274 14.4 The Structure of Vector Spaces and Geometric Algebras 275 14.4.1 A Vector Space 275 14.4.2 A Geometric Algebra 275 14.5 Quaternions Compared 281 14.6 Evaluation of an Integral in Equation (5.14) 283 14.7 Formal Derivation of the Spacetime Vector Derivative 284 References 287 Further Reading 291 Index 293 The IEEE Press Series on Electromagnetic Wave Theory JOHN W. ARTHUR earned his PhD from Edinburgh University in 1974 for research into light scattering in crystals. He has been involved in academic research, the microelectronics industry, and corporate R&D. Dr. Arthur has published various research papers in acclaimed journals, including IEEE Antennas and Propagation Magazine. His 2008 paper entitled "The Fundamentals of Electromagnetic Theory Revisited" received the 2010 IEEE Donald G. Fink Prize for Best Tutorial Paper. A senior member of the IEEE, Dr. Arthur was elected a fellow of the Royal Society of Edinburgh and of the United Kingdom's Royal Academy of Engineering in 2002. He is currently an honorary fellow in the School of Engineering at the University of Edinburgh.
Elementary Numerical Analysis 9780471433378 ISBN: 0471433373 Edition: 3 Pub Date: 2003 Publisher: John Wiley & Sons Inc Summary: Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems. The text introduces core areas... of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.[read more] Ships From:Multiple LocationsShipping:Standard, Expedited, Second Day, Next Day
MathsHere are a few notes that are useful when working with algebraic expressions and functions. Remember you simplify an expression by collecting like terms You can also simplify expressions by using rules of indices (powers) [IMAGE] [IMAGE] [IMAGE] To expand negative areas. It covers understanding that areas below the x axis are negative, calculating areas under a curve, some or all of which may be under the x axis. Before attempting this chapter you must have prior [...] solving equations with algebraic fractions. It covers understanding how to solve equations involving fractions, working with denominators with either constants or linear factors. Before attempting this chapter you must have prior knowledge of expanding brackets and factorising [...]
Instituzioni analitiche ad uso della gioventù italianituzioni analitiche ad uso della gioventu italiana is discussed in the following articles: discussed in biography Agnesi's best-known work, Instituzioni analitiche ad uso della gioventù italiana (1748; "Analytical Institutions for the Use of Italian Youth"), in two huge volumes, provided a remarkably comprehensive and systematic treatment of algebra and analysis, including such relatively new developments as integral and differential calculus. In this text is found
knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the deep mathematical insight they need to engage their students in learning mathematics in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining. Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT": M Multiple Approaches/Representations A Applications to Real Life T Technology H History N Nature of Mathematics: Reasoning and Proof S Solving Problems I Interlinking Concepts: Connections G Grade Levels H Honing of Mathematical Skills T Typical Errors This text is aligned with the recently released Common Core State Standards, and is ideally suited for a capstone mathematics course in a secondary mathematics certification program. It is also appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers.
Globalshiksha has come up with LearnNext Jharkhand Board Class 8 CDs for Maths and Science. Included lessons with syllabuses are in audio and visual format, solved examples, practice workout, experiments, tests and many more related to Jharkhand Board Class 8 Maths and Science. It also include a various set of visual tools and activities on each Lesson with Examples, Experiments, Summary and workout. You can understand all the concepts well, clear all doubts with ease through this Educational CD and get score in the exams. This multimedia comes with a useful Exam Preparation like Lesson tests usually 20-30 minutes in duration, which will help you to evaluate the understanding of each lesson and Model tests usually 150-180 minutes in duration, which cover the whole subject on the lines of final exam pattern. This package can help you to sharpen your preparation for final exams, identify your strengths and weaknesses and know answers to all tests with a thorough explanation, overcome exam fear and get well scores in final exams.
ELEMENTARY TECHNICAL MATHEMATICS helps you develop the math skills so essential to your success on the job! Ewen and Nelson show you how technical mathematics is used in such careers as industrial and construction trades, electronics, agriculture, allied health, CAD/drafting, HVAC, welding, auto diesel mechanic, aviation, and others. The authors include plenty of examples and visuals to assist you with problem solving, as well as an introduction to basic algebra and easy-to-follow instructions for using a scientific calculator. Each chapter opens with useful information about a specific technical career and you can learn more about each career by going to the Book Companion Website. You'll also have access to an online tutorial you can use at your own pace to improve your skills. Need more help? A live online tutor with a copy of your textbook is just a click away
Elementary Algebra - 3rd edition Summary: Elementary Algebra is a book for the student. The authors' goal is to help build students' confidence, their understanding and appreciation of math, and their basic skills by presenting an extremely user-friendly text that models a framework in which students can succeed. Unfortunately, students who place into developmental math courses often struggle with math anxiety due to bad experiences in past math courses. Developmental students often have never developed nor ...show moreapplied a study system in mathematics. To address these needs, the authors have framed three goals for Elementary Algebra: 1) reduce math anxiety, 2) teach for understanding, and 3) foster critical thinking and enthusiasm.The authors' writing style is extremely student-friendly. They talk to students in their own language and walk them through the concepts, explaining not only how to do the math, but also why it works and where it comes from, rather than using the "monkey-see, monkey-do" approach that some books take. ...show less 20109.26 +$3.99 s/h Good Extremely_Reliable Richmond, TX Buy with confidence. Excellent Customer Service & Return policy. $10.12 +$3.99 s/h VeryGood Bragg About Books NC Fayetteville, NC 2010 Hardcover OVERSIZED, CANNOT SHIP ITEM INTERNATIONALLY! There is NO apparent writing or highlighting in this book. Very good condition, $19.99 +$3.99 s/h New BookStore101 SUNNY ISLES BEACH, FL INSTRUCTOR EDITION!.ALL ANSWERS INCLUDED. Same as student edition.SHIPS FAST!! SAME DAY OR W/N 24 HOURS.EXPEDITED SHIPPING AVAILABLE TOO!!! $22.59 +$3.99 s/h Acceptable BookSleuth Danville, CA Fast Shipping ! Used books may not include access codes, CDs or other supplements. $34.96$35.28 +$3.99 s/h Good One Stop Text Books Store Saint Louis, MO 2010-01-13 Hardcover Good $41.96 +$3.99 s/h New Fourstar Books Williamsport, MD Hardcover New 0321577299 Brand New Never Used, choose expedited shipping if you need it quick. $9497
Description for Elementary Analysis The Theory of Calculus with Solutions repost screenshot Kenneth A. Ross, Elementary Analysis: The Theory of Calculus (with Solutions) S***r \| 2010 \| ISBN: 1441928111 \| 368 pages \| PDF \| 64,5 7,5 MB Designed for students having no previous experience with rigorous proofs, this text on analysis can be used immediately following standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.
Common Core State Standards (CCSS) for mathematics are rigorous. Now that most states have accepted the CCSS, they need to first understand the CCSS and then design a way to implement the CCSS in mathematics.... $ 10.29 This title is part of a brand new series which takes a fresh approach to planning by ensuring that children's interests are at the heart of all plans. Planning for the Early Years: The Local Community is packed... $ 13.29 How to Survive Your Freshman Year offers incoming college freshmen the experience, advice, and wisdom of their peers: hundreds of other students who have survived their first year of college and have something... $ 10.99 A University of Tradition is a fascinating compilation of history, customs, pictures, and facts about Purdue University from its founding in 1869 to the present day. Covering all aspects of Purdue, from the... $ 10.99 Plan for six weeks of learning covering all six areas of learning and development of the EYFS through the topic of the senses. The Planning for Learning series is a series of topic books written around the Early... $ 14It's no secret that college doesn't prepare students for the real world. Student loan debt recently eclipsed credit card debt for the first time in history and now tops one trillion dollars. And the throngs... $ 9.99 10.79 8.79 The CliffsTestPrep series offers full-length practice exams that simulate the real tests; proven test-taking strategies to increase your chances at doing well; and thorough review exercises to help fill in any...
Project Exchange California State Content Standards Math AII.2.0: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. Math LA.2.0: Students interpret linear systems as coefficient matrices and the Gauss-Jordan method as row operations on the coefficient matrix. Math LA.5.0: Students perform matrix multiplication and multiply vectors by matrices and by scalars. Math LA.6.0: Students demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly one solution, or have infinitely many solutions. Math LA.9.0: Students demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to solve systems of linear equations. Math LA.11.0: Students know that a square matrix is invertible if, and only if, its determinant is nonzero. They can compute the inverse to 2 x 2 and 3 x 3 matrices using row reduction methods or Cramer's rule.
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(From catalog 2012-2013) MA135 - College Algebra Course Description: MA135 College Algebra: Prerequisite:MA125, or a high school or transfer course equivalent to MA125, or an ACT math score greater than 23, or an SAT math score greater than 510, or a COMPASS score greater than 66 in the Algebra placement domain, or a COMPASS score 0-45 in the College Algebra domain. A consideration of those topics in algebra necessary for the calculus. Topics include:Solving equations and inequalities, graphing, functions, complex numbers, the theory of equations, exponential and logarithmic functions. 3:0:3 (From catalog 2011-2012) MA135 - College Algebra Course Description: MA 135 College Algebra A consideration of those topics in algebra necessary for the calculus. Topics include: Solving equations and inequalities, graphing, functions, complex numbers, the theory of equations, exponential and logarithmic functions. Prerequisite: MA 125, or a high school or transfer course equivalent to MA 125, or an ACT math score >= 23, or an SAT math score >= 510, or a COMPASS score >= 66 in the Algebra placement domain, or a COMPASS score 0-45 in the College Algebra placement domain. 3:0:3@ (From catalog 2010-2011)
Mathematics of the Securities Industry Numbers, ratios, and formulas are the lifeblood of the financial markets. Mathematics of the Securities Industry uses straightforward math and examples to explain every key number used on Wall Street, from the calculation of each number to why it is important and how best to use it. Completely up-to-date to include three-day settlement, decimalization, new tax laws, and more, it is today's easiest-to-use reference for measuring investment potential and accurately monitoring stock and bond performance. How does a market globalize? How do antitrust and trade policies speed up or slow down the process? How do firms take part in it? This book offers a comprehensive appraisal of the phenomenon from a ... This text analyzes the development and causal factors behind the geography of the commercial Internet industry. It presents an accurate map of Internet domains in the world, by country, by region, by ...
Guys, I am having a very tough time with my homework on Algebra 1. I thought this would be easy and hence didn't care to check till now. When I sat down to work on the problems today, I found it to be rather unsolvable. Can any one guide me by offering information on the existing tools that can guide me with brushing up my basics on , topic-kwds and topic-kwds. I have no clue why God made algebra, but you will be happy to know that a group of people also came up with Algebra Buster! Yes, Algebra Buster is a program that can help you solve math problems which you never thought you would be able to. Not only does it solve the problem, but it also explains the steps involved in getting to that solution. All the Best! Even I've been through times when I was trying to figure out a solution to certain type of questions pertaining to solving a triangle and gcf. But then I found this piece of software and I felt as if I found a magic wand. In a flash it would solve even the most difficult problems for you. And the fact that it gives a detailed and elaborate explanation makes it even more useful. It's a must buy for every math student. angle complements, simplifying expressions and system of equations were a nightmare for me until I found Algebra Buster, which is really the best math program that I have ever come across. I have used it through many math classes – Intermediate algebra, Intermediate algebra and Intermediate algebra. Just typing in the math problem and clicking on Solve, Algebra Buster generates step-by-step solution to the problem, and my math homework would be ready. I highly recommend the program.
Course Description: An investigation of topics, including the history of mathematics, number systems, geometry, logic, probability, and statistics. There is an emphasis throughout on problem solving. Recommended for general education requirements, B.S. degree. (a) ... understand culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior. (b) ... demonstrate knowledge of the signs and symbols of another culture. (c) ... participate in activity that broadens their customary way of thinking. Aesthetic Skills: The students will ... (a) ... develop an aesthetic sensitivity. It is also worth mentioning the NCTM (National Council of Teachers of Mathematics) "standards" for mathematics education, because they are also a list of some overall goals we strive for in this course: The students shall develop an appreciation of mathematics, its history and its applications. The students shall become confident in their own ability to do mathematics. (c) ... explore linear and exponential growth functions, including the use of logarithms, and be able to compare these two growth models. (d) ... explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system. (e) ... develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms. (f) ... explore the basics of probability. (g) ... learn descriptive statistics, including making the connection between probability and the normal distribution table. (h) ... learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations. (i) ... solve a variety of problems throughout the course which will require the application of several topics addressed during the course. Communication Skills: The students will ... (a) ... write a mathematical autobiography. (b) ... collect a portfolio of their work during the course and write a reflection paper. (c) ... do group work (labs and practice exams), involving both written and oral communication. (d) ... turn in written solutions to occasional problems. Life Value Skills: The students will ... (a) ... develop an appreciation for the intellectual honesty of deductive reasoning. (b) ... understand the need to do one's own work, to honestly challenge oneself to master the material. Cultural Skills: The students will ... (a) ... explore a number of different numeration systems used by other cultures, such as the early Egyptian and the Mayan peoples. (b) ... develop an appreciation for the work of the Arab and Asian cultures in developing algebra during the European "Dark Ages". (c) ... explore the contribution of the Greeks, especially in the areas of Logic and Geometry. Aesthetic Skills: The students will ... (a) ... develop an appreciation for the austere intellectual beauty of deductive reasoning. (b) ... develop an appreciation for mathematical eleganceThere will be a few assignments not generally included in a mathematics course, but which will, I hope, make your experience in this class more well-rounded than in a typical algebra course. These include the following: MATHEMATICAL AUTOBIOGRAPHY: Due: Monday, September 16 87% or more, "B" = 80% or more, "BC" = 77% or more, "C" = 70% or more, "CD" = 67% or more, and "D" = 60% or more. We will probably end up with about 800 possible points. My advice is simple: if you wish to earn a decent grade, make sure that you keep up with your work and that you turn in ALL the papers which are to be graded. I find that the surest way to receive less than a "C" is to make sure you miss some classes and fail to turn in all your work! ATTENDANCE POLICIES: Attendance is important in this class. There is really never a "good day" to miss because we will either be covering new material or working in groups on some problems. I will not formally reduce your grade for poor attendance, but I will take attendance throughout the course so that I can apply the 2-day rule when we take those practice exams (see above). I can also tell you that poor attendance is one of the best ways to hurt you overall chances of success - third floor, Murphy Center. The book publisher, Prentice-Hall, has provided a set of CDs that contain lectures for each chapter in the text, covering the main key ideas in that chapter. I will put this set of CDs on reserve in the library; you might want to consider watching some of these lectures, especially if you are having trouble with some material. These CDs should run in the CD-drive of any computer. I also want you to consider coming to see me if you have a problem with some material. Sometimes we can resolve in a few minutes a difficulty that can cause problems for weeks. I don't resent your coming – it's part of my job! I want your success as much as you do. BLACKBOARD: I'm not sure how much I will be using "Blackboard" but I will enter you into the system and it will give us a resource, at least for web sites that might be interesting and useful group-mates. Please feel free to come to my office to discuss problems you might be having. Please feel free to go visit the learning center for tutoring help if necessary
Number The students will develop an algebraic expression from geometric representations and ultimately graph quadratic equations with understanding. The students will also develop a better understanding of algebraic expressions by comparing with geometric, tabular, and graphical representationsThis lesson unit is intended to help teachers assess how well students are able to solve quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation.
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education. CS034Intro to Systems ProgrammingDoeppner & Van HentenryckLab 6Out: Wednesday 9 March 2005 What youll learn.Modern C+ comes with a powerful template library, the Standard Template Library, or STL. The STL is based on the independent concepts MAT125.R92: QUIZ 0SOLUTIONSNo score will be assigned for this quiz. The graph of the function f (x) is given below:11(a) Determine the domain and range of f (x). Domain: 4 < x < 1 and 1 < x < 4 (or, in other notations, (4, 1) and (1, 4). We Chemistry 112B: Organic Chemistry Winter 2008 Professor Rebecca Braslau Assigned Homework Problems The following problems are required, and must be turned in. Problems are to b e done without looking at the answers as much as possible, then corrected 1 Problem 37 section 4.1. We have the situation shown in the gure, where v is the velocity, (xb , yb ) are the coordinates of the runner, xa is the x-coordinate of the runners friend (we do not show the y -coordinate of the runners friend since it is MAT123 - Introduction to calculus Second Practice Midterm The Second Midterm will be on Tuesday 11/11 at 8:30pm at Harriman 137. Important: check the webpage to get a copy of Second Midterm of Fall 2007! Question 1. Compute: (a) log2 (16) (b) ln e3 + Math 127 - S2008 Practice Test for the Final Examination1. Show that the function y =Ccos(x) x2is a solution of the dierential equationx2 y + 2xy = sin(x). For what value of C does the solution satisfy the initial condition y(2) = 0? 2. Find th Answers for HW 9 3. Usually, one may compute the 1st, 2nd and 3rd derivatives of f at to get the 6 T3 . For this problem, one may also use sin(y + z ) = sin y cos z + cos y sin z to get the whole Taylor series of f. Just take y = x and z = .(Sinc Math 127 - Spring 2008 Practice for Second Examination1. Find the interval of convergence for the power series(1)n+1n=2(x 6)2n . n12 3n2. Find the MacLaurin series for the function ex 1 f (x) = . x3 3. Find the sum of the innite series 2 3 Calculus Early Exam February 5, 2003Instructions: The exam consists of 15 multiple choice questions. You have 90 minutes to answer all fteen questions. Be sure to record your answers on the opscan form. You are not allowed to use any books, notes, o MAT131 Spring 2003 Midterm II SolutionProblem Score Max 21 12 8 1 2 3 4 5 6 TotalUse of calculators, books or notes is not allowed. Show the all steps you made to find the answers. Write carefully, points may be taken off for meaningless stateme MAT 331: Mathematical Problem Solving with ComputersStony Brook, Fall 2008General Information: This course serves as an introduction to computing for the math student. After a general introduction to the use of the computers, we will turn to more Natasha Tuskovich Friday, June 12, 2009E. coli Bio-ThermometerIntroduction A biological thermometer would ideally be a simple, accurate and easily observable register of the organisms environment. A basic version is comprised of E. coli cells that Math 331, Fall 2008, Problems1. Compute IFS parameters and the similarity dimension of the following fractal.1.00.750.50.250.0 0.0 0.25 0.5 0.75 1.02. (a) Find the IFS parameters to generate atractor of the Picture: a right gasket of side Chapter 5 A turtle in a fractal garden1 Turtle GraphicsImagine you have a small turtle who responds to certain commands like move forward a step, move back a step, turn right, and turn left. Imagine also that this turtle carries a pen (or just lea MAT331 Exercises, Fall 0812.4Write a procedure in Maple that counts the frequency of letters in a string of text. For example, here is what it looks like when I use mine: freqs("time flies like an arrow, fruit flies like a bananna."); [" ",9], [
In order to provide you with quality study material and help students to obtain excellent education, Globalshiksha has come up with Topchalks Class XI Maths for CBSE students. This pack consists of 2 CD which is designed strictly on the basis of CBSE syllabus. Every chapter is given in systematic form to make it comprehensive and easy for the students. This CD is helpful for making strong foundation for your further studies. Product Specifications Brand Topchalks Class 11 std Subject Mathematics Educational Board CBSE Number of CD 2 CDs No. of Chapters 15 No. of lectures taught 456 Solved problems 1140 Fully Solved Question Papers 5 No. Of hours 85 hours Chapters Covered Sets Ø Introduction, sets and their representations Ø Empty sets, finite, infinite and equal sets Ø Subset, power set, universal set and examples Ø Intervals and Questions Ø Venn diagrams, operations on sets Ø Complement of set and questions Ø Practical problems on union and intersection of two sets Ø Properties of different sets Ø Questions Relations and Functions Ø Cartesian product of sets and ordered pair and triplets Ø Questions and properties of product of sets Ø Cartesian product and relations Ø Functions Ø Identity, constant, polynomial, quadratic, cubic functions Ø Rational, modulus, signum, greatest integer functions Ø Algebra of Real Functions Ø Domain, range, co-domain and examples Ø Questions Trigonometric Function Ø Revision of Class X Ø Degree measure Ø Radian measure, relation bewtween degree and radian Ø Trigonometric functions and sign of trigonometric functions Ø Value of trigonometric Ø Domain and range of trigonometric functions Ø Graph of sin x and cos x Ø Graph of tan x Ø Trigonometric functions of sum and difference of two angles Ø Trigonometric functions of sum and difference of two angles continued (product to sum and sum to product and some examples on these)
Ray's Arithmetic Curriculum by Mott Media Used in the 1800's, Ray's Arithmetic taught math to generations. This set presents principles and follow up each one with examples which include difficult problems to challenge the best students. Students who do not master a concept the first time can return to it later, work the more difficult problems, and master the concepts. Thus in these compact volumes is a complete arithmetic course to study in school, to help in preparation for ACT and SAT tests, and to use for reference throughout a lifetime. NOTE: The publisher, Mott Media, made the decision to keep prices down by switching from hardback to paperback. When each of the books in the series is reprinted, it will be in the paperback version. At present, the Primary Arithmetic and Intellectual Arithmetic are paperbacks. Ray's Arithmetic 8-Volume Set Ray's Arithmetic 8 Volume Set By Joseph Ray, Publisher: Mott Media Included in the Ray's Arithmetic 8-Volume Set are one of each of the following books: Key to Ray's New Higher Arithmetic Key to Ray's Higher Arithmetic Key to Ray's Higher Arithmetic has answers to problems in the higher book. This key provides basic answers. Hardback ISBN-13: 9780880620567 List $12.99 Sale Price $11.95 Parent Teacher Guide Parent-Teacher Guide for Ray's New Arithmetics By Ruth Beechick, Publisher: Mott Media The Ray's New Arithmetics Parent-Teacher Guide gives unit by unit helps for teaching; suggests grade levels for each book; provides progress chart samples for each grade and tests for each unit. It is written by Dr. Ruth Beechick who is known for her practical and academic approach to teaching. If you want help with teaching, planning, and structuring your curriculum, then you need this guide.
Students are able to interact with the program using different functions and different intervals. A multitude of functions can be investigated within minutes. Ambitious students can also start investigating the different commands and programming in Mathematica. There are several concepts in the programming syntax that one could spend time on to understand. Nontechnology Comparison Classroom examples on the blackboard can be done but with limitations. Students may get bogged down on the solving of algebraic equations. This module bypasses this issue and tries to focus the students on the existence of such a point, rather than the computations. Pertinent Issues While some of the code may intrigue some students, it may terrify others. This module was not written to have students understand the code behind it but rather to utilize its functionality. To the beginning student, few lines need to be changed to look at different functions on different intervals. Any value(s) that may need to be changed is spelled out in the heading of each section of code. How to use in the Classroom This module is a good exploration for the student to visualize and interpret the Mean Value Theorem. The best way for exploration is to have student at computer with copies of the program in front of them so they can explore at their own leisure.
DescriptionFeatures Students will find many opportunities to check and reinforce their understanding of concepts throughout each chapter: Student Practice problems are paired with every example in the text. The full solutions to each practice problem are located in the back of the text, allowing students to check their work as they go. The "How Am I Doing?" mid-chapter review exercises let students pause at a critical juncture to make sure they are "getting it." End-of-Section Exercises progress from basic to challenging, and each exercise set includes Verbal and Writing Skills, and Mixed Practice exercises. A Quick Quiz at the end of each exercise set contains three problems that cover the essential content of that section. This simple assessment tool measures whether students know when they are ready for new material, and when they need further review. A Concept Check question at the end of each Quick Quiz asks students to explain how and why a method works in their own words, forcing students to analyze problems and reflect on the mathematical concepts. Classroom Quizzes in the Annotated Instructor's Edition parallel every Quick Quiz, which allows instructors to quickly assess the understanding of the class at any point in the chapter. The End-of-Chapter Material provides several opportunities for review and reinforcement of key concepts: Updated! Chapter Organizers summarize the chapter topics, procedures, and corresponding examples all in one place to simplify chapter review. A "You Try It" column has been added to Chapter Organizers to provide another opportunity for practice! NEW! Assessment Check boxes on the "How Am I Doing?"Chapter Test encourage students to check their work. If students need extra help on any test problems, they can watch the Chapter Test Prep Videos, where all test solutions are worked out on video. NEW! The Math Coach follows every chapter test and provides helpful hints and coaching on the most difficult concepts and exercises types in that particular chapter. Examples similar to the Math Coach problems have been noted throughout the chapter with side-by-side examples and practice problems that encourage students to try the practice problem on the spot. Students can have an office hour with the authors when they watch the authors solve these key problem types on the New Math Coach Videos. The Chapter Test Prep and Math Coach Videos are available in MyMathLab and on YouTube. Use Math to Save Money features practical, realistic examples in every chapter of how students can use math to cut costs and spend less. Topics have been updated based on a student survey of more than 1,000 developmental math colleges. A Mathematics Blueprint for Problem Solving provides a consistent and interactive outline to help students organize their approach to problem solving. The Blueprint helps students decide where to begin, understand the process, plan subsequent steps, and successfully solve applications. Author
Algebra 2 Tutorials Algebra 2 builds upon previous algebraic concepts such as Powers, Roots, and Radicals and expand to more advanced levels such as Polynomials and Factoring and Conic Sections – Hyperbolas. Sophisticated applications are found in Exponents and Logs where you will develop special scales for measurement, used for the Richter scale for earthquake magnitude, and the pH scale for acidity. Methods for solving Systems of Linear Equations and Inequalities and Rational Functions are covered in our more basic topics which provide strong proficiency to master Matrices and Determinants. Algebra 2 is a highly integrated subject that establishes strong foundational skills and supports mastery at more advanced levels that are sure to challenge you. Linear Equations and Functions Everyone knows that you have to walk before you can run; therefore, we'll be tackling linear equations before moving onto direct variation equations. In Linear Equations and Functions we'll begin by explaining exactly what a function is by going over Functions vs. Relations. Once you have an understanding of what a function is, we'll review the most basic type of function in the form of linear equations. After reviewing linear equations, we'll go over Direct Variation Equations so that you will have a better understanding of slope, which is a concept that will stay with you until Calculus and beyond. AVAILABLE PATHWAYS Equations and Inequalities In Equations and Inequalities we begin by reviewing how to solve and graph equations and inequalities. After reviewing, we'll focus on working with special types of equations and inequalities involving absolute values. The goal is to help you understand how equations and inequalities can be applied to our everyday lives. AVAILABLE PATHWAYS Conic Sections - Hyperbolas If you've ever come across two identical twins you might have a hard time telling them apart. Likewise, before Conic Sections – Hyperbolas you might have had a hard time differentiating between a parabola and a hyperbola. Here our aim is to study The Hyperbola very closely. We will study such things as The Eccentricity of a Hyperbola and learn how to recognize The Graph of a Hyperbola. In the same way you can differentiate between twins by getting to know their personalities, we will differentiate between a parabola and hyperbola by understanding the differences in their behavior. AVAILABLE PATHWAYS Polynomials and Factoring Ready to earn your higher degree? In Polynomials and Factoring we will review how to recognize what a polynomial function is and how to work with Higher Degree Polynomials. This lesson teaches you how to recognize a polynomial function when you see one. In addition, we will go over how to determine the behavior of any polynomial and graph that behavior. With this knowledge you will learn how to convey a great deal of information in many different fields such as medicine, aeronautics, and even car racing. AVAILABLE PATHWAYS Powers, Roots, and Radicals Are your surgical tools ready? If not, find them quick, because we'll be operating on functions in no time! In Powers, Roots, and Radicals we will go over polynomial, root, and exponential functions. We will demonstrate how to perform several different operations on these functions including: addition, subtraction, multiplication, and division. We will also go over what it means to take The Function of a Function and what Inverse Functions are. The goal is to help you not only recognize these functions, but be able to perform different types of transformations on them as well. AVAILABLE PATHWAYS Rational Expressions Have you ever wondered what the difference is between simple algebraic expressions and rational expressions? Or maybe you have wondered what Algebraic Fraction Equations are. No?! Well...you are now! In Rational Expressions we will not only go over what rational expressions are, but how to manipulate and solve them using familiar methods such as multiplication and division and new methods such as Reducing through Basic Factoring. AVAILABLE PATHWAYS Sequences and Series It is human nature to look for patterns in the world around us. Since the purpose of mathematics is to relate to the world through numbers, it is logical that we try to find patterns in numbers. In Sequences and Series we go over what the Terms in Sequences represent and how to recognize patterns in a sequence or series. Because some patterns are quite complex, we will go over different types of patterns such as Geometric Series and Sequences. This all culminates with us trying to predict future events through the use of mathematical induction. AVAILABLE PATHWAYS Trigonometric Identities In Trigonometric Identities we will introduce the tools available to you when working with problems involving trigonometric functions. The goal is to not only help you understand how to prove that two sides of an equation are equal, but to make you comfortable with the different Trigonometric Techniques used to relate one trigonometric function to another. AVAILABLE PATHWAYS The Unit Circle There are six different trigonometric functions that you have been dealing with and each has their own behavior. Often times it can be difficult to remember how a particular function behaves but have no fear, The Unit Circle is here. We will go over what The Unit Circle is and how it can be used to represent trigonometric functions. You may even be moved to tears after understanding the beauty behind the Coordinates on the Unit Circle and how the different trigonometric functions are related to one another. AVAILABLE PATHWAYS Graphing Trigonometric Functions You have probably observed that if you throwing a rock in water causes ripples. What if you could model these waves by using a Sine Wave or a Cosine Wave? Remember that mathematics is just a means by which we try to model the world around us in terms of numbers. In Graphing Trigonometric Functions we will explore the different parts of a trigonometric function and show how you can manipulate them to even model ripples of water. AVAILABLE PATHWAYS Trigonometric Equations Have you ever wondered why a ladder placed against a wall might sometimes slide and at other times stay still? Although this is a physics problem, the physicists turn to mathematicians for a bit of help. Before you can solve this problem you will need to understand the mathematics behind the equations governing this problem. In Trigonometric Equations we will go over how to do just that by exploring concepts such as Inverse Sine. AVAILABLE PATHWAYS Statistics and Probability Have you ever wondered how a meteorologist can predict rain fall amounts or the liklihood of a sunny day? A lot of it has to do with Statistics and Probability, where we will be laying the foundation you will need in order to analyze data and make predictions from a set of data. For example, we will go over what the different Measures of Variation are and how finding the mean, median, and mode of a given set of data can help you determine the chances of an event, such as rain, occurring. AVAILABLE PATHWAYS Introduction to Matrices Neo, Neo, are you there? Could you find your way out of and into the Matrix like Neo did? In Introduction to Matrices we introduce Matrices and demonstrate how they are used to organize data. Once you understand a matrix's different elements we will go over how to perform different types of operations concerning matrices such as Adding and Subtracting Matrices and Matrix Multiplication. This knowledge will serve as your foundation when working with more advanced matrix concepts. AVAILABLE PATHWAYS Matrices In The Matrix, Neo asks Trinity, "What is the Matrix?" She replies, "The answer is out there, Neo, and it's looking for you, and it will find you if you want it to." In Matrices we will build upon the foundation set in Introduction to Matrices, providing more answers to your questions. We will introduce more complex operations such as Gaussian Elimination and Gauss-Jordan Elimination and demonstrate how to perform them. Learning these concepts will enable you to solve any nxn matrix. AVAILABLE PATHWAYS Determinants In Determinants we introduce one of the most important properties regarding matrices -- how to control mankind! Just kidding. However, we will demonstrate some new methods for working with matrices. Using Determinants we will show how to solve matrices more easily and even determine if a matrix has a solution without having to solve them completely.
More About This Book Setting up residence in a pizza parlor, Clifford Pickover focuses on procedures for solving problems, offering short, easy-to-digest chapters that allow you to quickly get the essence of a technique or question. From exponentials and logarithms to derivatives and multiple integrals, the book utilizes pepperoni, meatballs, and more to make complex topics fun to learn-emphasizing basic, practical principles to help you calculate the speed of tossed pizza dough or the rising cost of eggplant parmigiana. Plus, you'll see how simple math-and a meal-can solve especially curious and even mind-shattering problems. Authoritatively and humorously written, Calculus and Pizza provides a lively-and more tasteful-approach to calculus. "Pickover has published nearly a book a year in which he stretches the limits of computers, art, and thought." -Los Angeles Times "A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today." -Journal of Recreational Mathematics Related Subjects Meet the Author CLIFFORD A. PICKOVER is a research staff member at the IBM T. J. Watson Research Center. He is also a prolific author of books and articles relating to science, art, and mathematics, including Black Holes: A Traveler's Guide and Keys to Infinity, both
The book is the second revised edition of the textbook on Real Analysis of functions of one variable (first published in 2001 (Zbl 1093.26003)). The main feature of the book is its instructive character. The author tries to explain the most known questions of calculus and analysis on very simple examples and counterexamples by using geometrical illustration, analogies in other mathematical disciplines. In particular, he uses the ideas of recent books which are brilliant additions to a standard course of Analysis [{\it J. Appell}, Analysis in examples and counterexamples. An introduction to the theory of real functions. Springer-Lehrbuch. Berlin: Springer (2009; Zbl 1168.26001)]; [{\it V. M. Shibinskii}, Examples and counter-examples in a course on mathematical analysis. Moskva: Vysshaya Shkola (2007; Zbl 1198.26001)]. Another interesting characteristic of the book is the utilization of elements of foundation of the Set Theory, Number Theory and Analysis. This helps the reader to reach a better understanding of the main ideas of Real Analysis. In this sense the book is self-contained and can be recommended to private study or to the study of analysis on a higher level. The structure of the book is the following. It starts with some preliminaries presented in the Chapter 0 "Sets, Relations and Mappings". This is the basis for a presentation of the foundations of Analysis and Numbers Systems (Chapter 1 "Foundation of Analysis", Chapter 2 "Systems of Real Numbers"). In the main part of the book only general ideas are given. A more formal presentation is contained in Appendix A "Systems of Sets, Relations and Partitions" and in Appendix B "Construction of Real Numbers". Standard results from the Agenda of Analysis 1 for first year students in Pure and Applied Mathematics are presented in the next chapters. In a sense this presentation is close to the traditional classical books of Analysis in Germany, France and Russia. This material is gathered in Chapter 3 "Infinite Series", Chapter 4 "Continuous Functions in one Variable", Chapter 5 "Differential Calculus in one Variable", Chapter 6 "Elementary Transcendental Functions", Chapter 7 "Integral Calculus", Chapter 8 "Riemann Integral". Additionally, the author describes certain elementary facts of Complex Analysis in Appendix C "Elementary Complex Analysis". Surely, the book can be recommended as a textbook on Analysis 1 for first year students in Pure and Applied Mathematics. Reviewer: Sergei V. Rogosin (Minsk)
Math Success Deluxe is ideal for helping students at all learning levels find success. Inspire your child to keep learning while helping him or her build confidence in all areas of mathematics. This math software was created by educational experts to make the subject fun and easy to learn, from the basics all the way up to Algebra and Trigonometry. Featuring educator-endorsed and award-winning lessons including more than 1900 exercises and 300 fun activities, Math Success will improve comprehension in multiple subjects. Math Success Deluxe is a complete math learning system to help you get better grades fast - and it comes with free homework help from Tutor.com. Product Highlights Covers 80+ subjects 1,900+ exercises 300+ fun activities Easy-to-follow lessons For all learning levels Product Features Basic Math - More than 40 lessons cover math subjects to help prepare middle and high school students for more advanced concepts or help adult learners brush up on essentials Understand fractions and decimals Create factor trees How to get percentages Statistics explained Determine perimeter and area Pre-Algebra - Challenging problems are broken down in 66 simple lessons and more than 50 exercises, making pre-algebra subjects easy for every student to learn. How to reduce, multiply, compare fractions and more Figure out word problems Learn the Order of Operations When to use substitution Convert numbers to Scientific Notation Algebra I - Interactive quizzes, detailed explanations, and a helpful database of terms help make difficult subjects, including graphing, exponents, and more, easier for students to understand. Trigonometry - Students get help with more than 170 quiz questions, over 30 lessons, and 36 skill-building activities, plus useful resources give clear explanations on complex trigonometry subjects. How to graph sine and cosine Understand trigonometric functions and equations Learn polar and Cartesian coordinates The law of sines explained Master the trigonometric form of complex numbers Geometry - Build math skills for subjects that go beyond the classroom. Take the quizzes, use the animated exercises, and get helpful explanations of geometry subjects, from a circle to a quadrilateral. Non-Euclidean geometry explained Help with reasoning and equality Figure area, circumference and more Tips for space geometry Master angle measurements and vectors Probability and Statistics - Students will no longer be daunted by these advanced subjects with help from more than 30 lessons, over 165 quiz questions, and 25 skill-building activities.
Synopses & Reviews Publisher Comments: If you are looking for a quick nuts-and-bolts overview, turn to Schaum's Easy Outlines Schaum's Easy Outline of College Mathematics is a pared-down, simplified, and tightly focused review of the topic. With an emphasis on clarity and brevity, it features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form. Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give you quick pointers to the essentials. Expert tips for mastering college mathematics Last-minute essentials to pass the course Easily understood review of college mathematics Supports all the major textbooks for college mathematics courses Appropriate for the following courses: Introduction to Mathematical Modeling, Pre-Calculus, Discrete Mathematics, Trigonometry, College Algebra, Calculus
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The Math Book - Cliff Pickover In The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, author Clifford A. Pickover reveals the magic and mystery behind some of the most significant mathematical milestones as well as the oddest objects ...more>> The Mathemagician - Andrew Jeffrey "Magic of Maths" shows interweave magic and comedy with "clear positive and motivational messages about the learning of maths." A former teacher and professional magician based in the UK, Jeffrey also sells original products such as Maths at the Drop ...more>> Mathematica in Higher Education - Wolfram Research Lessons, resources, books, and classroom packs for making Mathematica software an integral part of math education in university and college classrooms. 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Book summary With over a million users around the world, the Mathematica ® software system created by Stephen Wolfram has defined the direction of technical computing for nearly a decade. With its major new document and computer language technology, the new version, Mathematica 3.0 takes the top-power capabilities of Mathematica and make them accessible to a vastly broader audience. This book presents this revolutionary new version of Mathematica. The Mathematica Book is a must-have purchase for anyone who wants to understand the revolutionary opportunities in science, technology, business and education made possible by Mathematica 3.0. This encompasses a broad audience of scientists and mathematicians; engineers; computer professionals; quantitative financial analysts; medical researchers; and students at high-school, college and graduate levels. Written by the creator of the system, The Mathematica Book includes both a tutorial introduction and complete reference information, and contains a comprehensive description of how to take advantage of Mathematica's ability to solve myriad technical computing problems and its powerful graphical and typesetting capabilities. Like previous editions, the book is sure to be found well-thumbed on the desks of many technical professionals and students around the world. [via]
YOU ARE HERE » Sections Mathematics Curriculum Goals: Students will acquire mathematical skills, including the ability to perform routine computations and symbolic manipulation. Students will develop an understanding of fundamental mathematical concepts. Students will become mathematical problem solvers. Students will learn to value mathematics and the quantitative nature of our world. Elementary The Lincoln Public Schools elementary mathematics program is balanced with respect to curricular content and instructional approaches. In addition to traditional computational skills, topics from geometry, algebra, data analysis, and measurement are included at appropriate levels. The program utilizes concrete materials and experiences within the context of teacher-directed instruction to convey meaning and help motivate students to learn mathematics. Middle School Although the mastery of fundamental skills remains important, the focus at the middle level shifts to algebra and geometry readiness. The middle level program stresses algebra and geometry readiness because knowledge of these subjects is essential for success in the mathematics course that follow. The district goal is for students to take Algebra in Grade 8. High School The high school curriculum is built around a core of topics that all students will have an opportunity to study regardless of the courses they take. These core topics come from the areas of algebra, geometry, measurement, data analysis and probability. In order to graduate from high school, students must take two-years of high school mathematics, including first-year algebra.
September 2007 This is the second installment of a new feature in Plus : the teacher package. Every issue contains a package bringing together all Plus articles about a particular subject from the UK National Curriculum. Whether you're a student studying the subject, or a teacher teaching it, all relevant Plus articles are available to you at a glance. A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling . Mathematical models are used not only in the natural sciences (such as physics , biology , earth science , meteorology ) and engineering disciplines (e.g. computer science , artificial intelligence ), but also in the social sciences (such as economics , psychology , sociology and political science ); physicists , engineers , statisticians , operations research analysts and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour. Mathematical models can take many forms, including but not limited to dynamical systems , statistical models , differential equations , or game theoretic models . The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is subtracted from the desired value to create the error signal, which is amplified by the controller. A signal-flow graph (SFG) is a special type of block diagram [ 1 ] —and directed graph —consisting of nodes and branches. Its nodes are the variables of a set of linear algebraic relations. An SFG can only represent multiplications and additions. Little Green Book Nearly everything that occurs in the universe can be considered a part of some system, and that certainly includes human behavior and, potentially, human attitudes as well. But this does not mean that systems theory, and thus graph algebra, is appropriate for use in all situations. There are many competing approaches to the study of social and political phenomena, and systems theory using graph algebra is only one such approach. From the publisher's description of the book: Graph Algebra: Mathematical Modeling with a Systems Approach introduces a new modeling tool to students and researchers in the social sciences. Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modeling that offers social scientists a variety of tools that are both sophisticated and easily applied. Key Features: (This is the first in a series on the use of Graph Algebraic models for Social Science.) Linear Difference models are a hugely important first step in learning Graph Algebraic modeling. That said, linear difference equations are a completely independent thing from Graph Algebra. (This is the second of a series of ongoing posts on using Graph Algebra in the Social Sciences.) First-order linear difference equations are powerful, yet simple modeling tools. They can provide access to useful substantive insights to real-world phenomena. They can have powerful predictive ability when used appropriately. Additionally, they may be classified in any number of ways in accordance with the parameters by which they are defined. And though they are not immune to any of a host of issues, a thoughtful approach to their application can always yield meaningful information, if not for discussion then for further refinement of the model. Data must be selected carefully. The predictive usefulness of the model is grossly diminished if outliers taint the available data. Figure 1, for instance, shows the Defense spending (as a fraction of the national budget) between 1948 and 1968. Note how the trend curve (as defined by our linear difference model from the last post : see appendix for a fuller description) is a very poor predictor. Whatever is going on here isn't a first-order process. This is sort-of related to my sidelined study of graph algebra. I was thinking about data I could apply a first-order linear difference model to, and the stock market came to mind. After all, despite some black swan sized shocks, what better predicts a day's closing than the previous day's closing? So, I hunted down the data and graphed exactly that:
MA THEME TICS Mathematics reveals hidden patterns that help us under- stand the world around us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from sci- ence; with inference, deduction, and proof; and with math- ematical models of natural phenomena, of human behavior, and of social systems. The cycle from data to deduction to application recurs everywhere mathematics is used, from everyday household tasks such as planning a long automobile trip to major man- agement problems such as scheduling airline traffic or man- aging investment portfolios. The process of "doing" math- ematics is far more than just calculation or deduction; it involves observation of patterns, testing of conjectures, and estimation of results. As a practical matter, mathematics is a science of pattern and order. its domain is not molecules or cells, but num- bers, chance, form, algorithms, and change. AS a science of abstract objects, mathematics relies on logic rather than on observation as its standard of truth, yet employs obser- vation, simulation, and even experimentation as means of discovering truth. M: ~ ~ ~ athematics is a science of pattern and order. The special role of mathematics in education is a con- sequence of its universal applicability. The results of mathematics theorems and theories-are both significant and useful; the best results are also elegant and deep. Through its theorems, mathematics offers science both a foundation of truth and a standard of certainty. In addition to theorems and theories, mathematics of- fers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimiza- tion, logical analysis, inference from data, and use of sym- bols. Experience with mathematical modes of thought builds searching for patterns Mathematical Modes of Thought Modeling Representing worldly phenomena by mental constructs, often visual or symbolic, that capture important and useful fea tures. Optimization Finding the best solution (least expensive or most efficient) by asking "what if' and exploring all possibilities. Symbolism- Extending natural language to symbolic represen- tation of abstract concepts in an economical form that makes pos- sible both communication and computation. Inference Reasoning from data, from premises, from graphs, from incomplete and inconsistent sources. Logical Analysis Seeking impli- cations of premises and searching for first principles to explain ob- served phenomena. Abstraction Singling out for spe- cial study certain properties com- mon to many different phenom- ena. 31 OCR for page 32 Mathematics Back to School Design a dog house that can be made from a single 4 ft. by ~ ft. sheet of plywood. Make the dog house as large as possible and show how the pieces can be laid out on the plywood before cut- ting. 32 mathematical power a capacity of mind of increasing value in this technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to sug- gest alternatives. Mathematics empowers us to understand better the information-laden world in which we live. Our Invisible Culture Mathematics is the invisible culture of our age. Although frequently hidden from public view, mathematical and sta- tistical ideas are embedded in the environment of technology that permeates our lives as citizens. The ideas of mathemat- ics influence the way we live and the way we work on many different levels: · Practical knowledge that can be put to immediate use in improving basic living standards. The ability to compare loans, to calculate risks, to figure unit prices, to understand scale drawings, and to appreciate the effects of various rates of inflation brings immediate real benefit. This kind of basic applied mathematics is one objective of universal elementary education. · Civic concepts that enhance understanding of public pol- icy issues. Major public debates on nuclear deterrence, tax rates, and public health frequently center on scien- tific issues expressed in numeric terms. Inferences drawn from data about crime, projections concerning population growth, and interactions among factors affecting interest rates involve issues with essentially mathematical content. A public afraid or unable to reason with figures is unable to discriminate between rational and reckless claims in pub- lic policy. Ideally, secondary school mathematics should help create the "enlightened citizenry" that Thomas lef- ferson called the only proper foundation for democracy. · Professional skill and power necessary to use mathemat- ics as a tool. Science and industry depend increasingly on mathematics as a language of communication and as a methodology of investigation, in applications ranging from theoretical physics to business management. The principal OCR for page 33 ...searchi1lg for patterns M athematics is a profound and powerful part of human culture. goal of most college mathematics courses is to provide stu- dents with the mathematical prerequisites for their future careers. · Leisure- disposition to enjoy mathematical and logical challenges. The popularity of games of strategy, puzzles, lotteries, and sport wagers reveals a deep vein of amateur mathematics lying just beneath the public's surface indif- ference. Although few seem eager to admit it, for a lot of people mathematics is really fun. · Cultural the role of mathematics as a major intellectual tradition, as a subject appreciated as much for its beauty as for its power. The enduring qualities of such abstract concepts as symmetry, proof, and change have been devel- oped through 3,000 years of intellectual effort. They can be understood best as part of the legacy of human culture which we must pass on to future generations. indeed, it is only when mathematics is viewed as part of the human quest that lay persons can appreciate the esoteric research of twentieth-century mathematics. Like language, religion, and music, mathematics is a universal part of human cul- ture. These layers of mathematical experience form a matrix of mathematical literacy for the economic and political fabric of society. Although this matrix is generally hidden from public view, it changes regularly in response to challenges arising in science and society. We are now in one of the periods of most active change. From Abstraction to Application During the first half of the twentieth century, mathe- matical growth was stimulated primarily by the power of l ``Ifyou want to under- stand nature, you must be conversant with the lan- guage in which nature speaks to users - Richard Feynman 33 OCR for page 34 Mathematics Strictly Speaking MATHEMATICAL SCIENCES is a term that refers to disciplines that are inherently mathematical (for example, statistics, logic, ac- tuarial science), not to the many natural sciences (for example, physics) that employ mathemat- ics extensively. For economy of language, the word "mathemat- ics" is often used these days as a synonym for "mathematical sci- ences," as the term "science" is often used as a summary term for mathematics, science, engineer- ing, and technology. 34 abstraction and deduction, climaxing more than two cen- turies of effort to extract full benefit from the mathematical principles of physical science formulated by Isaac Newton. Now, as the century closes, the historic alliances of mathe- matics with science are expanding rapidly; the highly devel- oped legacy of classical mathematical theory is being put to broad and often stunning use in a vast mathematical land- scape. Several particular events triggered periods of explosive growth. The Second World War forced development of many new and powerful methods of applied mathematics. Postwar government investment in mathematics, fueled by Sputnik, accelerated growth in both education and research Then the development of electronic computing moved math- ematics toward an algorithmic perspective even as it pro- vided mathematicians with a powerful too! for exploring patterns and testing conjectures. At the end of the nineteenth century, the axiomatization of mathematics on a foundation of logic and sets made pos- sible grand theories of algebra, analysis, and topology whose synthesis dominated mathematics research and teaching for the first two thirds of the twentieth century. . · . ~. ~ These tradi- onal areas nave now oeen supplemented oy major develop- ments in other mathematical sciences in number theory, logic, statistics, operations research, probability, computa- tion, geometry, and combinatorics. In each of these subdiscinTines~ __ 7 applications parallel theory. Even the most esoteric and abstract parts of mathematics number theory and Tocic. for example are now used routinely in applications (for example, in com- puter science and cryptography). Fifty years ago, the leading British mathematician G. H. Hardy could boast that number theory was the most pure and least useful part of mathemat- ics. Today, Hardy's mathematics is studied as an essential prerequisite to many applications, including control of au- tomated systems, data transmission from remote satellites, protection of financial records, and efficient algorithms for computation. ., . OCR for page 35 ...searching for patterns Mathematics is the foundation of science and technology. Without strong mathematics, there can be no strong science. in 1960, at a time when theoretical physics was the central jewel in the crown of applied mathematics, Eugene Wigner wrote about the "unreasonable effectiveness" of mathematics in the natural sciences: "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither under- stand nor deserve." Theoretical physics has continued to adopt (and occasionally invent) increasingly abstract math- ematical models as the foundation for current theories. For example, Lie groups and gauge theories exotic expressions of symmetry are fundamental tools in the nhv~icist's search for a unified theory of forces. ~, _ ~ , During this same period, however, striking applications of mathematics have emerged across the entire landscape of natural, behavioral, and social sciences. All advances in design, control, and efficiency of modern airliners depend on sophisticated mathematical models that simulate perfor- mance before prototypes are built. From medical technology (CAT scanners) to economic planning (input/output models of economic behavior), from genetics (decoding of DNA) to geology (locating of! reserves), mathematics has made an indelible imprint on every part of modern science, even as science itself has stimulated the growth of many branches of mathematics. Applications of one part of mathematics to another of geometry to analysis, of probability to number theory- provide renewed evidence of the fundamental unity of math- ematics. Despite frequent connections among problems in science and mathematics, the constant discovery of new al- liances retains a surprising degree of unpredictability and serendipity. Whether planned or unplanned, the cross- fertilization between science and mathematics in problems, "Equations are just the boring par' of mathematics. reattempt to see thi1'gs it' terms of geometry." - Stephen Hawking OCR for page 36 Mathematics Myth: As computers become more powerful, the need for mathematics will decline. Reality: Far from diminishing the importance of mathematics, the pervasive role of computers in science and society contributes to a greatly increased role for math- ematical ideas, both in research and in civic responsibility. Be- cause of computers, mathematical ideas play central roles in impor- tant decisions on the job, in the home, and in the voting booth. 36 theories, and concepts has rarely been greater than it is now, in this last quarter of the twentieth century. Computers Alongside the growing power of applications of mathemat- ics has been the phenomenal impact of computers. Even mathematicians who never use computers may devote their entire research careers to problems arising from use of com- puters. Across all parts of mathematics, computers have posed new problems for research, supplied new tools to solve old problems, and introduced new research strategies. Although the public often views computers as a replace- ment for mathematics, each is in reality an important too} for the other. Indeed, just as computers afford new opportu- nities for mathematics, so also it is mathematics that makes computers incredibly elective. Mathematics provides ab- stract models for natural phenomena as well as algorithms for implementing these models in computer languages. Ap- plications, computers, and mathematics form a tightly cou- pled system producing results never before possible and ideas never before imagined. Computers influence mathematics both directly- through stimulation of mathematical research and indirectly by their effect on scientific and engineering practice. Comput- ers are now an essential too} in many parts of science and engineering, from weather prediction to protein engineer- ing, from aircraft design to analysis of DNA. In every case, a mathematical mode! mediates between phenomena of sci- ence and simulation provided by the computer. Scientific computation has become so much a part of the everyday experience of scientific and engineering practice that it can be considered a third fundamental methodology of science-parallel to the more established paradigms of experimental and theoretical science. Computer models of natural, technological, or social systems employ mathemati- cally expressed principles to unfold scenarios under diverse conditions scenarios that formerly could be studied only through lengthy (and often risky) experiments or prototypes. The methodology of scientific computation embeds mathe OCR for page 37 ...searchi1'g for patterns matical ideas in scientific models of reality as surely as do axiomatic theories or differential equations. Computer models enable scientists and engineers to reach quickly the mathematical limits permitted by their models. Robotics design, for instance, often encounters limits im- posed not by engineering details, but by incomplete under- standing of how geometry controls the degrees of freedom of robot motions. Models of weather forecasting consistently reveal uncertainties that suggest intrinsically chaotic behav- ior. These models also reveal our severely limited knowledge of the mathematical theory of turbulence. Whenever a sci- entist or engineer uses a computer mode! to explore the fron- tiers of knowledge, a new mathematical problem is likely to appear. Computer models have extended the mathematical sciences into every corner of · . ~ . · · . sclentl~c anc . engineering practice. Whereas, traditionally, scientists and engineers who were engaged primarily in experimental research could get along with a small subset of mathematical skills uniquely suited to their field, now even experimentalists need to know a wide range of mathematical methods. Small errors of approxi- mation that are intrinsic to all computer models compound, like interest, with subtle and often devastating results. Only a person who comprehends the mathematics on which com- puter models are based can use these models effectively and efficiently. Moreover, as a consequence of current limits on computer models, further advances in many areas of sci- entific and engineering knowledge now depend in essential ways on advances in mathematical research. The Mathematical Community Because of its enormous applicability, mathematics is- apart from English the most widely studied subject in 37 OCR for page 38 Mathematics Back to School Two banks are offering car loans with monthly payments of $100. One has an interest rate of 16 percent; the other has a higher rate of 18 percent together with a premium of a free color televi- sion (worth $400~. If you need a $5,000 loan and would really like the color TV, which bank should you choose? 38 school and college. Present educational practice for mathe- matics requires approximately 1,500,000 elementary school teachers, 200,000 high school teachers, and 40,000 college and university teachers. Mathematics education takes place in each of 16,000 public school districts, in another 25,000 private schools, in 1,300 community colleges, 1,500 colleges, 400 comprehensive universities, and 200 research universi- ties. Roughly 5,000 mathematicians, principally those on the faculties of the research universities, are engaged in research. Only half of the nation's students take more than two years of high school-level mathematics; only one quarter take more than three years. That remaining quarter roughly one million enter colleges and universities with four years of mathematics. Four years later, about ~ 5,000 students emerge with majors in mathematics. One quarter of these students go on to a master's degree, but only 3 percent (about 400) complete a doctoral degree in the mathematical sciences. M athematics is the nation's second- largest academic discipline. Just to replace normal retirements and resignations of high school teachers will require about 7,000 to 8,000 new teach- ers a year, which is half of the expected pool of ~ 5,000 math- ematics graduates. Elementary school teachers, in contrast, are drawn primarily from the three quarters of the popula- tion who dropped mathematics after two or three courses in high school. For many prospective elementary school teach- ers, their high school experiences with mathematics were probably not positive. Subsequently, teachers' ambivalent feelings about mathematics are often communicated to chil- dren they teach. In sharp contrast to the eroding conditions of mathemat- ics teaching, one finds enormous vitality and diversity in the OCR for page 39 ...searching for patterns breadth of the mathematics profession. Over 25 different or- ganizations in the United States support some facet of pro- fessional work in the mathematical sciences. Approximately 50,000 research papers 20,000 by U.S. mathematicians- are published each year in 2,000 mathematics journals around the world. At the school and college level alone, there are over 25 U.S. publications devoted to students and teachers of mathematics. Students and faculty participate in problem-solving activities sponsored by these journals as well as learn about the ways in which current research can relate to curricular change. This massive system of mathematics education has had no national standards, no global management, and no planned structure despite the facts that each step in the mathemat- ics curriculum depends in vital ways on what has been ac- complished at all earlier stages and that scores of professions depend on skills acquired by students during their study of mathematics. Both because it is so massive and because it is so unstructured, mathematics education in the United States resists change in spite of the many forces that are revolution- izing the nature and role of mathematics. Undergraduate Mathematics Undergraduate mathematics is the linchpin for revitaliza- tion of mathematics education. Not only do all the sciences depend on strong undergraduate mathematics, but also all students who prepare to teach mathematics acquire attitudes about mathematics, styles of teaching, and knowledge of content from their undergraduate experience. No reform of mathematics education is possible unless it begins with revi- talization of undergraduate mathematics in both curriculum and teaching style. During the last two decades, as undergraduate mathemat- ics enrollments have doubled, the size of the mathematics faculty has increased by less than 30 percent. Workloads are now over 50 percent higher than they were in the post- Sputnik years and are typically among the highest on many campuses. Resources generated by the vigorous demand for undergraduate mathematics are rarely used to improve un "Between now aids the year 2000, for the firs t time in history, a ma- jority of all new jobs will require postsecond~ary education." Workforce 2000 39 OCR for page 40 Mathematics "Too many teachers over mathematics on a take it-or-leave-it basis in the universities. The result is that some of the brightest mathematical minds elect to lea ye it." Edward E. David, Jr. A Pipeline to Science The undergraduate mathematics major not only prepares students for graduate study in mathemat- ics, but also for many other sci- ences. Indeed, nearly twice as many mathematics majors go on to receive a Ph.D. in another sci- entific field rather than in the mathematical sciences them- selves. 40 dergraduate mathematics teaching. To administrators wor- ried about tight budgets, mathematics departments are often the best bargains on campus, but to students seeking stimu- lation and opportunity, mathematics departments are often the Rip Van Winkle of the academic community. R· · · . . . . . . . . . . . . form of undergraduate mathematics is the key to revitalizing mathematics education. During these same two decades, both the opportunity and the need for vital innovative mathematics instruction have increased substantially. The subject moves on, yet the cur- riculum is stagnant. Only a minority of the nation's colle- giate faculty maintains a program of significant professional activity. Even fewer are regularly engaged in mathematical research, but these few sustain a research enterprise that is the best in the world. Unfortunately, those who are most professionally active rarely teach any undergraduate course related to their scholarly work as mathematicians. Mathe- maticians seldom teach what they think about and rarely think deeply about what they teach. Departments of mathematics in colleges and universities serve several different constituencies: general education, teacher education, client departments, and future mathe- maticians. Very few departments have the intellectual and financial resources to meet well the needs of all these fre- quently conflicting groups. Worse still, most departments fait to meet the needs of any of these constituencies with energy, effectiveness, or distinction. Since almost everyone who teaches mathematics is edu- cated in our colleges and universities, many issues facing mathematics education hinge on revitalization of undergrad- uate mathematics. But critical curricular review and revital- ization take time, energy, and commitment essential in- gredients that have been stripped from the mathematics fac- ulLty by two decades of continuous deficits. Rewards of pro- motion and tenure follow research, not curricular reform; OCR for page 41 ...searching for patterns neither institutions of higher education nor the professional community of mathematicians encourages faculty to devote time and energy to revitalization of undergraduate mathe- matics. To improve mathematics education, we must restore in- tegrity to undergraduate mathematics. This challenge pro- vides a great opportunity. With approximately 50 percent of school teachers leaving every seven years, it is feasible to make significant changes in the way school mathematics is taught simply by transforming undergraduate mathematics to reflect the new expectations for mathematics. Undergrad- uate mathematics is the bridge between research and schools and holds the power of reform in mathematics education. 41
The MILE: The Mathematics Interactive Learning Environment The MILE, located in 301 Urban Life Building, was created to support the redesign of the delivery of Math 1111(College Algebra) and Math 1113(Precalculus). This state-of-the-art computer lab contains 82 computers for general student use and 1 ADA compliant computer. The lab also contains 2 printers for student use through their Panther Id account. One-on-one assistance is provided by peer tutors, graduate research assistants, as well as departmental faculty. Use of the lab is a required element for all sections of these MATH 1111 and 1113 beginning fall 2005. The MILE provides students with an array of interactive materials and activities through mathematical software(MyMathLab). This software is designed to engage the student in their learning process. Multimedia learning aids for students:MyMathLab includes a variety of multimedia resources – such as video lectures, animations, and audio clips – to help students improve their understanding of key concepts. Videos and animations are also accessible from individual online homework and practice exercises. Student study plan for self-paced learning:MyMathLab generates personalized study plans for students based on their test results. The Study Plan links directly to tutorial exercises for topics a student still needs to work on, and these exercises regenerate algorithmically to provide unlimited practice. The Study Plan is updated each time a student takes a test, so students can continually monitor their progress throughout the course. Free tutoring for students from the Math Tutor Center : Students using MyMathLab can use their instructor's Course ID to sign up for free math tutoring from the Math Tutor Center . The Tutor Center is staffed by qualified mathematics instructors who provide one-on-one tutoring via toll-free phone, email, and real-time Internet sessions. Students get immediate feedback while doing their homework assignments. If unsuccessful, they received help online through four different modes of learning. Free response questions help build students' use of mathematical notation.
Excursions In Modern Mathematics -with Excursions - 6th edition Summary: For 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 mathemat...show moreics 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
This volume contains the basics of what every scientist and engineer should know about complex analysis. A lively style combined with a simple, direct approach helps readers grasp the fundamentals, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition. Reprint of the Prentice-Hall, 1974Counterexamples in Analysis by Bernard R. Gelbaum John M. H. Olmsted These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition. read more $15.95 Foundations of Analysis: Second Edition by David F Belding Kevin J Mitchell Unified and highly readable, this introductory approach develops the real number system and the theory of calculus, extending its discussion of the theory to real and complex planes. 1991 edition. read more $24.95 A Second Course in Complex Analysis by William A. Veech Geared toward upper-level undergraduates and graduate students, this clear, self-contained treatment of important areas in complex analysis is chiefly classical in content and emphasizes geometry of complex mappings. 1967 editionAsymptotic Methods in Analysis by N. G. de Bruijn This pioneering study/textbook in a crucial area of pure and applied mathematics features worked examples instead of the formulation of general theorems. Extensive coverage of saddle-point method, iteration, and more. 1958 edition. read more Applied Analysis by Cornelius Lanczos Classic work on analysis and design of finite processes for approximating solutions of analytical problems. Features algebraic equations, matrices, harmonic analysis, quadrature methods, and much more. read more $24.95 Foundations of Modern Analysis by Avner Friedman Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Detailed analyses. Problems. Bibliography. Index. read more $11.95 Foundations of Mathematical Analysis by Richard Johnsonbaugh W.E. Pfaffenberger Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition. read more $22 $17.95 Topology for Analysis by Albert Wilansky Three levels of examples and problems make this volume appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important topological concepts. 1970 edition. read more $22.95 Intermediate Mathematical Analysis by Anthony E. Labarre, Jr. Focusing on concepts rather than techniques, this text deals primarily with real-valued functions of a real variable. Complex numbers appear only in supplements and the last two chapters. 1968 edition. read more $15.95 An Introduction to Mathematical Analysis by Robert A. Rankin Dealing chiefly with functions of a single real variable, this text by a distinguished educator introduces limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. 1963 edition. read more Analysis in Euclidean Space by Kenneth Hoffman Developed for a beginning course in mathematical analysis, this text focuses on concepts, principles, and methods, offering introductions to real and complex analysis and complex function theory. 1975 edition. read more Real Analysis by Gabriel Klambauer Concise in treatment and comprehensive in scope, this text for graduate students introduces contemporary real analysis with a particular emphasis on integration theory. Includes exercises. 1973 edition. read more $22.95 Applied Nonstandard Analysis by Prof. Martin Davis This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition. read more $14.95 Introduction to Analysis by Maxwell Rosenlicht Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition. read more $14.95 Introductory Complex Analysis by Richard A. Silverman Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition. read more
Introduction to Numerical Analysis This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New ... Numerical analysis is the branch of mathematics concerned with the theoretical foundations of numerical algorithms for the solution of problems arising in scientific applications. Designed for both ...
Answers to tell you the truth, math is actually fun when you get it, for me, now i'm taking precalc online, and it's just painful because i don't get a thing the book says!!! i know, why can't math be simpler?
Math Olympians Topical: Divisibility & The Remainder Problems This book is specially designed for students interested in participating in the Mathematics Olympiad, but even those who just have a casual interest in Mathematics will find the questions here intriguing and challenging. The questions in the book are arranged according to topic, and the detailed solutions and workings can be found at the back of the volume. We sincerely hope that by doing the questions in this book, students will understand and grasp the fundamental techniques required for critical Mathematical thinking.
MST3 Standard 3 - Mathematics Students will: •understand the concepts of and become proficient with the skills of mathematics; •communicate and reason mathematically; •become problem solvers by using appropriate tools and strategies; through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability. MST3.A CONTENT STRAND 2 - Algebra MST3.I.A Major Understanding 1 - Students will represent and analyze algebraically a wide variety of problem solving situations. MST3.I.A.07.02 - Add and subtract monomials with exponents of one MST3.I.A.07.03 - Identify a polynomial as an algebraic expression containing one or more terms MST3.I.A.07.04 - Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation MST3.I.A.07.05 - Solve one-step inequalities (positive coefficients only) (See G.07.09) MST3.I.A.07.06 - Evaluate formulas for given input values (surface area, rate, and density problems) MST3.I.A Major Understanding 3 - Students will recognize, use, and represent algebraically patterns, relations, and functions. MST3.I.A.07.07 - Draw the graphic representation of a pattern that can be expressed , as an equation or from table of data MST3.I.A.07.08 - Create algebraic patterns using charts/tables, graphs, equations, and expressions MST3.I.A.07.09 - Build a pattern to develop a rule for determining the sum of the interior angles of polygons MST3.I.A.07.10 - Write an equation to represent a function from a table of values MST3.CM PROCESS STRAND 3 - Communication MST3.I.CM Major Understanding 1 - Students will organize and consolidate their mathematical thinking through communication. MST3.I.CM Major Understanding 2 - Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others. MST3.I.CM.07.04 - Using both written and verbal form to share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols MST3.I.CM.07.05 - Answer clarifying questions from others MST3.I.CM Major Understanding 3 - Students will analyze and evaluate the mathematical thinking and strategies of others. MST3.I.CM.07.06 - Analyze mathematical solutions shared by other students MST3.I.CM.07.07 - Compare strategies used and solutions found by others in relation to their own work MST3.I.CM.07.08 - Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others MST3.I.CM Major Understanding 4 - Students will use the language of mathematics to express mathematical ideas precisely. MST3.I.CM.07.09 - Increase their use of mathematical vocabulary and language when communicating with others MST3.I.CM.07.10 - Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale MST3.I.CM.07.11 - Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing MST3.CN PROCESS STRAND 4 - Connections MST3.I.CN Major Understanding 1 - Students will recognize and use connections among mathematical ideas. MST3.I.CN.07.01 - Understand and make connections among multiple representations of the same mathematical idea MST3.I.CN.07.02 - Recognize connections between subsets of mathematical ideas MST3.I.CN.07.03 - Connect and apply a variety of strategies to solve problems MST3.I.CN Major Understanding 2 - Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole. MST3.I.CN.07.04 - Model situations mathematically, using representations to draw conclusions and formulate new situations MST3.I.CN.07.05 - Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics MST3.I.CN Major Understanding 3 - Students will recognize and apply mathematics in contexts outside of mathematics. MST3.I.CN.07.06 - Recognize and provide examples of the presence of mathematics in their daily lives MST3.I.CN.07.07 - Apply mathematics to solve problems situations that develop outside of mathematics MST3.I.CN.07.08 - Investigate the presence of mathematics in careers and areas or interest MST3.I.CN.07.09 - Recognize and apply mathematics to other disciplines and areas of interest and societal issues MST3.G CONTENT STRAND 3 - Geometry MST3.I.G Major Understanding 1 - Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes. MST3.I.G.07.01 - Calculate the radius or diameter, given the circumference or area of a circle MST3.I.G.07.02 - Calculate the volume of prisms and cylinders, using a given formula and a calculator MST3.I.G.07.03 - Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids) MST3.I.G.07.04 - Determine the surface area of prisms and cylinders, using a calculator and a variety of methods MST3.I.G Major Understanding 2 - Students will identify and justify geometric relationships, formally and informally. MST3.I.G.07.05 - Identify the right angle, hypotenuse, and legs of a right triangle MST3.I.G.07.06 - Explore the relationship between the lengths of the three sides of a right triangle (Pythagorean Theorem) MST3.I.G.07.07 - Find a missing angle when given angles of a quadrilateral MST3.I.G.07.08 - Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle MST3.I.G.07.09 - Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator MST3.I.G.07.10 - Graph the solution set of an inequality (positive coefficients only) on a number line (See A.07.05) MST3.M CONTENT STRAND 4 - Measurement MST3.I.M Major Understanding 1 - Students will determine what can be measured and how, using appropriate methods and formulas. MST3.I.M.07.01 - Calculate distance using a map scale MST3.I.M.07.02 - Convert capacities and volumes within a given system MST3.I.M.07.03 - Identify customary and metric units of mass MST3.I.M.07.04 - Convert mass within a given system MST3.I.M.07.05 - Calculate unit price using proportions MST3.I.M.07.06 - Compare unit prices MST3.I.M.07.07 - Convert money between different currencies with the use of an exchange rate table and calculator MST3.I.M.07.08 - Draw central angles in a given circle using a protractor (circle graphs) MST3.I.M.07.09 - Determine the tool and technique to measure with an appropriate level of precision: mass MST3.I.M Major Understanding 3 - Students will develop strategies for estimating measurements. MST3.I.N Major Understanding 1 - Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems. MST3.I.N.07.01 - Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, irrational numbers) MST3.I.N.07.02 - Recognize the difference between rational and irrational numbers (e.g., explore different approximations of Pi) MST3.I.N.07.03 - Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers MST3.I.N.07.04 - Develop the laws of exponents for multiplication and division MST3.I.N.07.05 - Write numbers in scientific notation MST3.I.N.07.06 - Translate numbers from scientific notation into standard form MST3.I.N.07.07 - Compare numbers written in scientific notation MST3.I.N.07.08 - Find the common factors and greatest common factor of two or more numbers MST3.I.N.07.09 - Determine multiples and least common multiple of two or more numbers MST3.I.N.07.10 - Determine the prime factorization of a given number and write in exponential form MST3.I.N Major Understanding 2 - Students will understand meanings of operations and procedures, and how they relate to one another. MST3.I.N.07.11 - Simplify expressions using order of operations Note: Expressions may include absolute value and/or integral exponents greater than 0 MST3.I.N.07.12A - Add and subtract integers MST3.I.N.07.12B - Multiply and divide integers MST3.I.N.07.13 - Add and subtract two integers (with and without the use of a number line) MST3.I.N.07.14 - Develop a conceptual understanding of negative and zero exponents with a base of ten and relate to fractions and decimals (e.g., 10 to the negative second power = .01 = 1/100) MST3.I.N.07.15 - Recognize and state the value of the square root of a perfect square (up to 225) MST3.I.N.07.16 - Determine the square root of non-perfect squares using a calculator MST3.I.N.07.17 - Classify irrational numbers as non-repeating/non-terminating decimals MST3.I.N Major Understanding 3 - Students will compute accurately and make reasonable estimates. MST3.I.N.07.18 - Identify the two consecutive integers between which the square root of a non-perfect square whole number less than 225 lies (with and without the use of a number line) MST3.I.N.07.19 - Justify the reasonableness of answers using estimation MST3.PS PROCESS STRAND 1 - Problem Solving MST3.I.PS Major Understanding 1 - Students will build new mathematical knowledge through problem solving. MST3.I.PS.07.01 - Use a variety of strategies to understand new mathematical content and to develop more efficient methods MST3.I.PS.07.02 - Construct appropriate extensions to problem situations MST3.I.PS.07.03 - Understand and demonstrate how written symbols represent mathematical ideas MST3.I.PS Major Understanding 2 - Students will solve problems that arise in mathematics and in other contexts. MST3.I.PS Major Understanding 3 - Students will apply and adapt a variety of appropriate strategies to solve problems. MST3.I.PS.07.07 - Understand that there is no one right way to solve mathematical problem but that different methods have advantages and disadvantages MST3.I.PS.07.08 - Understand how to break a complex problem into simpler parts or use a similar problem type to solve a problem MST3.I.PS.07.09 - Work backwards from a solution MST3.I.PS.07.10 - Use proportionality to model problems MST3.I.PS.07.11 - Work in collaboration with others to solve problems MST3.I.PS Major Understanding 4 - Students will monitor and reflect on the process of mathematical problem solving. MST3.I.PS.07.12 - Interpret solutions within the given constraints of a problem MST3.I.PS.07.13 - Set expectations and limits for possible solutions MST3.I.PS.07.14 - Determine information required to solve the problem MST3.I.PS.07.15 - Choose methods for obtaining required information MST3.I.PS.07.16 - Justify solution methods through logical argument MST3.I.PS.07.17 - Evaluate the efficiency of different representations of a problem MST3.R PROCESS STRAND 5 - Representation MST3.I.R Major Understanding 1 - Students will create and use representations to organize, record, and communicate mathematical ideas. MST3.I.R.07.01 - Use physical objects, drawings, charts, tables, graphs, symbols, equations or objects created using technology as representations MST3.I.R.07.02 - Explain, describe, and defend mathematical ideas using representations MST3.I.R.07.03 - Recognize, compare, and use an array of representational forms MST3.I.R.07.04 - Explain how different representations express the same relationship MST3.I.R.07.05 - Use standard and nonstandard representations with accuracy and detail MST3.I.R Major Understanding 2 - Students will select, apply, translate among mathematical representations to solve problems. MST3.I.R.07.06 - Use representations to explore problem situations MST3.I.R.07.07 - Investigate relationships between different representations and their impact on a given problem MST3.I.R.07.08 - Use representation as a tool for exploring and understanding mathematical ideas MST3.I.R Major Understanding 3 - Students will use representations to model and interpret physical, social, and mathematical phenomena MST3.I.R.07.09 - Use mathematics to show and understand physical phenomena (e.g., make and interpret scale drawings of figures or scale models of objects) MST3.I.R.07.10 - Use mathematics to show and understand social phenomena (e.g., determine profit from sale of yearbooks) MST3.I.R.07.11 - Use mathematics to show and understand mathematical phenomena (e.g., use tables graphs, and equations to show a pattern underlying a function) MST3.RP PROCESS STRAND 2 - Reasoning & Proof MST3.I.RP Major Understanding 1 - Students will recognize reasoning and proof as fundamental aspects of mathematics. MST3.I.RP.07.01 - Recognize that mathematical ideas can be supported using a variety of strategies MST3.I.RP Major Understanding 2 - Students will make and investigate mathematical conjectures. MST3.I.RP.07.02 - Use mathematical strategies to reach a conclusion MST3.I.RP.07.03 - Evaluate conjectures by distinguishing relevant and irrelevant information to reach a conclusion or make appropriate estimates MST3.I.PS Major Understanding 3 - Students will develop and evaluate mathematical arguments and proofs. MST3.I.RP.07.04 - Provide supportive arguments for conjectures MST3.I.RP.07.05 - Develop, verify, and explain an argument, using appropriate mathematical ideas and language MST3.I.RP.07.06 - Support an argument by using a systematic approach to test more than one case MST3.I.RP.07.07 - Devise ways to verify results or use counterexamples to refute incorrect statements MST3.I.RP Major Understanding 4 - Students will select and use various types of reasoning and methods of proof.
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Standards in this domain: Build a function that models a relationship between two quantities. F-BF.1. Write a function that describes a relationship between two quantities.★ Determine an explicit expression, a recursive process, or steps for calculation from a context. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. F-BF.2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★ Build new functions from existing functions. F-BF.3. Identify the effect on the graph of replacing f(x) by f(x) + k, kfF-BF.4.Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1. (+) Verify by composition that one function is the inverse of another. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. (+) Produce an invertible function from a non-invertible function by restricting the domain. F-BF.5. (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Laceyville SAT MathAlgebra is one of the main branches of mathematics; it concerns the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots. In addition to working directly with numbers, algebra also covers symbols, variables, and set elements.
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Course Requires a Media Kit to be Purchased by Course Sponsor (see additional details below): No Description: Note: This course is intended to teach and reinforce crucial academic skills to help students strengthen their background in the subject area prior to taking an advanced level course. Math is HOT! One of the most popular movies of 1998,"Good Will Hunting," was a story about a math nerd who solves the problem and gets the girl. Wall Street relies on complicated formulas from calculus to predict trends and forecast the likelihood of financial success based on many factors. Books about mathematics and numbers are flying off the shelves at bookstores across the country. A major fragrance manufacturer is busy developing a fragrance for men called "pi." What could explain this mysterious phenomenon? According to National Public Radio, smart is in and so is the study of mathematics. Introduction to Calculus is designed for students interested in college mathematics and particularly those who can't commit to a full year of study during their senior year. This semester-long course will cover limits, continuity, derivatives and their applications. We will examine the finer points of calculus and look at its specific applications to business and finance along the way.This course may be appropriate for Gifted and Talented middle school students that meet all course prerequisites. MediaKit Contents: Syllabus: Week 1: Fundamental Skills for Calculus Getting to know each other, recall some math skills learned in previous courses, and get familiar with the course. Week 2: A review of functions. Get to know each other and to review. Week 3: An introduction to limits. Explore the concept of limits. Week 4: Continuity A look at the definition, properties, and geometric representation of functions that are continuous and discontinuous. Week 5: Secants and tangents and lines, oh my. A look at one interpretation of the derivative of a function at a point. Week 6: Exponents, Radicals and the Power Rule. Rules for solving exponents and finding the derivatives by Power rule. Week 11: Trig Functions And Their Derivatives. Guide to trigonometric functions and finding their derivatives. Week 12: Good Golly Geometry Step into Geometry with areas, volumes and more of derivatives. Week 13: Rates Of Change More about derivatives and their applications in finding rates of change. Week 14: Other Uses Of Derivatives Cost, revenue and profit analysis, just some of the applications od derivatives to business and economics. Week 15: Wrapping it Up Final exam, final thoughts about the course. Course Objectives: This course follows the Topical Outline and objectives of the College Board as described for the first semester of Calculus AB. A complete listing is available online at Students will: analyze graphs geometrically and analytically estimate and calculate limits of functions describe asymptotic behavior in terms of limits involving infinity determine continuity geometrically and in terms of limits compute the derivative at a point describe and analyze rates of change compute the derivative of a function analyze the derivatives of trigonometric functions apply the derivative to optimization, related rates, and marginals interpret the derivative as a rate of change compute the derivative through a variety of methods
Globalshiksha is providing you LearnNext Goa Board Class 8 CDs for Maths and Science. This package contains the entire syllabus for Goa Board Class 8 Mathematics and Science for the academic year. Included lessons are in audio and visual format, solved examples, practice workout, experiments, tests and many more related to Goa Board Class 8 Maths and Science. It also include a various set of visual tools and activities on each Lesson with Examples, Experiments, Summary and workout. You can understand the concepts well, clear the doubts with ease through this Educational CD and get score in the exams. It also includes lesson tests of usually 20-30 minutes in duration, which will help you to evaluate the understanding of each lesson and Model tests of usually 150-180 minutes in duration, that cover the whole subject on the lines of final exam pattern. This CD comes with a useful Exam Preparation package that can help you sharpen your preparation for final exams, identify your strengths and weaknesses and know answers to all tests with a thorough explanation, overcome exam fear and get well scores in final exams.
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education. Math 1300 Special PolynomialsSection 4.2 NotesPatterns Certain polynomials can be factored by finding a pattern. This section deals with four special patterns for factoring polynomials: difference of squares, difference of cubes, sum of cubes, an Math 1313 Section 19280Popper 08 Form AFor questions 1 4, use the following information: A farmer has 150 acres of land suitable for cultivating crops A and B. The cost of planting crop A is $40/acre, whereas the cost of planting crop B is $60/a Definition Partial DerivativesWednesday, March 19, 2008 8:21 PMWhen we are asked to find the derivative of a function of a single variable,f ( x ), we know exactly what to do. However, when we have a function of two variables, there is some ambig M 13304.414.4: Trigonometric Expressions and IdentitiesAlgebraic Operations with Trig Functions We can manipulate expressions with trig functions using the same techniques we use when manipulating polynomials or rational functions. These techn Math 1300Section 4.3 NotesFactoring Polynomials Some trinomials that can be factored do not look like the special trinomials from the previous sections. Factor trinomials, written ax2 + bx + c, by doing the following rules: 1. Factor out the GCF Section 7.1 Experiments, Sample Spaces, and Events Experiments In this chapter, you will learn the basics of probability, but first we need to start with several definitions. Definition: An experiment is an activity with observable results. Examples Statistics 512 HW7For this problem use the CS dataset examined in previous problem sets, and use the model which uses only HSM and HSE as explanatory variables to predict the response GPA. On Homework 6, Problem 3 you examined some visual diagnosti VoluntaryActive engagementDefinitionsIntrinsically motivating Make-believe quality Play as selfAnthropological and Cultural ConnectionsPhilosophical Assumptions of PlayOverview of PlayPlay as fantasyThemesPlay as power Play as progres This is what the form page looks like:This is the code for the form: <CFFORM ACTION="register_send05.cfm" METHOD="POST"> <p><font size="2" face="Verdana, Arial, Helvetica, sans-serif">FirstName:</font> <input name="first_name" type="text" size="20" Introduction to Neurons In Action Graphs and questions about graphs stemming from this series of exercises from Neurons in Action. Effect of stimuli with different current on the action potential Effect of temperature on the action potential Effe COSC6373 ComputerVision DepartmentofComputerScience UniversityofHouston Assignment2:EgomotionRecoveryandMovingObjectDetection Due:4/10/09(11:59pm)The goal of this assignment is to segment moving objects from a video sequence. The detectionofmovingo COSC6397 Homework Assignment 5 (TCP in MANET)October 20, 2004Due date: Nov. 3, 2004; Maximum group size = 2 In this mini-project, we experiment with TCP performance in MANET.1Capacity of GridsIn the class, we analyze the capacity of a chain MA 154, Spring 2003 Exam 1 Grade Cutoffs A B C D 88 79 60 50Average was 64.8 15 scores of 100 759 students took the exam This curve is meant to let you know where you stand against the rest of the students in the course. We do not write down letter Affiliation: University of Connecticut Zhanna Glushan Animacy and Unacccusativity in Russian Basic Problem. Unaccusativity in Russian has received a substantial amount of attention in the literature (Babby (1980), Pesetsky (1982), Babyonyshev (1996), PHY 170 Procedure EnergyStep 1 Draw a before-and-after picture. Establish a coordinate system. Define symbols. Sketch a picture of the problem identifying where the moments in time (start and end) of interest. Identify what coordinate system you a Lesson 28 MA 152, Sections 4.1 and 4.2We have discussed powers where the exponents are integers or rational numbers. There also exists powers such as 2 3 . You can approximate powers on your calculator using the power key. On most one-liner scientif Title of the Instructional Unit: Famous African Americans Learning Goal: Learners will identify famous African Americans and their contributions to society. Objectives: The learners will identify the accomplishments of famous African Americans. They Acquiring Water Quality Data for Your Design ProjectEach group will download water quality information for their watershed Greens, Brays, Sims and Whiteoak Bayous in the Houston Metro Region (See Figure 1). This set of instructions will illustrate t Applied Electricity and Magnetism ELEE 2317 Fall 2008 Exercise Set #4 (Not to be turned in)Always draw a figure of the geometry where applicable. Always indicate vectors as such (e.g., A, A, A, A, A , but not simply A !) Gausss Law for planar struct
Accommodating Disabilities: Lehman College is committed to providing access to all programs and curricula to all students. Students with disabilities who may need classroom accommodations are encouraged to register with the Office of Student Disability Services. For more info, please contact the Office of Student Disability Services, Shuster Hall, Room 238, phone number, 718-960-8441. Course Calendar: We will try to cover the material in Chapters 1-6 of the book at a speed appropriate for maximal understanding and retention. Introduction to Linear Algebra before Ch 1 I will try to give a preview of important concepts in a little different way than Strang. We will redo it his way in Ch1 problems from class and pg 8: 2,3,4,7,15 due Jan 30 pg19: 1,2,3,4 due Feb 4 Hopefully this session wont take more that 1.5 weeks Due Feb 11 pg 8-9: 8,16,17,18,19 pg 19 7a,c,d;9,10,12,18,19 HW from class Show addition by vectors is the same as addition by algebra for vectors. Consider obtuse angles. Show that the dot product (inner product) is the same vectorially and algebraically when one of the vectors is along the x axis. Consider obtuse angles. Show that if A,B are two by two matrices and v is a 2X1 matrix then A(Bv) = (AB)v where we are using matrix multiplication (associativety) (extra credit) HW due Feb 18 Read through Ch 1 and first two sections Ch2 pg 40,41 1,2,4,9-12,15-20,22 HW due Feb 25 read 2.3 pg pg 51 1-5; pg 53 11, In 12,13,14 do what book asks but then work with Gauss-Jordan to solve by row reducing to identity. Can you see what the inverses are when they exist? HW due March 6 Read to page 70 p51 1,3,5,11a,12,13 p63 1,2,3,4,12,13,16,18 p75 1,2,3,4,5.6.7d Consider the equations x+2y=4; 3x+5y=7 -2x-3y=5; 4x-7y=8 x+y=5; -x-y=3 In each equation try use the method of Gauss-Jordan keeping track of the matrices that do row operations to find the inverse of the appropriate matrix to solve the equations. If the method fails explain why. Once you can find the inverse solve the equations just using matrix multiplication when the right hand side is a general 2x1 vector. Before the test Read to pg 88 pg 77-78 13,16,17,20 p89 6,10,12 (use that if there is a right inverse then there is a left inverse and hence an inverse),13 (use same thm),22,23,27 HW due April 22: Read 3.1,3.5 pgs127-129 1,2,3a,4,5,6,9,10,11 p178: 1,2,3,5,6,8,11,12,13,14 HW due May 1 p 129-130: 19,20,22,23,26 p178: 15,16,18,20,21,22 Final Exam: The Final Exam will be given during Finals Week on Wed May 22 from 11:00 to 1:00 in Gi205 (regular room). Department of Mathematics and Computer Science, Lehman College, City University of New York
Tailored to both the specification and the tier, this Student Book delivers exactly what students and teachers need to cover the unit in exactly the right depth. Synopsis: * Supports teachers' understanding of AO2 and AO3 through clearly labelled AO2/3 questions in the exercises. * Packed with graded questions reflect the level of demand required, so students and teachers can see their progression. * Includes worked examples throughout the book break the maths down into easy chunks. * Uses feedback to highlight common errors .
A well-thought-out example, that may serve as a good model for a course on mathematics for humanities students, is Gerald Holton and Stephen G. Brush's Physics, the Human Adventure: From Copernicus to Einstein and Beyond (Rutgers University Press, 2001). It's the third edition of Introduction to Concepts and Theories in Physical Science (Addison-Wesley, 1952). Holton and Brush is not intended to be an "easy" book. The authors write in the preface, "The book is intended for a year course (two semesters or three quarters) in a general education or core program, taken primarily by nonscience majors who have an adequate background in mathematics (up to but not including calculus)" (xiv). The goal of their book is to present "a comprehensible account -- a continuous story line, as it were -- of how science evolves through the interactions of theories, experiments, and actual scientists. We hope the reader will thereby get to understand the scientific worldview. And equally important, by following the steps in key arguments and in the derivation of fundamental equations, the readers will learn how scientists think" (xiv; emphasis in original). One of the features that makes Holton and Brush unique is that the book makes use of both the history and the philosophy of science to create the story line. A course on mathematics for humanities students ought to make use of the history and philosophy of mathematics for similar reasons. Doing so creates a context for students so that they can learn how mathematicians think.
This is going to be a great year. We are creating a new family of caring, trusting and committing to one another, so we can all succeed. I'm really blessed to have you all, and I hope that you all really enjoy your Math class this year. . Here is the Link for your online textbook: Algebra 2 Honors Textbook Link for Student Workbooks Calendar Graph Paper Check your grades here: Binder Format: You would need a Three ring binder with 7 dividers: {Questions, Homework, Classwork, Class Notes, Assessments, Vocabulary, Extras} Materials: Pencils, pens, graphing paper, highlighters, ruler, etc. This course will develop the studentís ability to use Algebra and Geometry concepts to solve real-world problems. Students will solidify their foundation in mathematics to meet the Sunshine State Standards (SSS) and to ensure success on the FCAT. A great resource to get you prepare for FCAT Testing: FCAT Explorer
If you haven't tried WolframAlpha, you really need to head over there immediately after reading this post. The great thing about this site is its ease of finding computational data. Do you have an algebraic equation you need solved? Type it in the search box and watch the magic happen. Ask for the population of France and get both the number and a chart of population growth for the last 30 years. Just for fun, type in the following formula: Taylor series of sin^3(x) No, I don't know what it means either, but Wolfram Alpha does! Here is the question. Would your math students benefit from using this site? Maybe not if you have a typical math class. If you expect your kids to sit down and do their homework in the confines of their room armed only with a calculator and their wits, you aren't paying attention. Kids today sit down with their laptop, mobile phone, calculator, iPod, and television all at the ready. They are connected. They are social. So maybe to use this site you might have to rethink what you want from your students for their homework. Maybe you want them to find the answer here and then explain in class how the answer was solved. Yes, they will get step-by-step instructions for algebra problems. Here is an example of a linear equation I just made up: If you assign a problem and then have the students discuss how it is solved so that they can teach others in the class, then Wolfram Alpha would be a great resource. It would ensure that the student is getting immediate, positive, correct feedback on how to solve problems. Of course, there are a ton of other ways to use Wolfram Alpha. You just need to check them out for yourself. OK, you don't have to go all the way over to the Wolfram Alpha site. You can search right here and see for yourself. Comments I agree with you wholeheartedly… WolframAlpha is an AMAZING tool. I am currently working on it to submit science content (on an elementary level)… I would love some feedback as to what questions and information you would like to see on the site/project! You can also email Robert with information too!! (you must love mathforum too??!!! Am I right??)
The Movement to improve college algebra has focused on revising both content and pedagogy to address the needs of other disciplines, society, and the workplace. The issue of incorporating small group projects is central to revising college algebra courses. Faculty in partner disciplines as well as employers look to mathematics to provide students with experience working in small groups. Assessment, time involvement, faculty development, and objectives are some of the issues that will be discussed. Modeling as the Central Theme in the First Two Years Sponsor: CRAFTY Organizer: Don Small (U.S. Military Academy) Moderator: Gary Krahn (U.S. Military Academy) Panelists: Traditional College Algebra is not working. That was the strong consensus of the participants in the National Conference to Improve College Algebra held at the U.S. Military Academy. This conclusion was based on the high FDW rates, outdated curriculum, small percentage of students who eventually take calculus I, and the negative impact these courses have on student perceptions of mathematics. In order to make College Algebra work, the participants recommended refocusing the courses on the needs of other disciplines, society, and the workplace. In particular, they recommended revising College Algebra courses to be real-world problem based and to include modeling with power and exponential functions, systems of equations, graphing, and difference equations. They also strongly emphasized communication skills, small group projects, and appropriate use of technology to enhance conceptual understanding, visualization, and inquiry as well as computation. Open Discussion on First Year Course Sponsor: CRAFTY Organizer: Don Small (U.S. Military Academy) Moderator: Bill Barker (Bowdoin College) Panelists: The panelists will reflect on the work of the MAA's Task Force on First Year College Level Courses and then the moderator will open the floor for discussion. Approximately 70% of college students enrolled in mathematics courses are enrolled in first year courses. Discussion is invited on both content and pedagogical issues, on the role of technology for teaching and learning, and on the purpose of these courses.

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