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Private Universe Project in Mathematics: Workshop 5. Building on Useful Ideas One of the strands of the Rutgers long-term study was to find out how useful ideas spread through a community of learners and evolve over time. Here, the focus is on the teacher's role in fostering thoughtful mathematics.,Englewood—Second Grade: Probing Student Thinking. How can a teacher know what an individual student is thinking when there are 24 or more students in the room? In Englewood, a second-grade teacher tries to follow her students' thinking by asking appropriate questions as sheWhere does our energy come from, and what are all the costs of using it 3401: Forging Alloys This lecture helps to understand how the properties of forgings evolve during the manufacturing process. General understanding of metallurgy and deformation processes is assumed. Author(s): TALAT,Klaus Siegert, Institut für Umformtechnik, License information Related content No related items provided in this feedLicense information Related content No related items provided in this feed NJ, work on a real-life problem based on Eadweard Muybridge's historic sequence of 24 photographs of a cat in motion. The question, "How fast is the cat moving in frame 10 and frame 20?," deals with one of the fundamental ideas of calculus. Students find several ways t4: Design Philosophy This lecture outlines the requirements on load bearing structures with respect to safety against failure; it introduces the design analysis process with methods of verification and partial safety factors; it describes the characteristic of loads and load combinations on structures; it introduces the subject of load and resistance factors in the verification methods; it describes the basic structural design properties of aluminium alloys versus steel. Some background and experience in structural Author(s): TALAT,Steinar Lundberg, Hydro Aluminium Structures
I am going to do MT1002 as a part of my economics degree in September, and I was thinking I should prepare myself by starting to read the course material. But the reading list for the course states 7 different books, and I really don't want do buy them all. Can anyone tell me which book of the following that gives the best overview over the MT1002 course? Personally I wouldn't buy any textbooks until the lecturers say which ones are the most important, and there will be some in the library anyway. From what I've heard from friends, there was a lot of revision at the beginning of the module (although I suppose it depends on your background in maths) so you should have time to brush up in September before you get to much new stuff. You're really better off asking questions like this in the St Andrews forum btw - someone else there might be able to help you a bit more.
Book Description Elements of Abstract and Linear Algebra is a survey of abstract algebra with emphasis on linear algebra. It is intended for students in mathematics, computer science, and the physical sciences. The first three or four chapters can stand alone as a one semester course in abstract algebra, yet they are structured to provide the background for the chapter on linear algebra. The most difficult part of the book is about groups, which are written in additive and multiplicative notation, and the concept of coset, which is confusing at first. Yet, after the first fourth chapters the book gets easier as the linear algebra follows easily. Finishing the chapters on linear algebra gives a basic one year undergraduate course in abstract algebra. The rest of the material completes the course. Those with little background can do the first three chapters in the first semester, and chapters 4 and 5 in the second semester. The presentation is compact and tightly organized, but still somewhat informal. The proofs of many of the elementary theorems are omitted. These proofs are to be provided by the professor in class or assigned as homework exercises. This text is written with the conviction that it is more effective to teach abstract and linear algebra as one coherent discipline rather than as two separate ones. Also with this text the professor does not extract the course from the text, but rather builds the course upon it. It is easier to build a course from a base than to extract it from a big book. Because after the student extract it, he still have to build it. The bare bones nature of this book adds to its flexibility, because the student can build whatever course he want around it.
Personal tools Views Best Practices in Mathematics Education Statistics Modules From APEC HRDWG Wiki Mathematics education is of vital importance in preparing today's students for the challenges and requirements of the 21st Century workforce. APEC has taken an interest in developing mathematics education effectiveness, and has developed modules to bring new ideas for teaching statistics and data analysis concepts into the classroom. Introduces the concepts of data and statistics, discusses various ways of representing interpreting data, and provides examples of descriptive and bi-variate statistical analyses. Also includes a discussion on misrepresenting data and how to identify flaws in data interpretation.
Beginning Algebra - 9th edition Summary: Get the grade you want in algebra with Gustafson and Frisk's BEGINNING ALGEBRA! Written with you in mind, the authors provide clear, no-nonsense explanations that will help you learn difficult concepts with ease. Prepare for exams with numerous resources located online and throughout the text such as online tutoring, Chapter Summaries, Self-Checks, Getting Ready exercises, and Vocabulary and Concept problems. Use this text, and you'll learn solid mathematical skills ...show morethat will help you both in future mathematical courses and in real life! ...show less New Book. Shipped from US within 4 to 14 business days. Established seller since 2000 $265.33 +$3.99 s/h New Extremely_Reliable Richmond, TX Buy with confidence. Excellent Customer Service & Return policy. $268.63 +$3.99 s/h New PROFESSIONAL & ACADEMIC BOOKSTORE Dundee, MI 0495831417272.27
I am happy to see that others besides myself have tried to use GAP as a pedagogical aid in teaching abstract algebra. I am currently teaching an undergraduate course, using Gallian's book, which I find to be an excellent text. My students are primarily computer programming majors, who take abstract algebra because they have to. Thus, one would think that my class is an ideal laboratory for introducing GAP to students. However, I can only report limited success. Perhaps some of you in the forum can give me some suggestions. I am reluctant to make assignments involving GAP, because I am fairly new to it myself. I would not know how to evaluate the results. Hence, the projects I suggest in class are "extra credit". I find the students' intellectual curiousity is insufficient to cause them to play with GAP on their own. A manual should include a section telling us mathematicians how to evaluate computer homework. I think the GAP manual is pretty intimidating to undergraduates. My students are struggling with concepts like "isomorphism" and "coset". Even at this level, they could benefit from some of GAP's capabilities, if they just ignore all the stuff about character tables, representation theory, etc. There is a much more user-friendly and simple program called "An Introduction to Groups / A Computer Illustrated Text" (comes with a disc) by D. Asche, available from IOP Publihsing for about $40. It does calculations in S_4, mainly. Even with this, you have to wait until Chapter 5 (in Gallian's text) before the students can use it. In my class, this is more than halfway through the first semester. I might consider doing Chapter 5 sooner just so I can use this software. Still, it seems that programmers ought to be more interested in GAP. There is a saying, "You can lead a student to a computer, but you can't make him think." Can we? At the undergraduate level? And with non-math majors? After I tackle this, I will work on making them like it!
The price you pay for the Algebra Buster is worth every penny, For the first time in my life I am actually able to do my algebra homework by myself. Richard Straton, OH The Algebra Buster is the perfect algebra tutor. It covers everything you need to know about algebra in an easy and comprehensive manner. Margaret Thomas, NY Cathy Dixx, OH12 : ti-83 solve a system of linear equations polynomial solution solver Special products are useful when we want to find products of polynomials fast. By beginning with the FOIL method the results solving nonhomogeneous second order differential equations facotr cubed binomials real estate accounting books solved problems of houghton mifflin math 5th grade multiplying, adding, subtracting and dividing powers simultaneous equation calculator online aptitude test in mathematics 2007 paper examples of math trivia mathematics word problems how to do cubic roots on ti-83 ti 83 plus find slope aptitude question paper with answer using algebrator to graph prentice hall mathematics algebra 1 workbook fraction formula algebra tutoring convert mixed number to decimal algebra programs math problem solver for algebra 2 free math word problem solver arranging descending and ascending numbers in maths worksheet complex expressions solver solving equation of 3rd power kumon papers solved aptitude test paper square and cube root formulas "free"+answers of exercises +algebra factor algebraic equations free laplace font multiply the common factor worksheets factoring parabolas simple equations for 5th graders "analysis questions" for quadratic equation factoring polynomials online factors and multiples printables&worksheets square root calculator free answers to math problems questions problems tutorials rings groups modules algibra softmath what is functions and types of functions in discrete mathematics.ppt solving whole numbers and fractions linear equations+ java rationalizing the denominator with unknowns answer key for prentice hall mathematics Algebra 1 workbook show written explains of least common multiple equations about integers and absolute value Algebra Expressions Finding Expressions for Quadratic Equations with points simplifying polynomials calculator fraction test for year 8 adding and subtracting fractions with integers algebrator free download online test of basic mathamatics automatic trinomial factoring machine math radical sheet free use online ti 89 calculators ALGEBRA FOR KIDS nonlinear differential equations add and subtract rational expression calculator graphing ellipses algebra with pizzazz answers simplify radicals with a variable study guide for 7th grade algebra free primary school past year exam papers simplify radical expressions with parenthesis The firrst order one unknown linear equation algoritms in visual basic 6
Search Course Communities: Course Communities Lesson 14: Quadratic Formula Course Topic(s): Developmental Math \| Quadratics Completing the square is applied to the general quadratic to derive the quadratic formula. Before an area application example is given, there is a quick review of the four methods that have been presented for solving quadratic equations. Complex numbers are introduced before the discriminant is presented.
Lakota Perspective:The Lakota perspective will be provided by way of daily interaction between student and instructor where traditional Lakota values such as patience, respect, and honor will be maintained.The students will be expected to aid the instructor with the inclusion of the Lakota perspective. Course Objectives: üChange word phrases into algebraic expressions and equations. üBuild, read, and interpret graphs. üSimplify expressions with the order of operations. üUse unit analysis and formulas from geometry. üSolve linear equations numerically, graphically, and algebraically. üPerform the four operations with integers and fractions. üSolve polynomial and quadratic equations. üSolve problems involving ratios and proportions. Attendance Requirements:Attendance requirements will follow OLC's attendance policy.If a student misses 3 consecutive classes, a total of 5 classes, or a total of 15 hours the instructor has the right to drop that student from the course. Attendance will be taken each hour.If you are late to class you will be counted absent for the first hour.If you leave class early, you will be counted absent for the last hour. Usually classes will be cancelled only because of severe weather.Check with the college center an hour or two before class is scheduled to start if you are uncertain.If the instructor is not present at the beginning of class, and the college center staff has not been called, you should wait at least 15 minutes past the class' normal start time.If the instructor is still not present, you may leave and will not be counted absent. Turn off cell phones before you come to class. Evaluation: Final grades will be figured using the following scale: 90-100 A 80-89B 70-79C 60-69D below 60F Your overall grade will be determined by the following: Exams: 4 at 100 points apiece400 possible Homework, class participation and attendance will be taken into consideration for students with grades on the borderline Final comprehensive test:100 possible Homework Exercises:Problems in each chapter will be assigned each class period and will be due at the next class.Homework will be discussed in class and students may be asked to explain their work at the board. No late homework will be accepted. Chapter Exams:If a student misses an exam it must be made up prior to the next class.It is the student's responsibility to get a hold of the instructor to set up a time to do the make up. Final Exam:The final exam will be a comprehensive final.All students having at least a 90% average at the time the final exam is to be given will not be required to take the final exam as long as they took all other exams throughout the semester. Suggestions to the Student:To succeed you need to attend class and do the suggested exercises weekly.Plan your study time, take good notes, and ask questions when needed.Your education will be only as good as the amount of effort you put into it. Your instructor's email address is given to you for a reason.Don't be afraid to ask questions via email throughout the week as you do your suggested exercises.Don't wait until the last minute to ask for help. Mathematics must be practiced on a daily basis.Set some time aside each day to do your homework.It's like learning to play a musical instrument.No matter how much you watch someone else do math, you must do it yourself to learn it.It is essential that you come to class each day and stay caught up on your suggested exercises. Disclaimer:Information contained in this syllabus was, to the best knowledge of the instructor, considered correct and complete when distributed for use at the beginning of the semester.However, this syllabus should not be considered a contract between Oglala Lakota College and any student.
Algebra 1 Units What is the role and meaning of the variable in mathematics? How do we use variables to generalize the arithmetic of real numbers? How do we represent mathematical relationships graphically, numerically, and analytically?
07923578Complex Analysis through Examples and Exercises (Texts in the Mathematical Sciences (closed)) This volume on complex analysis offers an exposition of the theory of complex analysis via a comprehensive set of examples and exercises. The book is self-contained and the exposition of new notions and methods is introduced step by step. A minimal amount of expository theory is included at the beginning of each section in the Preliminaries, with maximum effort placed on well-selected examples and exercises capturing the essence of the material. The examples contain complete solutions and serve as a model for solving similar problems given in the exercises. The readers are left to find the solution in the exercises; the answers, and occasionally, some hints, are given. Special sections contain so-called Composite Examples which consist of combinations of different types of examples explaining some problems completely and giving the reader an opportunity to check all his previously accepted knowledge. Audience: This volume is intended for undergraduate and graduate students in mathematics, physics, technology and economics interested in
concept of understanding in mathematics with regard to mathematics education is considered in this volume. The main problem for mathematics teachers being how to facilitate their students' understanding of the mathematics being taught. In combining elements of maths, philosophy, logic, linguistics and the psychology of maths education from her own and European research, Dr Sierpinska considers the contributions of the social and cultural contexts to understanding. The outcome is an insight into both mathematics and understanding.
The mathematics curriculum presents a vision of mathematics that is designed to meet the diverse needs of students in every school and student. The curriculum represents high academic standards across a broad spectrum of mathematics topics. It establishes the basis for a challenging program of study that will increase student achievement in mathematics. The mathematical topics are organized by strands: Algebra, Data Analysis, and Probability, Measurement, Number and Operations, Geometry. These strands extend the K-12 mathematics, providing continuity, and ensuring a smooth transition across elementary, middle, and high school programs. Algebra is listed as a topic in the K-5 curriculum to alert K-5 teachers that the foundation of algebraic skills is being formed at the elementary level. The mathematics curriculum is designed to support teachers as they instructionally maximize each child's mathematical experiences. Teachers are urged to provide for movement through the curriculum regardless of a student's current grade level. The use of concrete objects (manipulatives) and visual models is vital for students to understand concepts and explore processes. Knowledge acquisition requires a transition from concrete through pictorial, to the more abstract for all students at all levels and ages. Incorporating technology in instruction is imperative in order to empower students to keep pace with the information age and to be competitive in the job market; it will enhance and provide flexibility in the learning environment. Calculators and computers are essential tools for learning and doing mathematics at all grade levels. Students should be able to solve practical problems, investigate patterns, explore strategies, and focus on the process of solving problems rather than on tedious computation unrelated to applications. Communication is a vital link. Thinking, speaking, writing, and applying mathematics are invaluable assets. Teaching students these skills can be facilitated through questioning, discussions, reports, projects, journals, oral presentations, experiments, summarizing collected data, and hypothesizing. Collectively, these experiences help students make transitions between informal, intuitive ideas to more abstract and symbolic mathematics language. Reading, writing, and discussing mathematics promote clarity of thought and facilitate deeper understanding of concepts and ideas. Students will improve and gain confidence in their own abilities to explain.
PEX Quantitative Literacy GenEd Quantitative Literacy courses present mathematical thinking as a tool for solving everyday problems, and as a way of understanding how to represent aspects of a complexworld. They are designed to prepare students as citizens and voters to have the ability to think critically about quantitative statements, to recognize when they are misleading or false, and to appreciate how they relate to significant social or political issues. While computation may be part a QL course, the primary focus is not computational skills. Quantitative Literacy courses are intended to teach students how to: Understand quantitative models that describe real world phenomena and recognize limitations of those models; Perform simple mathematical computations associated with a quantitative model and make conclusions based on the results; Recognize, use, and appreciate mathematical thinking for solving problems that are part of everyday life; Understand the various sources of uncertainty and error in empirical data; Retrieve, organize, and analyze data associated with a quantitative model; and Communicate logical arguments and their conclusions. Courses
Prerequisites The lectures "Grundlagen der Mathematik" and "Algebraische Strukturen" are assumed. Overview Most of mathematics is concerned at some level with setting up and solving equations, for example to model applications in science and engineering. In many cases this involves tedious computations which are difficult to get right or too extensive to be carried through by hand. Two mathematical disciplines, numerical analysis and, more recently, computer algebra originated from this problem. Calculations in numerical analysis are carried through approximately. They are very efficient, but subject to rounding errors. Calculations in computer algebra are carried through exactly. They are usually less efficient and not always applicable (it may not be possible to solve huge systems of equations in due time, the input data may only be given approximately, there are no exact ways of representing the solutions). However, computer algebra methods often provide more mathematical insight. Through infinite precision arithmetic, they allow us to actually compute, for instance, in the ring of integers and in the field of rationals, in finite prime fields, in algebraic number fields, and in arbitrary Galois fields. In fact, there is a much larger variety of algebraic structures in which algebraic algorithms allow us to manipulate algebraic objects or the structures itself. Computer algebra is interdisciplinary in nature, with links to quite a number of areas in mathematics, with applications in mathematics and other branches of science, and with constantly new and often surprising developments. Algebraic algorithms allow us in many cases of theoretical and practical interest to study explicit examples. In this way, pure mathematics becomes accessible to experiments. Particular fruitful interactions unfold between computer algebra and algebraic geometry, number theory, and group theory. Algebraic algorithms open up new ways of accessing subareas of these key disciplines of mathematics, and they are fundamental to practical applications of the disciplines. Conversely, challenges arising in algebraic geometry, number theory, and group theory quite often lead to algorithmic breakthroughs. This lecture gives an introduction into basic algorithms, with particular emphasis on algorithms for experiments in number theory, commutative algebra, and algebraic geometry, with applications in cryptography and robotics. In addition to theoretical exercise sessions, there will be practical training sessions in programming and implementing some of the algorithms in the object-oriented programming language Python and in the computer algebra system SINGULAR, respectively. Exercise sheets for the exercise classes At most three names are allowed to appear on the homework you hand in. Nevertheless you are encouraged to discuss in larger groups. There will be a new sheet of exercises every Thursday. You have to submit your solutions every subsequent Thursday, 11.45 am in the corresponding shelves in building 48, 2nd floor ( beside room 48-208 ). Credit points Regularly, active and successful participation in the exercise classes is required to achieve an "Übungsschein". This includes scoring at least 40% of the exercise points and presenting own solutions on the black board. You have to pass an oral exam at the end of the term in order to get credit points for this lecture. If you are in doubt whether or not you need an Uebungsschein, please ask your academic advisor ("Fachstudienberater" in German). In case you study mathematics, you may find him here. Literature Cohen: A Course in Computational Algebraic Number Theory. Springer, 1993.
co730 Our Price Rs.600 Discount Rs.131 Master Sat Ii Math 1c And 2c 4th Ed (Master The Sa... With detailed reviews and expert test-taking strategies, this guide helps prepare you for the exam. It includes extensive review of math subjects ranging from algebra and geometry to trigonometry and statistics. Additional resources include, review questions and full-length practice tests at the end of each chapter to reinforce what you have learned. Feature and benefits include: - Four full-length practice tests - Diagnostic tests to help students identify the areas in which they need improvement - Detailed review of fundamental subject principles, followed by practice questions
Find out about... • Romance! How little kids meet each other on the bus • Cuisine! What pie you shouldn't order . . . unless you're rich • Travel! Parts of Kansas you've never been to • Fashion! Hairless anteriors and gold chains • Music! The newest hit "Unselfish Love" by accordionist Rockin' Rita, age 4 while learning all of advanced algebra, including... Ratio Proportion & Variation Radicals Logarithms Graphing Systems of Equations Conics Functions Linear Programming Partial Fractions Math Induction Sequences Series Matrices Permutations & Combinations Unlike all other math programs, this one also has: • Material from Modern Bus & Electric Journal • Why Rita could never be 50 feet tall • A 12-page True Fairytale History of Mathematics from the counting numbers to the complex numbers • A short discussion of tachyons (which travel faster than the speed of light) . . . and all of these are just in the first two chapters! Some answers are included in the textbook, the rest are included in the Companion Guide. The Companion Guide divides Advanced Algebra into daily lessons. It contains answers to all of the questions that do not have answers in the textbook. The Companion Guide also contains many additional advanced algebra exercises for those who want more drills. Are you teaching a class using the Life of Fred Advanced Algebra? The Companion Guide will provide you with lecture notes and outlines for each lecture. There are additional problems to present at the blackboard that are not in the textbook, additional insights to present in class. It also provides quiz and test materials. Life of Fred Advanced Algebra Companion Guide is a hardcover textbook containing 128 pages. This book is not consumable. All answers are written on separate paper or in a notebook. Life of Fred: Zillions of Practice Problems for Advanced Algebra $31.47CAD / $29.97USD Life of Fred: Zillions of Practice Problems for Advanced Algebra Need a lot of practice or stuck on a particular kind of problem? Requested by many readers, this book contains questions keyed directly to the chapters and topics of Life of Fred: Advanced Algebra. The answer to every problem is worked out in complete detail. In this book you will find: • Ten exponential equations worked out step by step. • Over 40 problems dealing with functions. • Sixteen imaginary number problems solved in detail. • Eleven linear programming problems — each taking about a page to solve. • A bonus six-page introduction to Turing Machines. This book is mandatory for those who need it. The Zillions of Practice Problems Slogan: If your cat can work through all the problems in this book, your cat can teach Advanced Algebra at any school in the nation. Life of Fred Zillions of Practice Problems for Advanced Algebra is a hardcover textbook containing 240 pages. This book is not consumable. All answers are written on separate paper or in a notebook. This is an optional book of extra questions for those who feel the need for extra practice.
Secondary Curricula Intelligent mathematics software that adapts to meet the needs of ALL students. Our adaptive curricula, Cognitive Tutor software, is based on over 20 years of research into how students think and learn. The software was developed around an artificial intelligence model that identifies weaknesses in each individual student's mastery of mathematical concepts. It then customizes prompts to focus on areas where the student is struggling, and sends the student to new problems that address those specific concepts. The result is a powerful learning tool with the most precise method of differentiating instruction available. Cognitive Tutor Software Documents & Brochures 2012 Program Guide (Middle & High School)Explore our Middle School and High School Math Series featuring our innovative, research-based software and textbooks for students in grades 6-12, and Professional Development for educators of Grades K-12.
WINTER 2011 Math 10 Practice for Exams As part of your studying for quizzes, you should review homeworks and do more practice problems. As part of your studying for exams, you should review homeworks and quizzes and do more practice problems. Many sources of practice problems, and practice exams and quizzes are listed on this page. Many of the problems here have come from actual old exams.
Mathematics, General Colleges A general program that focuses on the analysis of quantities, magnitudes, forms, and their relationships, using symbolic logic and language. Includes instruction in algebra, calculus, functional analysis, geometry, number theory, logic, topology and other mathematical specializations
Mr. Stutz is the "Man of Math" at Pocantico Hills Middle School. He teaches the 7th and 8th grade math. 7 th GRADE GENERAL MATH This course covers typical grade 7 topics required by the State Education Department. These topics include basic operations, ratio, proportion, geometry, probability, statistics, and pre-algebra. This course culminates in a school final exam. ADVANCED MATH-7th GRADE This course is intended for those students who are interested in taking Sequential I/Math A in grade 8 and covers the grade 7 and grade 8 general math curriculums. The course culminates in a school final exam. Prerequisite: teacher recommendation. GENERAL MATH-8th GRADE This course covers typical grade 8 topics required by the State Education Department. Grade 7 topics are reviewed and expanded. New topics include: the Pythagorean Rule, the use of sine, cosine, and tangent, relations, functions, and graphing, transformations and constructions. Special attention is placed on problem solving. The course culminates in a Grade 8 State Math exam. SEQUENTIAL I/Math A-8th Grade Accelerated This is the first course in an integrated sequence of mathematical study that covers topics in logic, algebra, polynomials and factoring, coordinate and transformational geometry, graph theory, probability, and statistics. Traditional Sequential I work is covered and expanded upon. Problem-solving skills and concepts are emphasized. This course culminates in a school final exam. Students next year will take the New York State Math A exam in either January or June depending on their choice of High School. Prerequisite: Successful completion of the Advanced Math 7 course with at least a grade of 85 and teacher recommendation.
Prealgebra (cloth) - 6th edition Summary: Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. ''Prealgebra,'' Sixth Edition was written to help students effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success. Whole Numbers and Introduction to Algebra; Intege...show morers and Introduction to Solving Equations; Solving Equations and Problem Solving; Fractions and Mixed Numbers; Decimals; Ratio, Proportion, and Triangle Applications; Percent; Graphing and Introduction to Statistics; Geometry and Measurement; Exponents and Polynomials For all readers interested in prealgebra46 +$3.99 s/h New Cloud 9 Books FL West Palm Beach, FL Hardcover New 032164008X
5thLarge heavy quarto, softcover, Great for home study. 790 pp. including index. 5th Edition. For high school student or college student. Discuses operations with whole numbers, ...fractions, decimals, ratios and proportions, percents, geometry and measure, statistics, real numbers, intro to algebra. Study Pack is for Basic College Math, and is new in shrinkwrap, unopened. Includes lectures, solutions manual, tutorial. (for a basic college math course)Read moreShow Less More About This Textbook Overview Maintaining its hallmark features of carefully detailed explanations and accessible pedagogy,this edition also addresses the new AMATYC and NCTM Standards. In addition to the changes incorporated into the text,a new integrated video series and multimedia tutorial program are also available. Designed for a one-semester arithmetic or basic math skills course,this successful worktext is appropriate for lecture,learning center,laboratory,or self-paced
Media: CD-ROM Product details Delivery Destinations: Visit the Delivery Destinations Help page to see where this item can be delivered. Product Description Learners build links between numbers and physical movements around a grid. Grid Algebra is, without doubt, a sophisticated classroom tool that actively supports learning. How can I get hold of it? Grid Algebra is available from ATM. Grid Algebra is a software package developed by Dave Hewitt to support learners as they develop their understanding of early algebra. Learners can be observed as they deal confidently with notation that is far from simplistic. The software enables a powerful visual, and dynamic representation of the ideas that underpin this aspect of mathematics.
Colin Clark has just published a book Math Overboard. Photograph by: Photo Submitted , NEWS And he's tried to capture some of that knowledge and experience in a new book he has just self-published called Math Overboard. "It's a book to completely review school mathematics from kindergarten to Grade 12 and make sense of it. Making sense of math could be a subtitle," said Clark, adding it might sound like it's a study book for high school students but it's actually for any adult who wants to understand the logic behind mathematics. Teaching for as long as he has, the 80-year-old math and physics major said he got the idea for the book after seeing students pay visits to his office time and time again with difficulties grasping concepts. He didn't have easy answers for them as most resources on the subject didn't delve much deeper than memorizing formulas and read like, well, a math book. "It goes back to the laws of arithmetic — you need to know the laws to do algebra. It is absolutely fundamental to explain why something is true, such as why it doesn't matter what order you add two numbers together, or multiply two numbers together." Clark believes the book is of particular use to undergrads, his original intended audience when he started writing. As a first-year calculus professor on many occasions, Clark witnessed a lot of bright students drop out of their programs or switch majors because they simply couldn't overcome the numbers hurdle. He believes some people may not have received good instruction in pre-university years, were absent during important classes, or just never picked it up. "I had a student some years ago say 'Look, I can't hope to understand math but I need to pass this course. So if I memorize the techniques, will that work?' said Clark. "I said 'no, that doesn't work at the university level at all,' and it didn't. She failed." Math Overboard, which was three years in the making, features problems to solve on every page and diagnostic tests to help readers avoid future errors. It comes in two parts — the first part, selling for $24 (US), was just released and covers up to Grade 10. The other part will be released in about three months, dealing with advanced topics, such as trigonometry and probability. Clark has written five other books in the past, but were all intended for entirely different audiences with names like Mathematical Bioeconomics, he said. Retiring in 1994, Clark has been involved in the field of math all his life. He once considered careers in both engineering and physics, but ended up finding a lot of enjoyment working with biologists. "They had all the field data, and I had all the mathematical skills they needed to analyze that data," said Clark.
Mathematics develop the mathematical skills, knowledge and understanding to enable them to function effectively and successfully in the world beyond school; experience success within mathematics at whatever level they are working at; develop the confidence to enable them to independently apply mathematics to a range of problem solving and investigative situations; appreciate and enjoy the pattern, power and universality of mathematics; develop the independent, reflective and analytical learning habits which will help them develop into life-long learners. All year groups are taught a mixture of number, shape & space, algebra, data handling and problem solving . Key Stage 3 Year 7 Students are taught in mixed ability groups using a mixture of projects and a highly successful individualised learning programme which ensures that they work on activities which match their level of need. Students are tested regularly and are encouraged to take responsibility for their own learning, though students who are not ready for such responsibility are not left to their own devices! Years 8 and 9 These students follow a more traditional route, where they are set into broad ability groupings – 3 groups in each half year. Tested at regular intervals, groupings can change throughout the year. All groups follow an individual number programme to ensure that students leave KS3 with a high level of numeracy. Problem solving activities are incorporated throughout to enable students to apply the maths they have learnt. Key Stage 4 Years 10 and 11 Students are set according to the teacher assessment level at the end of Year 9: whole year testing will continue at the end of KS3 regardless of the abolition of SATs. Each group then follows a programme which is suitable for their ability using the OCR syllabus B. Students take one final exam in June of Year 11, either the Higher Tier paper which has target grades of A* - D or the Foundation Tier paper which has target grades of C - G. Key Stage 5 In the Sixth Form, there are three different areas of mathematics that students can choose to study. Statistics is particularly useful for those taking Biology, Geography or Economics and Business Studies at A Level. Mechanics, often called Applied Mathematics, is the branch of mathematics to choose for students who are studying Design Technology, Chemistry or Physics at A Level. Many of the topics in the Physics and Mechanics syllabi overlap; taking these two subjects is certainly a strong combination. Pure Mathematics is the universal language of mathematics. It is an essential part of any of the A or AS Levels taken. There are 6 modules for each of the branches of mathematics. Students study 6 in total to obtain an A Level: eg C1, C2, C3, C4 (compulsory core modules) plus M1, M2 (Mechanics) or S1, S2 (Statistics). Further Maths is also offered to some students. This includes the modules Further Pure 1, Further Pure 2, D1, D2 (decision), either M1, M2 or S1, S2. Edexcel is the exam board used for all modules.
The struggle of a student in each subject is a tough job and has always been a heavy burden for students. If you are one of the students who have struggled to load and mathematics courses, it is important to find ways to help you understand, understand and learn each concept is most effective for you .. Calculus is one of the hardest parts in which even the normally high-achieving students may find it a struggle. The competition is huge and requires a short learning time students looking for an ideal way to learn about, understand, and understanding of calculus. Although the students pay attention in class, they still do not have much time to understand without the help of a professional tutor who has the best qualifications and knowledge of calculus is very high. Here students will learn to know effective and efficient tricks from the most simple to the difficult. If you are experiencing difficulty in learning calculus, you are not alone! Calculus is one of the most difficult subjects for many students, even those who are usually high achievers. A professional tutors who understand the "language" of calculus from basic to the most difficult to make you familiar with the special "language" calculus. If you are already familiar with basic to difficult "language" calculus, you can be one of the most easy to understand, and even the most fun for you to do assignments and homework on calculus! Eduboard established to assist students in learning and to know better the all kinds of subjects especially calculus, which is based on a special kind of logic. Eduboard presence makes every student to be easy to implement all kinds of problems in a particular subject "language" calculus. Some students learn best with different steps, and in different environments, from the others. In eduboard environment, you will find the most effective and efficient learning calculus. You can prove to yourself how eduboard will give you the best of way of learning mathematics in particular the "Calculus" the most effective and efficient in All products are free bar coded in the current market situation. Even products retail such as chocolate or small pens have a unique bar code to identify exactly. Of bar code symbols as defined in the specific height and width of the tapes, and the distance between the rods. May represent numerical data of each of these rods, alphanumeric data, user data, depending on the type of symbology used by the user. Every bar should have the barcode scanner to read the data of a beginning and an end of the bar exactly. Some Bar codes have known no other cash bar before the end of the bar, such as the checksum. Once the scanner calculates the sum is the same for the value of the precision bar code checksum. This ensures an exact calculation with minimal faults. Barcode Software is used to design and print Bar codes on labels. 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This metadata is used for a) the cause, b) the route, c) Save & Deliver d) restoration of documents efficiently and effectively. Every moment of our lives there are many thoughts was born in the good way and bad. Some of this was just a dream and a vision to be something that can be realized. Most of the time, we can't distinguish between dreams and visions. Some of us think that they are the same, but we have to remember one thing, but not all dreams turn into vision. Clearly, the purpose of an event can be written in a quotes to help others have the additional knowledge and to complete a paper or a birthday card. One person will be different from the others in a life event, and it can all be found in the form of citations written by the perpetrator intentionally to help you make greeting cards and or whatever you're doing. We can see that there are people who say that they've got a dream and then they put their dreams into a small box and close it. They put the box away in a distant place and just watch them from there are only. They brought it from its place occasionally and look into it to find out that they are still there. They may big dreams, but the owners never even bother to get it out of the box. With excerpts from the writings of events experienced by a person who can be found in quotes box, you will get a great insight to take your dream from the box. You can see a variety of life event's citations by copying and pasting this link ( on your browser. Many people say in their hearts and minds "We want to live a successful". Are you as well? When we get a chance, many of us lose it when there is a chance that maybe dating only once. Through this article you will find the ideal way to fast and you can easily make your life a success with only a few chances in life. 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begins with error analysis of Newton's method and a comparison of multiplication algorithms. It then covers high-precision division, which is required for Newton's method, and discusses the complexity of division and computing square roots. ... Description: This lecture begins with a review of graphs and applications of graph search, discusses graph representations such as adjacency lists, and covers breadth-first search. Instructor: Erik Demaine Description: Overview of course content, including an motivating problem for each of the modules. The lecture then covers 1-D and 2-D peak finding, using this problem to point out some issues involved in designing efficient algorithms. Instructor: Srini Devadas Description: Sorting is introduced, and motivated by problems that become easier once the inputs are sorted. The lecture covers insertion sort, then discusses merge sort and analyzes its running time using a recursion tree. Instructor: Srini Devadas
...It basically involves calculations in the opposite direction compared to differential calculus; so in applications, we can begin with knowledge of acceleration and obtain the velocity of an object. Courses also sometimes cover series and sequences. Precalculus covers the mathematical knowledge necessary to prepare for calculus
0 What it is: I'm not generally one to get excited about math especially algebra, geometry, and uggh calculus. But, I think if I had access to a tool like GeoGebra I might have enjoyed them (or at least understood them) more. GeoGebra is a free dynamic geometry system that lets students complete constructions with points, vectors, segments, lines, conic sections, and functions and change them dynamically afterward. Equations and coordinates can also be entered directly; this means thatGeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum. (If you didn't catch that you are not a high school math teacher wink). If you are a high school or college math teacher or know someone who is…that description just made you feel a little excited. GeoGebra is a free multi-platform download. How to integrate GeoGebra into your curriculum: Use GeoGebra to help your students understand complicated or abstract math concepts. This software is amazing for your visual learners…again a reason this should have existed when I was in school! Allow your students to explore math concepts with this software and to practice their learning. You can also use GeoGebra to create dynamic math worksheets for your students. Very cool! Tips: Make sure to check out the examples section for some great GeoGebra uses. You can also attend free online workshops to learn how to use GeoGebra. For some great ideas and further explanation of GeoGebra check them out on Wikipedia. Please leave a comment and share how you are using GeoGebra in your classroom.
Elementary Functions: Algebra and Trigonometry is an introductory Mathematics course preparing students for Calculus. Topics include: the real number system; inequalities; functions and their inverses; exponential and logarithmic functions; trigonometric and inverse trigonometric functions; complex numbers; polynomial and rational functions and systems of equations. The class meets four times per week for 50 minutes each class period. Classes are composed of 35 students meeting in a lecture hall. Classes are generally lecture style interspersed with interaction among students working together in small groups. Calculator use features prominently throughout the course. The topic of the lesson, The Distance Between a Point and a Line, examines an algebraic approach and a calculator based approach to problem solving. The lesson took place in the 10th week of a 15 week term. The class met in the early afternoon. Attendance was good and students came to class on time. There were no significant academic problems. The class atmosphere was noticeably congenial – students were friendly and comfortable with one another and the instructor. The lesson involved significant calculator work. Students were accustomed to in-class calculator exercises and working together on their calculators. Executive Summary The lesson topic is the distance between a point and a line using an algebraic approach and a calculator based approach to problem solving. Learning Goals: The immediate academic learning goals of this lesson were to develop students' understanding of the derivation of the point to line distance formula and to develop the ability to apply the point to line distance formula to solve problems. The ongoing academic learning goals of this lesson were to develop the ability to use the calculator to build structures to solve problems involving systems of equations, to develop a greater understanding of the similarities between calculators and other forms of technology, and to further develop strategies for solving multi-step problems. Instructional Design: The lesson was divided into five steps. The first step was instructor led and involved the determination of the shortest distance between a specific point and a specific line using the techniques of algebra and paper and pencil. The second step mimicked the first but rather than using paper and pencil the instructor and students used either a TI 89 or TI-Voyage 200 calculator. During the third step of the lesson the instructor and students then developed the point to line distance formula for any point and any line using the TI 89 or TI-Voyage 200 calculator. The fourth step of the lesson involved the students verifying the formula by using the developed formula along with the point and the line from parts one and two to determine if the developed formula did indeed yield the same results as their previous calculations. Finally, in step five the students worked collaboratively and then independently on an assignment related to the lesson. Major Findings about Student Learning: The students with the assistance of the instructor were able to build the appropriate structures using either a TI 89 or TI-Voyage 200 calculator to solve a problem involving systems of equations and to derive a formula involving systems of equations. The students were collaboratively and individually able to apply the developed formula to other problems in the assignment. Students questioned each other and the instructor more often during the collaborative work period than during the instructor led portion of the lesson. Some students did have an underlying misunderstanding of the benefits of a formula.
Search Course Communities: Course Communities Lesson 22: Functions as Models Course Topic(s): Developmental Math \| Functions This lesson focuses on finding appropriate non linear functions to model real world phenomena. Various cases are examined before the absolute value function and equations and inequalities are introduced.
Quiz and Formula Sheet Philosophy: Numerical computation is a motley collection of tools, many of which require you to use a lot of equations. Memorizing complex equations is not an effective use of your time, hence the formula sheet. This sheet is not meant to be an exhaustive recipe for each method; rather, it contains the truly dense, hard-to-remember formulas that are used in SOME of the methods. Here's the way to use it: if you needed to flip back in the book to check something (method algorithm, equation, minus sign) while you're doing a homework problem, and what you looked up is not either in the list below or easily derivable by ten seconds of thought, you should spend some time understanding where it comes from and/or committing it to memory. If you feel that some equation that is missing from the sheet is not worth this time, send me mail. Most quiz problems are derived directly from the homework problems, with an occasional "concept" problem thrown in, which you'll be able to do if you EITHER went to class OR did the reading. An example of the latter is "what's the difference between the secant method and the false position method?" There will be a concept-level exam during the final exam period. It will consist of conceptual questions like - here's a problem. what methods solve it? - here's a method. what kinds of problems does it solve? - what's the idea behind method x - how does it work? - what's the conceptual difference between methods x and y? - what breaks method x? - how would you parallelize method x? - what's the effect of changing parameter x in method y? This will not require any algebra, arithmetic, or manipulation/use of formulae. It may require some manipulation of symbols and is likely to require several drawings. I would suggest that you study for the test as follows. Review all of the assigned problems, quizzes, and programming assignments. Think about how you would know when to use each method and how the solutions would change with different numbers, more or fewer points, points in different order, etc. Make yourself a study sheet: a list of problem types and methods, and make sure you know the mapping between the two, as well as the differences between different methods, and what kinds of problems break each method. Finally, go over the reading and class notes and highlight important concepts. ============================================================ Formula Sheet for CSCI3656 ============================================================ TAYLOR SERIES: The second equation from the bottom of page A-3 in appendix A, plus the remainder equation at the top of page A-4. These also appear in my Taylor Series notes: the first equations on pages 2 and 4, respectively. SECANT METHOD: The lower equation on p44 FIXED-POINT METHOD: The boxed error convergence condition in the middle of p58 The Aitken acceleration formula at the bottom of p58, including the definitions of D1 and D2. (This combines the two equations I put up in class. I'll also give you those two equations, in case you prefer working the algorithm that way.) MULTIPLE ROOTS: The boxed equation on p79 CROUT REDUCTION: eqns 2.20 and 2.21 on p138 SOLVING NONLINEAR EQUATIONS: eqn 2.40 on p175 eqn 2.42 on p176 LAGRANGIAN POLYNOMIALS: - eqn 3.1 on p225 CUBIC SPLINES: - the matrix equation at the bottom of p243 - the equations for the a_i, b_i, c_i, and d_i at the top of p245 - the definition of divided difference at the bottom of p229 (note: this is a section that we skipped, but we need this one piece of notation for the formulae in the cubic spline section) BEZIER CURVES AND B-SPLINES: - the boxed eqns on p250 - the top boxed eqn on p251 - eqn 3.17 and the eqns for x_i(u) and y_i(u) on p254 LEAST SQUARES: - the "normal eqns" for lines (eqn 3.23) - the "normal eqns" for degree-n polynomials (eqns 3.25 and 3.26) DERIVATIVES FROM DATA: - the "formulas for computing derivatives" on pp373-374, !EXCEPT FOR! the first two (that is, you should memorize the forward, backward, and center difference ones. note that the backward difference formula isn't in this textbook. use your lecture notes.) - eqn 5.21, for use in extrapolation INTEGRALS FROM DATA: - the boxed "newton-cotes" equations on p376. note that these three equations have other names: trapezoidal, simpson's 1/3, and simpson's 3/8, respectively. - the composite trapezoidal (eqn 5.30), simpson's 1/3 (eqn 5.35) and simpson's 3/8 (eqn 5.36) rules - the versions of those same three rules, complete with error terms, that appear in the shaded box on p387 - eqn 5.21, for use in extrapolation - table 5.14, for use in computing integrals by Gaussian quadrature, along with the change-of-variable formula at the bottom of p390 ODE SOLVERS: - the RK4 equations - the Adams(-Bashforth) formula on p466, and its 2nd-order cousin, which I gave in class: X(t_{n+1}) = X(t_n) + h/2 [3 F(X_n,t_n) - F(X_{n-1},t_{n-1})] here, I'm using capitals (X,F) to show quantities that may be vectors. the former has O(h^4) error, while the latter has O(h^2) error.
Summary: This best-selling text balances solid mathematical coverage with a comprehensive overview of mathematical concepts as they relate to varied disciplines. The text provides an appreciation of mathematics, highlighting mathematical history, and applications of math to the arts and sciences. It is an ideal book for students who require a general overview of mathematics, especially those majoring in liberal arts, the social sciences, business, nursing and allied health fi...show moreelds. Let us introduce you to the practical, interesting, accessible, and powerful world of mathematics today-the world of A Survey of Mathematics with Applications, Expanded. ...show less Hardcover Very Good 032150108X Cover has light shelf wear, but corners are not bumped. Pages are crsip and clean. Spine is straight and binding is tight. Small tear near spine inside front cover. $15.00 +$3.99 s/h VeryGood SciFiEtcBN Knoxville, TN Addison Wesley, 2007. Hardcover Eighth Edition. Very Good/No Jacket as Issued. Cover shows moderate shelf and edge wear. No highlighting, underlining or any other marks. NO INTERNATIONAL SHIPPING OR P...show moreRIORITY SHIPPING AVAILABLE FOR THIS BOOK. ...show less $22.94 +$3.99 s/h VeryGood Books4u31 Asheville, NC 8th edition hardcover, no marks noted in text, All of our products are cleaned with an disinfectant for your protection before shipping AND AS ALWAYS SHIPPED IN 24 HOURS $37.46 +$3.99 s/h VeryGood AlphaBookWorks Alpharetta, GA 03215010840.00 +$3.99 s/h VeryGood Goodwillbound Waterloo, IA 2007 Hardcover Very good Excellent condition; Only very minor tear on upper edge of cover-no other wear; Pages clean and crisp Your purchase is helping someone with a disability find a job! Thank y...show moreou
People who don't learn or understand this material probably won't use it, but people who do may be surprised to find where it is useful. This applies not just to the content of the course, but to its association with careful, creative thinking. It will probably be up to you to find places where you can use this mathematics. But depending on your career, you may find that things that are now obvious to you are not known to others; or on the other hand, you may find it taken for granted that you know this material and much more. But most likely, you may actually use the subject of this course and the skills you've gained, without even realizing it. In reality, the questions and complaints mentioned above are all too frequently tacit, and it may be that much more difficult to bring these issues to a point of real discussion. Sometimes these complaints only show up on teachers' end-of-term evaluations. There are certainly more useful responses for individual students in individual situations than those offered here. The key point, however, is for the teacher to be able to listen to these kinds of questions and implicit challenges as having serious substance in them, that strike to the root of the problems of teaching and learning mathematics. ACKNOWLEDGMENTS The authors are grateful to the editor for his very useful suggestions. BIOGRAPHICAL SKETCHES Sandra Keith is a professor of mathematics at St. Cloud State University MN. Just as Einstein allegedly wanted to ride on a ``beam of light'', she has been interested in getting into the minds of students to understand how they think! She has worked with exploratory writing assignments and other interactive teaching methods. She served as director and edited Proceedings for the National Conference of Women in Mathematics and Sciences and was assistant editor of Winning Women (MAA). Her interests include better public relations for mathematics, improving the mathematical environment for women and minorities, better advising, and mathematical networking. Jan Cimperman is an assistant professor at the same school. Her interests include mathematics education, particularly, teaching elementary teachers. She frequently gives workshops on the MCTM Standards and the use of manipulatives to explore mathematical concepts at the K-6 level. She is interested in the variety of ways in which students learn.
Description of TallTales Math Book 2: Pre-Algebra by Educational Impressions Written by Elizabeth Hoover. ABOUT THE SERIES: Highly creative story problems spark curiosity and help students appreciate math as a powerful tool for solving real-life questions. Each book in the series is divided into 3 sections: Review Sheets—These lessons present important mathematical concepts and teach students computational skills. Step-by-step directions and easy-to-understand definitions clearly explain each concept and procedure. This section will also serve as a useful reference for the lessons in the last 2 sections. Skill-Builder Sheets—Creative story problems use mystery and humor to hold students' interest. Each lesson deals with a particular skill, and students are aware of the skill being practiced. Extra-Practice Sheets—These pages add an additional challenge for students who understand the concepts and have mastered the computational skills. Problems are similar to those in the second section; however, students are not told which skills are involved. Grades 5–8. ABOUT PRE-ALGEBRA: The following concepts are covered: Variables; Using Addition, Subtraction, Multiplication & Divisions to Solve Equations; Combining Like Terms; Working with Fractions Containing Parentheses and Negative & Positive Integers; Writing Algebraic Expres-sions; Writing Equations for Word Problems; and Using Proportion to Solve Equations. 64 pages. Product: TallTales Math Book 2: Pre-Algebra Vendor: Educational Impressions Binding Type: Paperback Media Type: Book Number of Pages: 64 Weight: 0.9 pounds Length: 11 inches Width: 10 inches Height: 1 inches Vendor Part Number: 057-2AP Subject: Algebra, Calculus & Trig, Math Learning Style: Auditory, Kinesthetic, Visual Teaching Method: Charlotte Mason, Classical, Traditional, Unit Study, Unschooling There are currently no reviews for TallTales Math Book 2: Pre-Algebra.
Mathematics Course Descriptions Algebra I Algebra I is the study of mathematical patterns and ideas. It is balanced between learning skills, exploring concepts, and solving problems. Technology is used to gather, interpret, and represent data from real-world situations. Creating and using mathematical models is a theme throughout. Algebra is integrated with geometry, probability, and statistics. Topics covered include equations-linear, quadratic, and exponential-as well as systems of equations and inequalities, functions, and fractals. Geometry This course is investigation-driven and activity-based. It covers topics of Euclidean Geometry such as deductive proof, properties of polygons, circles, similar/congruent triangles, parallel lines, area and volume, the Pythagorean Theorem, basic concepts of right triangle trigonometry, and general ideas of transformations. Computer technology and traditional Geometry tools are used in the investigations. Applications of Geometry concepts to various arts areas are incorporated within the course. Algebra II Algebra II is primarily the study of functions-linear, exponential, polynomial, and parametric-through the use of data. Introductory trigonometry, statistics, and probability topics are also explored. Students use calculators, computers, and data gathering devices to investigate all topics. Throughout the course students discover the sense behind the mathematics, rather than simply learn steps for solving problems. Small group work, discussion, and the real world interpretation of the mathematics are stressed. Applications to the arts are woven throughout the curriculum. Advanced Mathematics This course is designed to serve students who are preparing for Calculus or further work in mathematics. As a pre-calculus course, it offers an analytical, graphical and numerical approach to understanding polynomials, exponential functions, logarithms, and a wide variety of trigonometry topics. Additional topics may include polar graphs, conic sections, matrices, sequences, and series. Real life applications and data interpretation are integral parts of this course of study. Advanced Placement Statistics This course introduces the students to the basic concepts of one of the most important fields of mathematics most people ever encounter. Statistics is about data, and data are numbers with a context. Students learn to make statements of facts and inferences and to state a level of confidence in their inferences. They become proficient in accurately communicating statistical concepts, including methods of data collection and valid interpretations of data. The course follows the topics outlined in the Advanced Placement curriculum in preparation for the AP Test in May. Advanced Placement Calculus This course covers approximately one and one-half semesters of college calculus. Students completing the course successfully are prepared to take the AP Calculus AB exam. Topics include limits, continuity, differentiability; optimization, related rates, separable differential equations, and slope fields; indefinite integrals, Riemann Sums, definite integrals, the Fundamental Theorem of Calculus, and applications of the definite integral. The course material is explored through class discussions, small group activities and investigations, sample exam questions, and individual study of problems.
representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from and readers can download source code and solutions to selected exercises from the book's web page. less
Maths By definition, Mathematics is an abstract science which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra (Oxford English Dictionary). At St Mark's Church of England Academy, the Mathematics department is committed to raising the standards of Mathematics of all of its students, so that they develop their skills in using algebra, numbers, shapes and data effectively in all areas of the curriculum and the skills necessary to cope confidently with the demands of further education, employment and adult life. Year 7 students are actively encouraged to think logically and complete work clearly demonstrating their reasoning; using symbols to represent unknown information in order to solve problems; manipulating numbers using basic number operations; collecting, analysing and displaying data using a variety of charts and graphs. All this learning takes place in classrooms with state of the art Interactive White boards and under the guidance of very passionate teachers to engage our young learners. In the long term, all students will sit the GCSE Mathematics in Year 11, leading to further study in our sixth form for the more-able students and for those who might want a career in the mathematical fields. Furthermore, as Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences, we, as part of a team are dedicated to inspiring the brilliant minds of tomorrow.
Numeracy & Popular Maths books and eBooks Featured Books This unique new book provides essential preparation for graduates and managers who face numerical psychometric tests. Packed with plenty of expert tips, and with the emphasis firmly on acquiring the necessary key skills, no other book provides this level of support Only an elementary knowledge of math is needed to enjoy this entertaining compilation of brain-teasers. It includes a mixture of old and new riddles covering a variety of mathematical topics: money, speed, plane and solid geometry, probability, topology, tricky puzzles and more. Carefully explained solutions follow each problem
Abstract Algebra II – mth402 (3 credits) This is the second course in a two-part course sequence presenting students with the applications of abstract algebraic theories. Students will investigate rings, fields, and the basic theorems of Galois theory. Quotient Rings Determine elements of F[x]/I, where F is a field and I is the ideal (p(x)). Apply the fundamental homomorphism theorem for rings. Decide if a mapping is a homomorphism of rings. Polynomials Apply the properties of unique factorization domains as a generalization of polynomials and integers. Use the factorization process. Use the division algorithm to divide polynomials. Explain properties of polynomials
MAA Review [Reviewed by P. N. Ruane, on 01/10/2011] The preface of this book greets the reader with the statement 'Welcome to the study ofmathematical reasoning', surely an indictment of the way mathematics is taught at all stages up to the high school level. High school students may have seen a few things proved here and there — but they will have been taught nothing about proof in general. For example, the word 'Pythagoras' too often denotes a rule about triangles, whose justification is that it seems to work. Generally speaking, schools do not even encourage students to develop their own informal methods of justification. An example of this is given by part (a) of exercise 11 in section 1.4 (Basic Methods of Proof). Here, the reader is asked to decide whether the following statement is a proof of the fact that, if a is an odd integer, then a2 + 1 is even: 'Let a be odd. Then, by squaring an odd, we get an odd. An odd plus an odd is even. So a2 + 1 is even' Had this statement been made by a student at the primary or secondary school level, it would be a good indication that he/she had already been introduced to the 'study of mathematical reasoning'. Unfortunately, without such informal preparation for encounter with formal mathematical proof, students will find it all the more difficult when they eventually meet it as undergraduates. Anyway, one of the aims of this book, now in its 7th edition, is to introduce the reader to the main types of mathematical proof, and to analyse the logical basis of each one. The other main aim is to develop 'major ideas' needed for continuing work'. Such ideas are dealt with in the first five of the book's chapters, which are called 'Logic and Proof', 'Set Theory', 'Relations and Partitions', 'Functions' and 'Cardinality'. Examples of the advanced mathematics, to which the title refers, appear throughout the book, but particularly in the last two chapters: 'Concepts of Algebra' and 'Concepts of Analysis'. Written in classic textbook style, the book introduces each topic by means of very basic examples. Hundreds of carefully graded exercises ease the path to the rigorous treatment of more difficult ideas (e.g., the Axiom of Choice, the Heine-Borel theorem etc). The all-pervading theme is that of proof and that many different forms of proof appear in a variety of mathematical contexts. Many of the exercises require students to grade various 'attempts' at proofs, which is one of the book's many strong points. Solutions or hints are provided for a good proportion of the included exercises. This latest edition is based upon the same goals and core materials as previous editions, but with some re-organization and many new examples and exercises. Pre-requisite knowledge is now more clearly defined and full details of the changes are provided in the preface. I have no doubt in saying that this book would serve as excellent basis for a foundation course in any undergraduate mathematics programme. Peter Ruane has retired from the very pleasant task of preparing students to meet the challenge of teaching mathematics in primary and secondary schools in the UK.
Purchasing Options Features Provides extensive coverage of the latest release of MAPLE, version 7.0 Supports the presentation of MAPLE commands and common functions with specific examples, discussion, and graphics that illustrate the expected output Covers all MAPLE packages, with particular attention to the Linear Algebra package Includes a step-by-step guide to the MAPLE programming language Offers downloads of supplemental files and examples of the MAPLE commands used in the book on the Internet at Summary Maple is a very powerful computer algebra system used by students, educators, mathematicians, statisticians, scientists, and engineers for doing numerical and symbolic computations. Greatly expanded and updated from the author's MAPLE V Primer, The MAPLE Book offers extensive coverage of the latest version of this outstanding software package, MAPLE 7.0 The MAPLE Book serves both as an introduction to Maple and as a reference. Organized according to level and subject area of mathematics, it first covers the basics of high school algebra and graphing, continues with calculus and differential equations then moves on to more advanced topics, such as linear algebra, vector calculus, complex analysis, special functions, group theory, number theory and combinatorics. The MAPLE Book includes a tutorial for learning the Maple programming language. Once readers have learned how to program, they will appreciate the real power of Maple. The convenient format and straightforward style of The MAPLE Book let users proceed at their own pace, practice with the examples, experiment with graphics, and learn new functions as they need them. All of the Maple commands used in the book are available on the Internet, as are links to various other files referred to in the book. Whatever your level of expertise, you'll want to keep The MAPLE Book next to your computer.
Here we present a few examples of how real benefits are achieved by rigorously applying mathematical programming and optimization on real-world problems. Optimal Schedules Optimization is a powerful tool for determining workable schedules that are in accordance with certain requirements. Examples include Put together a lesson plan taking into account teacher availability and teacher preferences such as morning/afternoon sessions, preferred classes, or days without lessons. At the same time restricted lab availability is taken into account, gaps in teachers' schedules are minimized, and all required subjects are taught for each class. Create a seminar schedule for multiple locations, topics, and audiences. The requirements to be met are instructor availability in terms of skills/topic coverage, instructor willingness to travel certain distances and to give a certain number of courses, meet customer requirements (offer specific courses within certain time periods in certain regions), and to minimize travel cost. In a specific implementation we managed to maximize the number of offered training courses for high school teachers across three U.S. states while observing constraints such as travel restrictions, trainer skills and availability, and course demand and frequency. The computed plans do not conflict with business and trainer constraints while the effort to come up with a workable plan was reduced from three days to an hour. The problem was formulated as a mixed-integer linear program (MILP) and included approx. 75 locations, 100 instructors, 25 time slots, and 20 different courses. Depending on the specific constraints, the resulting schedule contains about 200-250 scheduled courses during the planning period of one quarter. Optimize utilization of beds in a hospital depending on total number of beds, allocations to certain departments, expected duration of the individual stays in the hospital, required safety quantities, etc. The benefits of optimization include maximized utilization of available beds, minimized waiting time, minimized bottlenecks, and increased visibility into the hospital supply chain. Other Applications Apart from optimizing schedules there is an endless list of other applications where using applied mathematics and in particular optimization, greatly improves profitability. Beyond more common areas like route planning, location determination in a logistics network, and commission structures in a multi-level marketing environment, here are examples of successful projects we have done: Web-based optimal chemical formulation and blending: Upon entering a set of desired chemical and physical properties of the end product on a web page the application computes the optimal chemical formulation in terms of meeting the specifications while minimizing cost and returns the result in the user's web browser. The benefits for sales and marketing include more accurate quotes within significantly shorter response times.
Creativity, Giftedness, and Talent Development in Mathematics (HcCreativity, Giftedness, and Talent Development in Mathematics (Hc) Book Description A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education Series Editor Bharath Sriraman, The University of Montana Our innovative spirit and creativity lies beneath the comforts and security of today's technologically evolved society. Scientists, inventors, investors, artists and leaders play a vital role in the advancement and transmission of knowledge. Mathematics, in particular, plays a central role in numerous professions and has historically served as the gatekeeper to numerous other areas of study, particularly the hard sciences, engineering and business. Mathematics is also a major component in standardized tests in the U.S., and in university entrance exams in numerous parts of world. Creativity and imagination is often evident when young children begin to develop numeric and spatial concepts, and explore mathematical tasks that capture their interest. Creativity is also an essential ingredient in the work of professional mathematicians. Yet, the bulk of mathematical thinking encouraged in the institutionalized setting of schools is focused on rote learning, memorization, and the mastery of numerous skills to solve specific problems prescribed by the curricula or aimed at standardized testing. Given the lack of research based perspectives on talent development in mathematics education, this monograph is specifically focused on contributions towards the constructs of creativity and giftedness in mathematics. This monograph presents new perspectives for talent development in the mathematics classroom and gives insights into the psychology of creativity and giftedness. The book is aimed at classroom teachers, coordinators of gifted programs, mathcontest coaches, graduate students and researchers interested in creativity, giftedness, and talent development in mathematics. Popular Searches The book Creativity, Giftedness, and Talent Development in Mathematics (Hc) by Bharath Sriraman (author) is published or distributed by Information Age Publishing [159311978X, 9781593119782]. This particular edition was published on or around 2008-07-31 date. Creativity, Giftedness, and Talent Development in Mathematics (Hc) has Hardcover binding and this format has 312 number of pages of content for use. This book by Bharath Sriraman
A Level Mathematics Introduction: Mathematical knowledge provides an important key to understanding the world in which we live. Mathematics can enter our lives in a number of ways: we buy things, read a newspaper, or time a process. Mathematics, for many of us, also extends into our chosen profession: civil servants need to analyse data, economists need to recognize financial trends; and engineers need to take account of stress patterns in physical materials. Whether you view maths as a language, central to our understanding of the world, or as a series of satisfying puzzles to solve or even as a thing of beauty there is no denying its prevalence in the world.
Peer Review Ratings Overall Rating: This site consists of a small collection of java applets in elementary mathematics that can be used for classroom demonstrations. It mainly provides supplementary material to enhance visual understanding of concepts that are being explained elsewhere. The applet collection is an incomplete translation of the German version at: (Java 1.1) or (Java 1.4). Learning Goals: The applets provide interesting visual representations of several common topics, especially in Geometry, Precalculus and Calculus, and allow interactive manipulation. Two versions are available using Java 1.1 or Java 1.4. The 1.1 versions run successfully on MACs with older operating systems and browsers and on PC?s with older operating systems. The 1.4 version does not.The Java 1.1 version will not beupdated in future. The Java 1.4 version requires a Java machine of thisversion which can be downloaded from Evaluation and Observation Content Quality Rating: Strengths: This site contains a collection of java applets in elementary mathematics ? grouped into Arithmetic (1) , Elementary Geometry (8), Stereometry (2), Spherical Geometry (1), Trigonometry (1), Vector Analysis (2), Analysis (2), Complex Numbers (1).The arithmetic applet, for example, features metric unit conversions for length, area and volume at four different levels of difficulty. The geometry examples such as sum of angles of a triangle and angle subtended in a semicircle were particularly visually attractive. The complex number example provided an attractive combination of graphical and algebraic display that covered multiplication and division as well as addition and subtraction Concerns: The arithmetic example did not include instructions for how to enter answers and had some difficulty displaying symbols such as powers. The visual geometry examples did not include any calculations or explanations. The algebraic calculations in the complex number example did not include any intermediate steps. Potential Effectiveness as a Teaching Tool Rating: Strengths: Paired with an explanation, most of these applets can significantly enhance presentations on geometry. Some applets can be used to present proofs in an intuitive, fairly painless manner. The code can be downloaded and used for non-commercial purposes for those who want to experiment and develop further. Different language versions may be useful in some circumstances ? German, Spanish, Italian, Indonesian and Korean are available Concerns: The material would need additional teacher explanations to be useful for most students at this level of content. Some applets are not very convincing demonstrations of the concepts involved; this is mainly due to lack of documentation. Ease of Use for Both Students and Faculty Rating: Strengths: The applets are generally simple and uncluttered with a strong visual effect. Concerns: The instructions for using the applets are cursory or non-existent ? for example how to enter answers in the unit conversion applet. There are no background explanations of the mathematics involved so these would be needed to supplement visual understanding. Other Issues and Comments: Useful as a supplement to other explanations of the material. Physics and astronomy applets are also available at the same site.
Our courses are located on the campuses of Harvard and Northeastern Universities. [learn more...] The Math Circle The Math Circle gives all students a chance to enjoy math through exciting topics that are normally outside the school curriculum. Its classes are collegial rather than competitive, its instructors experienced, committed and enthusiastic. Our classes begin with a free discussion of ideas and play of invention around a developing problem; then - once insight blossoms - we link this insight formally to axioms, aiming for elegance and clarity. While the courses are mathematically rigorous, the atmosphere is friendly and relaxed. We want our students to feel free to express their ideas, to suggest their own approaches, and to make mistakes. We work in a spirit of friendship, cooperation, and enjoyment of one another. Weekday Sessions are for younger students with no prior exposure to algebra. Harvard classes meet initially in room 310, Harvard Science Center. The Math Circle does not discriminate on the basis of race, creed, color, national or ethnic origin in the administration of its educational and admission policies. We are non-profit and welcome contributions.
We have math classrooms with computers at most campuses. Specialized math software we use includes Mathematica and Minitab. See "Support Request" here for specific resources to help you with math software.
Search Course Communities: Course Communities Lesson 30: Exponential Functions Course Topic(s): Developmental Math \| Exponentials Beginning with a formal definition of an exponential function, the lesson then compares the graphs of increasing and decreasing exponential functions. A comparison between exponential and power functions follows, which leads to methods for determining the (p) value in the power function (h(x) = kx^p) and the value of the base( b) in the exponential function (f(x) = ab^x). A procedure for solving exponential equations is presented before a population application problem is solved. The lesson concludes with a discussion about using graphs to find approximate solutions to exponential equations.
5 Steps to a 5 500 AP Calculus AB/BC Questions to Know by Test Day (5 Steps to a 5 on the Advanced Placement Examinations Series) Organized for easy reference and crucial practice, coverage of all the essential topics presented as 500 AP-style questions with detailed answer explanations 5 Steps to a 5: 500 AP Calculus AB/BC Features: 500 AP-style questions and answers referenced to core AP materials Review explanations for right and wrong answers Additional online practice Close simulations of the real AP exams Updated material reflects the latest tests Online practice exercises Customer Reviews: Disappointed By Jude - April 5, 2012 This book offers good practice questions. But there are issues with the publication. Some questions are ill-formed. For example, question #347 says "Use a Riemann sum to find area A on the interval [0,4] using 4 equal subdivisions." Aren't you forgetting something? Like do you want me to calculate a LEFT Riemann sum, or a RIGHT Riemann sum, or a Mid-point Riemann sum? The question as stated, cannot be answered. Here's the beginning of question #212... "If the function y is differentiable at x=a such that dy/dx does not exist at x=a ..." WHOA!!! Stop the presses! You're contradicting yourself. Question #57 asks for dy/dx, where y = 7 + 5^(x^2 + 2x - 1). None of the multiple choice answers are correct! This is an exponential function (base 5) whose derivative will contain the factor ln(5), but none of the answer choices contain ln(5). Moreover, the back of the book has a spurious solution leading to an answer that's completely... read more So many mistakes By Student - April 7, 2013 A good concept for a study book made completely useless by the sheer amount of mistakes. It is so frustrating to be unable to get through 10 of these questions without finding an error in the answer key. This book wastes my valuable studying time and my lack of trust in its content discourages me from using it. So many mistakes... By Andy Miller "andymiller20" - December 1, 2012 I teach AP Calculus and thought this book would be a good resource bank from which I could take questions for my students to do. There are a lot of good questions but there are so many mistakes in both the questions (some of which are mentioned in other reviews) and many of the answers and explanations at the back. Some of these are complete nonsense. The answer to the related rates question 197 is the worst I have found so far where they manage to get parts a and c completely wrong and do a terrible job of explaining part b. If was a student taking the course I would find this very confusing. The book is only useful if you already know how to do the questions and can weed out the dodgy ones before you use them for anything.
Foreword Volume 2, Three Skills for Algebra Logic, that is a mastery of rule- and pattern-based reason is needed in all disciplines. In particular, it may lead to precision reading and writing. If you cannot read precisely, how will you understand and how will you see errors in your own work or that of others. The first chapter on logic or rule-based reason shows the difference between one- and two-ways implication rules. Not seeing this difference is a source of confusion. Seeing the difference is a first step towards the better understanding of the implications, suggestions, rules or information met in daily life, at work and in school or college. The initial chapters on reason talk about chains of reason, about islands and divisions of knowledge and about longer chains of reason.The last chapters on logic connect the ideas of a rule being true or not with the common ideas of a rule being obeyed, disobeyed and/or not disobeyed. (In retrospect, there should also be a discussion of when a rule applies or not. In the latter case, the rule is vacuously true -holds vacuously.) Altogether, the logic chapters provide a unique mathematics-free introduction to the direct and indirect definition and rule-based thinking that appeared in Euclid's work a long time ago (2300 years ago) Three Skills For Algebra understanding and explaining reason and math Volume 2 by Alan M. Selby Ph. D. Printed in Canada ISBN 0-9697564-2-9 Three Skills for algebra are as follows. We can talk about numbers and quantities. The words or adjectives used here may be used in mathematics after arithmetic. There is more to mathematics than just doing arithmetic. We can describe calculations that might be done (or postponed) with words alone or with an (algebraic) shorthand notation. The description of calculations that might be done is also part of mathematics after arithmetic. There is more to mathematics than just doing arithmetic. We can change the way a number or quantity is computed. Some rule-based reason is required here. There is more to mathematics than just doing arithmetic. The first skill, talking about numbers and quantities, use words to describe them, gives a unique comprehension of numbers and quantities apart from but parallel to the the shorthand role of letters and symbols in mathematics. The separation here is needed for a clearer, more precise understanding of& the shorthand, symbolic, way of writing and reasoning that we call algebra. Alan Selby Montreal, 1995 Three Skills For Algebra - the Best Chapters The following logic and algebra chapters may make the hard easier. Chapter 7 will test and enrich arithmetic skills - catch a few errors in
Mathematics: Placement/Exemption The general education requirements for all three schools, the College of Arts & Sciences, the School of Business Administration, and the School of Music, include a mathematics requirement. In the case of the School of Business Administration, the requirement is very narrowly defined to be MS101 plus one course selected from among MS226, MS201 and MS222. For the other two schools, the choice of course is left up to the student, although their major may require specific math courses. Many Bachelor of Science majors require one or more calculus courses, which have Precalculus (MS101) as a prerequisite. If a studentís major requires a math course, that course can be used to satisfy the general education requirement; it is not necessary for the student to take an additional math course. Mathematics Placement Exam - Earn Exemption Credit For MS101: All students are strongly encouraged to take the mathematics placement exam. The exam is designed primarily to determine whether students remember high school algebra. A student who does well on this exam earns exemption credit for MS101. This partially satisfies the mathematics portion of the general education requirements for students in the School of Business Administration, and it completely satisfies the requirement for all other students. MS101 is a prerequisite for all of the calculus courses, so students interested in a major that requires them to take calculus (which includes most majors in the natural sciences, computer science, and digital arts) should take the placement exam in the hope of being able to proceed directly with the calculus course. The mathematics placement exam is given at beginning of each semester and can be taken at any time during the year at the Mathematics department office in Elizabeth Hall. The examination is a 20-question, multiple-choice test. Students may not use calculators on this test, and it may only be taken once. There is a practice exam located at: MS101 - Precalculus: MS101 is designed to prepare students for taking a calculus course. Students should take MS101 only if they intend to subsequently take a calculus course, and only after attempting to earn exemption credit by taking the placement exam. The 150-level mathematics courses are recommended for students who will not be taking calculus. 150-Level Mathematics Courses: The 150-level mathematics courses (MS 151, 152, 153, . . . , 159) are designed to be accessible to all students. These courses have no prerequisites (MS101 is NOT a prerequisite). Course descriptions can be found at " Choosing a Mathematics Course." Science and math oriented students who are able to earn exemption credit for MS101 generally find the pace in these courses slow, and should take one of them only if they are motivated by a strong interest in the topic. Exemption Credit From Other Examinations: Students who take a mathematics exam in the College Level Examination Program (CLEP), International Baccalaureate Program (IB), or an Advanced Placement (AP) exam may score well enough to earn exemption credit for one or more math courses that can be used to satisfy the mathematics portion of their general education requirements. If a student earns credit for a calculus course, MS101 will automatically be waived as a prerequisite for any subsequent calculus courses they take. Contact the Mathematics Department for further details.
Do the Math: Secrets, Lies, and Algebra Tess loves math because it's the one subject she can trust—there's always just one right answer, and it never changes. But then she starts algebra and is introduced to those pesky and mysterious variables, which seem to be everywhere in eighth grade. When even your friends and parents can be variables, how in the world do you find out the right answers to the really important questions, like what to do about a boy you like or whom to tell when someone's done something really bad? Will Tess's life ever stop changing long enough for her to figure it all out? Do the Math #2: The Writing on the Wall...
ELEMENTARY STATISTICS: A BRIEF VERSION is for introductory statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. In recent editions, Al Bluman has placed more emphasis on conceptual understanding and understanding results, along with increased focus on Excel, MINITAB, and the TI-83 Plus and TI-84 Plus graphing calculators; computing technologies commonly used in such courses. The 6th edition of Bluman, Elementary Statistics: A Brief Version provides a significant leap forward in terms of online course management with McGraw-Hill's homework platform, Connect Statistics – Hosted by ALEKS. Statistic instructors served as digital contributors to choose the problems that will be available, authoring each algorithm and providing stepped out solutions that go into great detail and are focused on areas where students commonly make mistakes. From there, the ALEKS Corporation reviewed each algorithm to ensure accuracy. The result is an online homework platform that provides superior content and feedback, allowing students to effectively learn the material being taught. show more show less List price: $151.00 Edition: 6th 2013 Publisher: McGraw-Hill Higher Education Binding: Trade Paper Pages: N/A Size: 8.75" wide x 10.75
The use of math worksheets to improve student learning in preparatory chemistry The use of math worksheets to improve student learning in preparatory chemistry Author: Sullivan, Alicia Nicole Abstract: When am I ever going to use this?" (Pleacher, 1998) Many students ask themselves this question throughout grade school, high school, and college during math class. A scientist knows the answer, but a non-scientist may feel that math classes are a waste of time (Angel and LaLonde, 1998). There exists a correlation between math and science; that is why those who struggle with math do not pursue the sciences. Through years of data, the strongest evidence in how a student will perform in their college chemistry class is how well they scored in their high school math courses and how they performed on the math portion of their SATs (Andrews and Andrews, 1979). Fifty percent of freshman chemistry students drop out or fail chemistry; these students switch to non-science majors or drop out of college altogether (Angel and LaLonde, 1998). Often times these dejected students pursue a liberal studies degree and in turn teach elementary school, teaching math. If these teachers never saw the connection between math and chemistry, how can they help their students understand when they are going to use the math they are learning? (Worthy, 1982) Something must be done to stop this cycle. Sources of Data: The practices and attitudes to math related chemistry questions by 376 science-major students enrolled in an undergraduate chemistry course at California State University, Sacramento, were characterized by an introductory math quiz and survey. An additional survey and a sequence of worksheets were administered throughout the course and responses to the worksheets and worksheet related exam questions were analyzed. Conclusions Reached: Students should have the option to complete mathematic worksheets that refresh their math knowledge and help them solverelated math questions on their chemistry exams. Students' academic performance is enhanced by the use of worksheets that aid the practical application of mathematics to chemistry education.
Curriculum Design: Pre-requisites/Co-requisites/Exclusions To introduce the basic concept of a limit, together with the derived concepts of convergent series, continuous functions and differentiation. To present the most important results connected with these concepts. At the end of the module students should be able to • quote and understand the definition of a limit of a sequence or a function in its various forms; • understand proofs using these definitions, and write simple examples of such proofs; • demonstrate the convergence or divergence of the geometric and harmonic series and other standard series • know and apply the basic tests for convergence of infinite series; • calculate limits of particular functions involving products and ratios of polynomials and power series; • understand the proofs of the intermediate value theorem and the theorem on boundedness of continuous functions, and apply these theorems;
A Level Further Mathematics Introduction: If you choose Further Maths you will be studying for two A-levels in Maths. This could mean that you spend half your time in College doing Maths. You have to really enjoy the subject. It is highly recommended if are considering studying a degree in Maths, Physics, Engineering or Economics at one of the best universities. Although you will get a whole A-level in a year it is not recommended for students who just want to get their Maths out of the way and do not intend to continue to the second year. It may be possible to pick up an AS in Further Maths in the second year which would involved just three of the six extra modules.
Schaum's Outline of Beginning Finite Mathematics thorough review-- with worked examples--of the fundamentals of linear equations and linear growth. Topics covered include games theory, descriptive statistics, normal distribution, probability, binomial distribution, and voting systems and apportionment. The guides that help students study faster, learn better- and get top grades. This review of beginning calculus is updated to reflect the latest course scope and sequences, with expanded explanations ... An ideal course text or supplement for the many underprepared students enrolled in the required freshman college math course, this revision of the highly successful outline (more than 348,000 copies ...
Mathematics Page Content MATH 100. Basic College Mathematics (3; F, S) Three hours per week. This course may not be used to satisfy the University's Core mathematics requirement. Students may not enroll in this course if they have satisfactorily completed a higher numbered MATH course. An overview of basic algebraic and geometric skills. This course is designed for students who lack the needed foundation in college level mathematics. A graphing calculator is required. MATH 104. College Algebra (3; F, S) Three hours per week. Prerequisite: MATH 100. This course may not be used to satisfy the University's Core mathematics requirement. Qualitative and quantitative aspects of linear, exponential, rational, and polynomial functions are explored using a problem solving approach. Basic modeling techniques, communication, and the use of technology is emphasized. A graphing calculator is required. MATH 110. The Mathematics of Motion & Change (3; F, S) Three hours per week. Prerequisite: MATH 104. A study of the mathematics of growth, motion and change. A review of algebraic, exponential, and trigonometric functions. This course is designed as a terminal course or to prepare students for the sequence of calculus courses. A graphing calculator is required. MATH 112. Modern Applications of Mathematics (3; F, S) Three hours per week. Prerequisite: MATH 104. Calculus concepts as applied to real-world problems. Topics include applications of polynomial and exponential functions and the mathematics of finance. A graphing calculator is required. MATH 140. Calculus I (4; F, S) Four hours per week. Prerequisite: A "C" or better in MATH 110. Rates of change, polynomial and exponential functions, models of growth. Differential calculus and its applications. Simple differential equations and initial value problems. A graphing calculator is required. MATH 141. Calculus II (4; F, S) Four hours per week. Prerequisite: A "C" or better in MATH 140. The definite integral, the Fundamental Theorem of Calculus, integral calculus and its applications. An introduction to series including Taylor series and its convergence. A graphing calculator is required. MATH 150. Introduction to Discrete Structures (3; S) Three hours per week. Prerequisite: A "C" or better in one of MATH 110, MATH 112 or MATH 140. An introduction to the mathematics of computing. Problem solving techniques are stressed along with an algorithmic approach. Topics include representation of numbers, sets and set operations, functions and relations, arrays and matrices, Boolean algebra, propositional logic, big O and directed and undirected graphs. MATH 199. Special Topics (var. 1-4; AR) May be repeated for credit when topic changes. Selected topics of student interest and mathematical significance will be treated. MATH 206. Statistical Methods in Science (4; S) Four hours per week. Prerequisite: A "C" or better in MATH 140. Credit cannot be awarded for both MATH 205 and MATH 206. Concepts of probability, distributions of random variables, estimation, hypothesis testing, regression, ANOVA, design of experiments, testing of assumptions, scientific sampling and use of statistical software. Many examples will use real data from scientific research. A graphing calculator is required. MATH 220WI. Mathematics & Reasoning (3; S) Three hours per week. Prerequisite: ENGL 103 and a "C" or better in MATH 141. Fundamentals of mathematical logic, introduction to set theory, methods of proof and mathematical writing. MATH 306. Regression & Analysis of Variance Techniques (3) Three hours per week. Prerequisites: A "C" or better in MATH 141, and a "C" or better in either MATH 205 or MATH 305. Theory of least squares, simple linear and multiple regression, regression diagnostics, analysis of variance, applications of techniques to real data and use of statistical packages. MATH 307. College Geometry (3) Three hours per week. Prerequisite: A "C" or better in MATH 141. A critical study of deductive reasoning used in Euclid's geometry including the parallel postulate and its relation to non-Euclidean geometries. MATH / PHIL 330. Symbolic Logic (3) Three hours per week. A study of modern formal logic, including both sentential logic and predicate logic. This course will improve students' abilities to reason effectively. Includes a review of topics such as proof, validity, and the structure of deductive reasoning. MATH 351. Applied Mathematics (3; F) Three hours per week. Prerequisite: A "C" or better in both MATH 300 and MATH 331. Advanced calculus and differential equations methods for analyzing problems in the physical and applied sciences. Calculus topics include potentials, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Differential equations topics include series solutions, special functions, and orthogonal functions. MATH 354. Introduction to Partial Differential Equations and Modeling (3; S) Three hours per week. Prerequisite: A "C" or better in both MATH 300 and MATH 331. Modeling problems in the physical and applied sciences with partial differential equations, including the heat, potential, and wave equations. Solution methods for initial value and boundary value problems including separation of variables, Fourier analysis, and the method of characteristics. MATH 400SI. History of Mathematics (3) Three hours per week. Prerequisite: A "C" or better in MATH 220WI and junior or senior status. This course may not be used to satisfy the University's Core mathematics requirement. A study of the history of mathematics. Students will complete and present a research paper. Students will gain experience in professional speaking. MATH 411. Introduction to Real Analysis (3) Three hours per week. Prerequisite: A "C" or better in both MATH 220WI and MATH 300. Foundations of real analysis including sequences and series, limits, continuity, and differentiability. Emphasis on the rigorous formulation and writing of proofs. MATH 412. Introduction to Complex Variables (3) Three hours per week. Prerequisite: A "C" or better in both MATH 220WI and MATH 300. Algebra of complex numbers, analytic functions, elementary functions, line and contour integrals, series, residues, poles and applications. MATH 423. Algebraic Structures (3) Three hours per week. Prerequisite: A "C" or better in MATH 220WI. An overview of groups, rings, fields and integral domains. Applications of abstract algebra. MATH 440. Special Topics (var. 1-3; AR) Prerequisite: A "C" or better in MATH 220WI or consent of the instructor. May be repeated for credit when topic changes. Selected topics of student interest and mathematical significance will be treated. MATH 501. Introduction to Analysis (3) Three hours per week. A study of real numbers and the important theorems of differential and integral calculus. Proofs are emphasized, and a deeper understanding of calculus is stressed. Attention is paid to calculus reform and the integrated use of technology. MATH 502. Survey of Geometries (3) Three hours per week. An examination of Euclidean and non-Euclidean geometries. Transformational and finite geometries. MATH 503. Probability & Statistics (3) Three hours per week. Probability theory and its role in decision-making, discrete and continuous random variables, hypothesis testing, estimation, simple linear regression, analysis of variance and some nonparametric tests. Attention is paid to statistics reform and the integrated use of technology. MATH 504. Special Topics (3; AR) Three hours per week. May be repeated for credit when topic changes. Course content will vary depending on needs and interests of students. MATH 507. Number Theory (3) Three hours per week. An introduction to classical number theory. Topics include modular arithmetic, the Chinese Remainder Theorem, primes and primality testing, Diophantine equations, multiplicative functions and continued fractions. MATH 510. Seminar in the History of Mathematics (3) Three hours per week. Important episodes, problems and discoveries in mathematics, with emphasis on the historical and social contexts in which they occurred. MATH 515. Combinatorics (3) Three hours per week. A survey of the essential techniques of combinatorics. Applications motivated by the fundamental problems of existence, enumeration and optimization. MATH 520. Linear Algebra (3) Three hours per week. Applications of concepts in linear algebra to problems in mathematical modeling. Linear systems, vector spaces and linear transformations. Special attention will be paid to pedagogical considerations. MATH 531. Theory of Ordinary Differential Equations (3) Three hours per week. Existence and uniqueness theorems. Qualitative and analytic study of ordinary differential equations, including a study of first and second order equations, first order systems and qualitative analysis of linear and nonlinear systems. Modeling of real world phenomena with ordinary differential equations. MATH 600. Thesis Seminar (1-3) One to three hours per week. Research guidance. May be repeated for credit up to a total of three semester hours. MATH 699. Thesis Preparation and Research (1) Master of Arts in Mathematics students who have not completed their thesis and are not enrolled in any other graduate course must enroll in MATH 699 each fall and spring semester until final approval of their thesis. This course is Pass/Fail and does not count towards any graduate degree.
We have been using both 2D and 3Dgraphics to illustrate many mathematical concepts so far. In these pages we will formalize some of the programming that was taken for granted. In this chapter we will see several different types of 2D plots, some special plots relevant to engineering, and the procedure for creating basic animation These pages emphasize generating 2D graphicsand plots using the command lineand function calls rather than use the interactive plot editor for independence and exposure to programming. Once again much more can be done than presented in these pages
This handbook covers basic math concepts with formulas and calculations required for water system operations. Includes: using a calculator; basic principles; working with equations; linear, area and volume calculations; and conversions. Water system calculations include head and head loss; chemical dosage and feed rates; electricity and power costs; softening calculations; and more. Prepare for exams using the review problems with solutions, common formulas and conversion tables. 5th edition. 231 pgs. 2007
Appropriate for one- or two-semester Advanced Engineering Mathematics courses in departments of Mathematics and Engineering. This clear, pedagogically rich book develops a strong understanding of the mathematical principles and practices that today's engineers and scientists need to know. Equal... Appropriate for a one-term course focusing on C as a language for applications programming. The text takes a true introductory approach by assuming no prior programming experience in C or any other language.
* Links the maths with the chemical applications in integrated, double page presentations, helping the student to appreciate and understand the relevance and importance of the maths. * Detailed guidance on the mechanics of the mathematical manipulations required, set in the context of chemistry, helps to develop the student's mathematical ability and understanding. * Practice problems (with answers) at the end of each section include both simple mathematical practice and real chemical examples, to give the student a thorough grounding in the mathematical techniques required.* More detailed problems, again with answers and covering a wider range of chemical themes, at the end of each broad topic give the student the ability and confidence to recognise when particular mathematical manipulations are required, and to apply them when necessary.
Jetzt kaufen Langtext Principles of Linear Algebra with Mathematica(r) uniquely addresses the quickly growing intersection between subject theory and numerical computation. Computer algebra systems such as Mathematica(r) are becoming ever more powerful, useful, user friendly and readily available to the average student and professional, but thre are few books which currently cross this gap between linear algebra and Mathematica(r). This book introduces algebra topics which can only be taught with the help of computer algebra systems, and the authors include all of the commands required to solve complex and computationally challenging linear algebra problems using Mathematica(r). The book begins with an introduction to the commands and programming guidelines for working with Mathematica(r). Next, the authors explore linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule. Basic linear algebra topics, such as vectors, dot product, cross product, vector projection, are explored as well as the more advanced topics of rotations in space, rolling a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear programming, linear transformations from Rn to Rm, the geometry of linear and affine transformations, and least squares fits and pseudoinverses. Although computational in nature, the material is not presented in a simply theory-proof-problem format. Instead, all topics are explored in a reader-friendly and insightful way. The Mathematica(r) software is fully utilized to highlight the visual nature of the topic, as the book is complete with numerous graphics in two and three dimensions, animations, symbolic manipulations, numerical computations, and programming. Exercises are supplied in most chapters, and a related Web site houses Mathematica(r) code so readers can work through the provided examples. Aus dem Inhalt Preface. Conventions and Notations. 1. An Introduction to Mathematica. 1.1 The Very Basics. 1.2 Basic Arithmetic. 1.3 Lists and Matrices. 1.4 Expressions Versus Functions. 1.5 Plotting and Animations. 1.6 Solving Systems of Equations. 1.7 Basic Programming. 2. Linear Systems of Equations and Matrices. 2.1 Linear Systems of Equations. 2.2 Augmented Matrix of a Linear System and Row Operations. 2.3 Some Matrix Arithmetic. 3. Gauss-Jordan Elimination and Reduced Row Echelon Form. 3.1 Gauss-Jordan Elimination and rref. 3.2 Elementary Matrices. 3.3 Sensitivity of Solutions to Error in the Linear System. 4. Applications of Linear Systems and Matrices. 4.1 Applications of Linear Systems to Geometry. 4.2 Applications of Linear Systems to Curve Fitting. 4.3 Applications of Linear Systems to Economics. 4.4 Applications of Matrix Multiplication to Geometry. 4.5 An Application of Matrix Multiplication to Economics. 5. Determinants, Inverses, and Cramer' Rule. 5.1 Determinants and Inverses from the Adjoint Formula. 5.2 Determinants by Expanding Along Any Row or Column. 5.3 Determinants Found by Triangularizing Matrices. 5.4 LU Factorization. 5.5 Inverses from rref. 5.6 Cramer's Rule. 6. Basic Linear Algebra Topics. 6.1 Vectors. 6.2 Dot Product. 6.3 Cross Product. 6.4 A Vector Projection. 7. A Few Advanced Linear Algebra Topics. 7.1 Rotations in Space. 7.2 "Rolling" a Circle Along a Curve. 7.3 The TNB Frame. 8. Independence, Basis, and Dimension for Subspaces of Rn. 8.1 Subspaces of Rn. 8.2 Independent and Dependent Sets of Vectors in Rn. 8.3 Basis and Dimension for Subspaces of Rn. 8.4 Vector Projection onto a subspace of Rn. 8.5 The Gram-Schmidt Orthonormalization Process. 9. Linear Maps from Rn to Rm. 9.1 Basics About Linear Maps. 9.2 The Kernel and Image Subspaces of a Linear Map. 9.3 Composites of Two Linear Maps and Inverses. 9.4 Change of Bases for the Matrix Representation of a Linear Map. 10. The Geometry of Linear and Affine Maps. 10.1 The Effect of a Linear Map on Area and Arclength in Two Dimensions. 10.2 The Decomposition of Linear Maps into Rotations, Reflections, and Rescalings in R2. 10.3 The Effect of Linear Maps on Volume, Area, and Arclength in R3. 10.4 Rotations, Reflections, and Rescalings in Three Dimensions. 10.5 Affine Maps. 11. Least-Squares Fits and Pseudoinverses. 11.1 Pseudoinverse to a Nonsquare Matrix and Almost Solving an Overdetermined Linear System. 11.2 Fits and Pseudoinverses. 11.3 Least-Squares Fits and Pseudoinverses. 12. Eigenvalues and Eigenvectors. 12.1 What Are Eigenvalues and Eigenvectors, and Why Do We Need Them? 12.2 Summary of Definitions and Methods for Computing Eigenvalues and Eigenvectors as well as the Exponential of a Matrix. 12.3 Applications of the Diagonalizability of Square Matrices. 12.4 Solving a Square First-Order Linear System if Differential Equations.
Comment: This copy of "Head Start to AS Maths" is brand new and waiting for you in our UK warehouse. Order before 1.30pm and we'll send it today and it should be with you within 4 working days for UK or 10 working days for EU. This book is designed to help bridge the gap between GCSE and AS Level Maths. It's full of clear notes and helpful practice to recap the most difficult topics from GCSE Maths that students need when going on to study AS Level Maths. Everything you need to know for all the exam boards is explained clearly and simply, in CGP's chatty straightforward
MATHEMATICS PROGRAM MODELS FOR OHIO HIGH SCHOOLS Runtime: 6:25 An introduction to six model programs in high school mathematics The ODE Mathematics Program Models offer six (6) different sequences of courses that take an applications, blended, or connected approach to the high school mathematics curriculum. The ORC Pacing Guides (upper left navigation bar) feature a schedule of topics, links to best practice lessons, teaching tips, and rich problems to engage students in exploration, analysis, and application of big ideas in mathematics. (Below is a brief summary of Ohio Department of Education draft, June 2006) In Ohio, the commitment is that all students will graduate from high school fully prepared for the demands of the workplace and further study. There are many ways a curriculum can be configured to respond to this commitment. In the area of secondary mathematics, the Department of Education has developed three different models for mathematics programs in grades 9-12. The mathematics content for the Models is specified in five of the Ohio Academic Content Standards: Number, Number Sense and Operations; Measurement; Geometry and Spatial Sense; Patterns, Functions and Algebra; Data Analysis and Probability. Equally important for effective curricula and for student learning is the sixth standard, Mathematical Processes, which includes five strands: problem solving, reasoning, communication, representation, and connections. Authentic problem solving requires students not simply to get an answer but to develop strategies to analyze and investigate problem contexts. Reasoning involves examining patterns, making and testing conjectures, and creating and evaluating arguments. Oral and written communication skills give students tools for sharing ideas and clarifying their understanding of mathematical ideas. Mathematics uses many different forms of numerical, algebraic, geometric, and physical representation to embody mathematical concepts and relationships. A coherent curriculum will help students make connections between mathematical concepts and between mathematics and other subjects they study. In the Program Models, these mathematical processes are developed through course design and through experiences with rich contextual problems. Descriptions of the Mathematics Program Models The models are presented in terms of years of study (Year 1 through Year 5), recognizing that some students will start the secondary mathematics curriculum in grade 8 and others in grade 9. The models emphasize the importance of every student taking mathematics in each of the four years of high school, and they provide appropriate courses for all students in grade 12. Characteristics Common to All Three Program Models Although the models offer distinctive ways of approaching the mathematics described in the Ohio Academic Content Standards, they share several basic characteristics. Each demonstrates how the Standards can be implemented through a curriculum and how instruction can be organized to improve student learning; Each prepares students to achieve or exceed the proficiency level on the mathematics portion of the Ohio Graduation Test in grade 10 and to achieve or exceed the requirements to enter Ohio college and university mathematics and logical reasoning; Each displays the connectedness and coherence of the mathematics studied in each course and across the courses in a sequence. Each assumes appropriate use of technology with dual goals: (1) student proficiency with foundational skills and basic mathematical concepts using basic manual algorithms and (2) student competency in using appropriate technology to encourage mathematical exploration and enhance understanding. Distinctive Characteristics of the Three Models Model A This model uses the applications of mathematics to motivate mathematical topics in algebra and geometry. Model B This model blends the mathematics of the various content strands. Data topics are woven throughout the model with a data project in Year 3. Model C. This model features a classic sequence of courses that emphasizes connections across content strands. Data analysis topics have been added to the familiar high school mathematics curriculum. Each of Models A, B, and C prepares students to take a calculus course in their first year of college. Model A', Model B', and Model C', provide curricula for students who will probably not study calculus.
This study of Principles of Finance students was designed for use as a part of a regional university's school of business accreditation process by the AACSB: The International Association for Management Education. It focuses on measuring outcomes in the area of research/quantitative analysis, examining 1) start-of-semester student competency in various aspects of basic algebra, 2) the relationship between start-of-semester algebra competency and performance in finance tests, and 3) the relationship between start-of-semester algebra competency and ability to graph linear functions associated with finance. The study results indicate that students exhibited particular difficulty with three areas of algebra that are important to the study of basic finance: solving "word problems," graphing linear functions, and solving first degree linear equations. The study results also indicate high levels of correlation between start-of-semester algebra skills and finance test scores. Finally, the results indicate that many students exhibit ongoing difficulty with graphing linear functions such as the security market line, cost-volume-profit relationships, and EBIT-EPS.
Product Information tracks. This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in other courses.
Search Course Communities: Course Communities Computing Speed Course Topic(s): Developmental Math \| Quadratics The purpose of this lesson is to develop an understanding of quadratic functions. We use the linear relation between distance, constant speed and time and the quadratic relation between the vertical distance of a falling object and time. From these, students will develop two new quadratic functions. The graph of one of these provides a picture of the physical phenomenon they have viewed. This lesson should take one day of class time.
This set covers all basic skills that involve factoring and exponents. Great for students that are new to algebra and advanced math skills. Topics include: Writing Exponents, Values of Expressions, Exponents to Numbers, Multiplying and Dividing Exponents, Prime Factors, Least Common Multiple, Greatest Common Factor, Rewrite by Factoring, Scale factors, Factoring Applications
MATH 110 HOMEWORK AND QUIZ PROBLEMS FALL 2012 PAGE 1 8/28/12 ec Questions on the weekly quiz (in recitation) will usually be taken from the list of homework problems, both assigned and recommended, and from examples in the text. The homework to be handed in via MyMathLab consists of odd numbered problems, which have answers in the textbook, and complete solutions in the student solutions manual. If you get stuck on an even numbered problem, do some of the nearby odd numbered problems. You should keep a notebook with all of the assigned homework problems, and as many of the recommended problems that you have time to work. That will help you study for quizzes and hour exams. Think of it as if you were keeping a journal for an English class. If you work all of the homework problems, you will have worked on the majority of the test and quiz questions. In the assignments to be handed in via MyMathLab, part A allows you to use the program to find a similar solved problem, but in part B you do not have that option. Use your textbook to find similar examples. In college you should expect to work at least two hours outside of class for each lecture.
I used this textbook and the software form Key curriculum last year. I really liked the book and I think that my students also understood Geometry more in depth. With my honors section I was able to go faster and actually get to the proof sections at the end of the book, but with my regular classes we could not. The hardest part of implementing the program was time management. As you know each lesson has a couple of investigation. Sometimes some groups took a long time to do an investigation and that would distract them and others. Also, there are no definitions in the book. Kids have to come up with the definitions of shapes, and sometimes they are not on target. I usually gave them time to come up with one and discussed them as a class, but then adopted the one that came in the teacher's resource book. I then gave them a copy of those definitions to keep. In order not to use the geometry class time for the software, I used their computer lab time. I had to coordinate with the computer teacher and convince her to allow me to do that. I also had to show up at those lab times to help the students with the software. I think that the computer activities really reinforced what they learned in the classroom. I hope I answered your question. If you have more specific questions please do not hesitate to write back. -Roya, for the Teacher2Teacher service roya@mathforum.org
Introductory Algebra Through Applications 0201312239 9780201312232 Introductory Algebra Through Applications: Throughout this text, motivating real-world applications, examples, and exercises demonstrate how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive side-by-side format, pairing each example with a corresponding practice exercise, encourages students to get actively involved in the mathematical content from the start. Unique Mindstretchers target different levels and types of student understanding in one comprehensive problem set per section. Mindstretchers incorporate related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and cultural connections. To show how mathematics has evolved over the centuries, in many cultures, and throughout the world, each chapter features a compelling Cultural Note that investigates and illustrates the origins of mathematical concepts. Diverse topics include art, music, the evolution of digit notation, and the ancient practice of using a scale to find an unknown weight. «Show less Introductory Algebra Through Applications: Throughout this text, motivating real-world applications, examples, and exercises demonstrate how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive... Show more» Rent Introductory Algebra Through Applications
This course is a continuation of Analytic Geometry and Calculus II, extending the skills of differentiation and integration by learning new techniques and working with partial derivatives and double and triple integrals. Other major topics include cylindrical and spherical coordinates, quadric surfaces, vector functions, vector analysis, Green''s theorem and Stoke''s theorem. GENERAL EDUCATION APPLICABILITY CSU GE Area B: Physical and its Life Forms(mark all that apply) = B4 - Mathematics/Quantitative Thinking; UC Transfer Course: CSU Transfer Course: STUDENT LEARNING OUTCOMES Upon completion of the course, the student will be able to Use the Cartesian, polar, cylindrical, and spherical coordinate systems effectively. Use scalar and vector products in applications. Use vector-valued functions to describe motion in space. Extend the concepts of derivatives, differentials, and integrals to include multiple independent variables. Solve simple differential equations of the first and second order. REQUISITES Prerequisite: MATH C152A. Partial Differentiation 1. Functions of two or more variables a. Limits b. Continuity c. Geometric interpretation d. Derivatives 2. Tangent planes and normal lines 3. The directional derivative 4. The gradient 5. The chain rule 6. Linearization and differentials 7. Maximum-Minimum problems a. Use of derivatives for extreme values b. Lagrange multipliers c. Methods of least squares 8. Higher order derivatives B. Multiple Integrals 1. Functions of two or more variables a. Plane area b. Volume c. Center of mass d. Moments of inertia e. Polar coordinates f. Surface area 2. Triple Integrals a. Volume b. Center of mass c. Moments of inertia d. Cylindrical coordinates e. Spherical coordinates C. Vectors and Parametric Equations 1. Parametric Equations in Kinematics 2. Parametric Equations in Analytic Geometry 3. Vectors in two dimensions a. The i and j components b. Vector algebra c. Unit and Zero Vectors 4. Space Coordinates a. Cartesian b. Cylindrical c. Spherical 5. Vectors in Space 6. Scalar Product of Two Vectors a. Algebraic properties b. Orthogonal vectors c. Vector projection 7. Vector Product of Two Vectors a. Algebraic properties b. Area 8. Equations of Lines and Planes 9. Product of Three or More Vectors 10. Cylinders 11. Quadric Surfaces D. Vector Functions and Their Derivatives 1. Derivative of a Vector Function 2. Velocity and Acceleration 3. Tangential Vectors 4. Curvature and Normal Vectors 5. Differentiation of Products of Vectors 6. Polar and Cylindrical Coordinates E. Multi-Dimensional Vector Analysis 1. Vector fields 2. Surface integrals 3. Line integrals 4. Green's Theorem 5. Stokes' Theorem METHODS OF INSTRUCTION--Course instructional methods may include but are not limited to Discussion; Lecture; Other Methods: A. lecture and discussion of all course concepts. B. demonstration of developing proofs and solving application problems. C. reading textbooks and journals to see presentations different than those of the instructor. D. assignments and quizzes E. the use of computational and other types of mathematical software OUT OF CLASS ASSIGNMENTS: Out of class assignments may include but are not limited to A. Reading assignments. B. Bi-weekly homework assignments. METHODS OF EVALUATION: Assessment of student performance may include but is not limited to A. tests on course content, to include solving equations as well as demonstration of specific skills B. quizzes (in-class and take-home) to include solving equations as well as demonstration of specific skills C. group work to analyze and solve application problems TEXTS, READINGS, AND MATERIALS: Instructional materials may include but are not limited to
Math 171: Math for Elementary Educators I Common Course Numbering This course was previously known (prior to Summer 2010) as Math 121; only the course number and title have changed. Course Description Math 171 is intended for prospective and current elementary school teachers. The course examines problem-solving techniques and mathematics related to topics taught at the K–8 level. Topics include number theory, set theory, functions and the use of technology. Who should take this course? Prospective and current elementary school teachers. You should consult the planning sheet for your program and consult an advisor to determine if this course is appropriate for you. Who is eligible to take this course? The prerequisite for this course is Math 90 or Math 95 with a grade of 2.0 or higher. Students new to EdCC with an appropriately high Accuplacer score may also take Math 171. Is this course transferable? This course may transfer to certain universities if the student enrolls in a teacher-preparation program; consult an advisor or see the Transfer Center to determine transferability. What textbook is used for this course? The tenth edition of Reconceptualizing Mathematics for Elementary School Teachers by Judith Sowder, Larry Sowder and Susan Nickerson.
Mr. Jim Joyer, MS Office Information Office Schedule Monday Wednesday 4:30 pm - 5:00 pm Downtown, 125 4:30 pm - 5:00 pm Downtown, 125 Biography James Joyer earned a bachelor's degree in Marketing Education from The University of South Florida and he graduated Magna Cum Lauda with a master's degree in Educational Leadership from Nova Southeastern University. "Jim" has worked in the field of education for 22 years. During this time-period he has taught mathematics, science and reading at the middle, high school and college level. He has been a national trainer in the areas of Building Classroom Rapport and Crisis Response. He has been an adjunct instructor at St. Petersburg College for over 10 years. Mr. Joyer's philosophy is all students can learn. "Learning requires you to set a goal, make a plan on how to meet that goal, seek the resources necessary to achieve it and lot's of work." This course # was formerly MAT 0024. Prerequisite(s): MAT 0018 or appropriate score on the SPC mathematics placement test. This is the second course in the college-preparatory two-course sequence (MAT 0018 and MAT 0028) designed to prepare students for college-level mathematics courses. This course is a study of the basic skills and concepts of basic algebra from the view of a college student who needs an understanding of basic algebra. Major topics include operations on signed rational numbers, simple linear equations and inequalities in one variable, operations on polynomials (including beginning techniques of factoring), integer exponents, brief introduction to radicals, introduction to graphing, applications, and other basic algebra topics. A minimum course grade average of C (minimum 70% accuracy) is required for successful completion. This course does not apply toward mathematics requirements in general education or toward any associate degree. 47 - 62 contact hours.
On selecting a constituent part of MU the "Overview of publishing activities" page will be displayed with information relevant to the selected constituent part. The "Overview of publishing activities" page is not available for non-activated items. The study text "Chosen Chapters from Algebra" is aimed at students of the bachelor study programme Teaching assistant to a teacher of Mathematics at primary and lower secondary schools. Its objective is to provide students with a brief survey of the construction of number systems (natural numbers, integers, rational numbers, real numbers, and complex numbers), including the theory of divisibility in the domain of integers and the representation of numbers in positional numeral systems. The next important part of the text is focused on basic notions and theorems from the theory of polynomials and solving of algebraic equations. The text is supplemented with a short introduction to the theory of cyclic groups, factor groups and Boolean algebra.
CliffsQuickReview course guides cover the essentials of your toughest classes. You're sure to get a firm grip on core concepts and key material and be ready for the test with this guide at your side. Whether you're new to functions, analytic geometry, and matrices or just brushing up on those topics, CliffsQuickReview Precalculus can help. This guide... more... Navigate politics, paperwork, and legal issues Find your instructional style and make learning fun for your students! Gain the upper hand on your first day of school! This friendly guide reveals what they didn't teach you in your education classes, offering practical advice and tons of real-life examples to help you set up and maintain an orderly... more...
Thompsons Calculus?re the starter, the playbook is in your hands, you... ...During the last century comprehension lesson/s usually comprised students answering teachers' questions, writing responses to questions on their own, or both. There is not a definitive set of strategies, but common ones include summarizing what you have read, monitoring your reading to make sure... design of parts and assemblies. ...My I...
Introductory Algebra and Geometry This subdivision is dedicated to bridging the gap between the mathematical layperson and the student who is ready to learn calculus and higher mathematics or to take on any other endeavour that requires an understanding of basic algebra and (at least Euclidean) geometry. The histories of Wikiversity pages indicate who the active participants are. If you are an active participant in this subdivision, you can list your name here (this can help small subdivisions grow and the participants communicate better; for large subdivisions a list of active participants is not needed). Please remember: if you have an account here people can write you a message also in the future, because IP addresses change !
geometr... read more Regular Polytopes by H. S. M. Coxeter Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition. Shape Theory: Categorical Methods of Approximation by J. M. Cordier, T. Porter This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. 1989 editionProjective Geometry by T. Ewan Faulkner Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960 edition. Non-Riemannian Geometry by Luther Pfahler Eisenhart This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition. The Elements of Non-Euclidean Geometry by D. M.Y. Sommerville Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figuresProduct Description: geometry plays in a wide range of mathematical applications. Bonus Editorial Feature: Harold In the Author's Own Words: "I'm a Platonist — a follower of Plato — who believes that one didn't invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered." "In our times, geometers are still exploring those new Wonderlands, partly for the sake of their applications to cosmology and other branches of science, but much more for the sheer joy of passing through the looking glass into a land where the familiar lines, planes, triangles, circles, and spheres are seen to behave in strange but precisely determined ways." "Geometry is perhaps the most elementary of the sciences that enable man, by purely intellectual processes, to make predictions (based on observation) about the physical world. The power of geometry, in the sense of accuracy and utility of these deductions, is impressive, and has been a powerful motivation for the study of logic in geometry." "Let us revisit Euclid. Let us discover for ourselves a few of the newer results. Perhaps we may be able to recapture some of the wonder and awe that our first contact with geometry aroused." — H. S. M. Coxeter Harold
All Faculty, Staff and Students can download and install Mathematica from Wolfram. All you need is to set up an account on Wolfram's webpage with your SSU email account. Here are the directions on how to do this. Students who are interested in sports can participate in Intramurals or Sports Clubs. Intramural sports offer students the opportunity to create their own teams and compete against other SSU players. You can visit our Sports Clubs section here. Interested in an amazing student driven environment where community, human awareness & diversity, leadership, service, and FUN is paramount? MOSAIC, an acronym for "Making Our Space An Inclusive Community", is a living and learning community made with you in mind. Syntactics: Relations among signs in formal structures Pragmatics: Relation between signs and the effects they have on the people who use them There is something unsatisfying and lacking, however, in the concept of the body, which undermines the very effort to ground (mathematical) knowledge differently than in the private cogitations of the isolated mind. The purpose of this paper is to argue for a more radical approach to the conceptualization of mathematical knowledge that is grounded in dialectical materialist psychology (as developed by Lev Vygotsky), materialist phenomenology (as developed by Maine de Biran and Michel Henry), He presents a way of understanding knowing and learning in mathematics that differs from other current approaches, using case studies to demonstrate contradictions and incongruences of other theories–Immanuel Kant, Jean Piaget, and more recent forms of (radical, social) constructivism, embodiment theories, and enactivism–and to show how material phenomenology fused with phenomenological sociology provides answers to the problems that these other paradigms do not answer.
Math Electives This revision of Boyce & DiPrima's market-leading text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Like previous editions, the new 9th edition of Elementary Differential Equations is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. Differential Equations: An Introduction to Modern Methods and Applications is designed for an introductory course in differential equations. It emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. Accounting matters-- that's the underlying message of the new Fifth Edition. More than ever before, this edition shows students the relevance of accounting across all business segments, regardless of their chosen major or profession. This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract.
Re: Why is quiz part often harder than content in a maths textbook? It seems a convention that maths teachers leave the hardest part in problems. I am forced to agree. I have seen some where the problems are undoable even if you are familiar with the chapter
Upper School Classrooms Math 6th Grade Mastery of skills and number sense related to multiplication and division with fractions, decimals, and percents; exploring topics in measurement, geometry, and probability; pre-algebra topics including proportions, algebraic notation, solving equations, and integers. 7th Grade Pre-algebra; use of algebraic formulas, graphs, and tables to represent patterns and functions, both abstract and applied; use of decimals and fractions in algebraic equations; applying algebra to percent and proportion problems; properties of real numbers; extension of geometry and measurement to three-dimensional shapes. 8th Grade Algebra; formal work with algebraic notation; solving and graphing equations and systems of equations of different forms; solving and graphing inequalities; polynomials and rational expressions; quadratic equations; use of the quadratic formula; radical expressions and equations.
Teachers and Tutors: Ends and values below and site lessons and lesson ideas will help you provide your students with a stronger base for calculus and for earlier high school mathematics. Explore this site for lesson ideas if you were press-ganged into mathematics instruction or if you would like ideas and methods for easing and avoiding common fears and difficulties. Welcome. Online books and further webpages on learning and teaching mathematics and pattern based reason may develop critical thinking, improve reading and writing, and provide a base for learning or teaching college and high school mathematics. Site books are online in full with prequels and postscripts. Kind reviews implies some site chapters and lessons may entertain and inform. More starting point suggestions - not bad - for site exploration Test or improve reading, writing critical thinking and problem solving skills with the leading logic chapters in Volume 2. Logic mastery may ease or avoid learning difficulties, and so make further studies easier - just add effort. lotsa of it. Improve the quality of written work in mathematics with this formula evaluation format. It and its vertical alignment of equal signs shows how to do and record evaluation steps, so that they can be seen and checked. The format here can and should also be used with arithmetic expressions, step by step. The format here for "showing work" makes the domino effects of care and mistakes easier to see. Why do we study slopes, factored polynomials and the max-min analysis of functions in high school? Answer are given by this light calculus preview and then online chapters 2 to 7 in Volume 3, Why Slopes and More Math. Check basic arithmetic skills with the exercises in Chapter 7 of Volume 2, Three Skills for Algebra. These exercises with hints of algebra are for students in senior high school mathematics, or the first days of calculus. Answers are provided. Success in mathematics requires respect for how later skills and concepts depend on earlier ones. If one site element is not to your liking, try another. Each one is different. Study what you need now for the next test or final examination, good luck. Then explore more site material, as much as you can swallow or digest, before your next mathematics course begins. Site books and sections include many more lessons in arithmetic, algebra, geometry, calculus and real analysis. The essay Mathematics ... which way to go, how and why below introduces site aims and content. Site material is not perfect - parts need to be rewritten. But site content in the essay below and in site lessons or lesson ideas give possible remedies, remedies which need to be tried, tested and even improved, for many problems facing instruction aimed at student mastery of ideas and methods, those of service to daily and adult life and/or college studies. Site lessons and lesson ideas in giving or describing how to teach logic and mathematics directly provides a standard to meet or exceed in direct and indirect course design and delivery. "Would you tell me, please, which way I ought to go from here?" "That depends a good deal on where you want to get to," said the Cat. "I don't much care where--" said Alice. "Then it doesn't matter which way you go," said the Cat. "--so long as I get SOMEWHERE," Alice added as an explanation. "Oh, you're sure to do that," said the Cat, "if you only walk long enough." (Alice's Adventures in Wonderland, Chapter 6) -- Different ends and values for instruction leads to disagreement on what should be met, how and why. No position on mathematics education will please all. The site position is based on a technical view of how later concepts and skills depend on earlier ones, and in particular on what mastery of calculus requires from earlier studies at the high school and even primary school level. However, preparation for calculus should not be the only aim for earlier schooling. For more context and motivation and for less student alienation, ideas and methods with take-home value clear to students and their parents may provide another focus, a maximal one, for early instruction. Clear ends and values may focus and motivate mathematics education and in the process lead to fewer topics. Then skill and concept development may proceed with quality first and quantity second. Site Origins & Limitations Writing began offline in the last few days of 1990 to address two mathematics education obstacles: First, common fears and difficulties may be explained by concept and skill development steps to big for most, not all. Second, student alienation from mathematics mastery may be explained by those fears and difficulties, combined with an absence of reasons or context for mastery of concepts and skills, one at a time, one after another. Since 1990 or so in Canada, the UK and the USA, many teacher education programs advocate pychological theories of learning in which instruction aimed at student mastery of given ideas and methods is regarded as substandard and unreliable end for instruction. Unreliability may be reduced by addressing the two obstacles just mentioned. However in practice for decades before and after 1990, educational authorities have set final examinations which hope for mastery of ideas and methods in mathematics and other disciplines in a repeatable and reproducible manner. If the conflict seen here between educational theory and practice leads to course design and delivery with little or no respect for how later ideas and methods depend on earlier ones, then we have a third obstacle to student mastery of higher level ideas and methods in mathematics. While holding student back a grade or two will harm their self-esteem, the continual promotion of students in schools without respect for how mastery of later ideas and methods stands on mastery of earlier ones will eventually undermine and destroy student skills and confidence. Site material in providing lessons and lesson ideas, and in offering ends and values below may, albeit not all certain, ease the foregoing problems in logic and mathematics education. The composition of ideas and methods, offline in 1990 and online since summer 1995, was and remains an iterative affair. It was guided by inductive principles for instruction aimed at student mastery of given skills and concepts. met in 1981 outside of mathematics. Every master of mathematics knows how mathematical induction may fail, and by analogy how such instruction may fail. In particular, Common fears and difficulties may be explained by steps missed and by steps too big, not for all, but for most. Remedies may follow from smaller or alternative steps to make mastery of key skills and concepts easier and quicker. Site technical and wordy remedies for common fears and difficulties will fail when and where students and schools do not respect how later skills and concepts depend on earlier ones. The student or school wanting algebra be taught well without a previous mastery of exact arithmetic with decimals, fractions and signs is setting the stage for a mastery of algebra too weak for strong courses in mathematics at the college and senior high school level. Skill and concept development to succeed has to respect how later ideas and methods stand on earlier ones. While no amateur nor professional has the right to impose a mathematics education program on students, parents and educational authorities, today any one may propose one online. The reforms or remedies here like those elsewhere need to be tried and tested before general use. Incomplete ideas for reform rushed into service may disrupt education more than it helps. Principles for instruction no matter how good need to be fully supported by lessons and lesson plans likely to work in a repeatable and reproducible manner for more. By fall 2011, site lessons and lessons ideas for addressing content, that is concept and skill, mastery difficulties were essentially online in full but in some need of editing and pruning. Between spring 2012 and 2013, the issue of why and what to learn or teach in logic and mathematics was addressed first in a first phase program for mathematics and logic instruction, and then in the ends and values outlined below. Here again, there is some work to be done in identifying and presenting skills and concepts with take-home value for daily or adult life in ways that may also serve further instruction. While the site author has a doctorate in mathematics with ten plus years of experience in instruction, the composition of site material in the last two decades has been generally without further classroom experience. So the composition of site ends, values and lesson ideas has mostly been a post-classroom experience driven by inductive principles and standards for concept and skill development, and by kind reviews. For students, which way to go in mathematics and how far depends on the motivation found in school or which they bring to school. High marks provides motivation for those who like to perform for themselves or for parents and teachers. Further motivation of a social nature comes if a student likes a teacher, belongs to a group of students who are competing academically, or has parent who favours hard work in school and college. But the apart from that, the short- and long-term end and values below offer sounder context for skill and concept development. Courses in mathematics and science are in part like movies or books. What a course covers, how and why, is often a mystery before its end and to often after. For most students, the question why learn or study a subject or a topic appears. The appearance is a sign of intelligence. Some students have parents who say mathematics mastery is important. But nany have parents who in recalling their experience express a dislike for mathematics after primary school. But if we combine ends and values from earlier times, we may arrive at overlapping sets of ends and values for learning and teaching primary and high school mathematics. These ends and values are easily understood and repeated, and likely to be just right for some. The first two ends reflect the actual or potential needs of adult or daily life, and in trades and activities that do not require common studies. The third end reflect the needs of calculus-based college programs and of advanced, senior high school science courses. The first two ends are more immediate than the third end. For the first two ends, if not the third, over-preparation is better than under-preparation to students and their families earn their livelihoods and to rationally defend their interests in a world where daily behaviour, and contracts involving money matters or income have huge consequences for individuals and their families. For mathematics and logic instruction, preparing children and teenagers to earn income as adults may meet the need of employers, but more importantly, it may and should meets the needs of students and their families for earning income in employment or self-employment, and defending their own interests while changing jobs or being fired from a long-term post. While high school, trade school, undergraduate university programs and graduate university programs may open doors for gainful employment, education too long or too much may also distract from gainful employment. Showing students early how to handle money matters in daily and adult life from not going into debt while buying or selling to evaluating the immediate or long-term value of a mortgage, a pension plan or the income stream and benefits of a job with or without benefits may help them face or avoid common situations and difficulties. Early mathematics skill development may serve common arithmetic and geometric needs in daily and adult life. That may include say the common needs of precollege trades and professions. Preparation for daily or adult life at home, at work and in travel requires us to count, measure and calculate with money, time, length, area, volume, speed and rates of change on paper or with the geometric help of maps, plans and diagrams carefully drawn to scale. Arithmetic mastery may include formula evaluation. Early skill development should make us want to avoid the domino effects of errors. That has value for all multistep methods in- and out-side of mathematics. Early skill development, well done, may make mastery of routine skills and concept common, while providing a partial base for college studies. Focus mostly on method and ideas with actual and then take-home value may lead students and their families to value and want mathematics and logic in early instruction. The scout motto "be prepared" for what may come applies. For better and worse, numerical and logical skills and concepts are needed in daily and adult life to understand others, to read and write instructions precisely, and to correct yourself or others. There is a great risk of making incorrect decisions if you do not fully understand the numerical and logic reasoning used in arguments and agreements between yourself and others. Mastery of logic and basic mathematics, the more the better, will help you quietly recognize faulty decision making, yours or that of others. In early or later development of mathematics, or of reading and writing abilities, logic mastery leads to more or full precision in reading, writing, speaking and listening. This precision will ease or avoid confusion in following and giving instructions in many arts and disciplines at home, in school and in the workplace. Logic mastery sooner rather than later is best for its take-home value. But when may depend on each student. Before or beside logic mastery, early skill development may emphasize how to do and record measurement and arithmetic steps precisely, so that the steps can be seen and verified, and so that students become aware of the need to avoid the falling domino effect of errors. In this falling domino effect, a mistake in one step leads the following steps to being in error, except in the lucky case where a second or further mistake cancels the effect of the earlier ones. For that, there should be no credit. Plug: The leading math-free chapters of online Volume Three Skills for Algebra on implication rules and their use in deductive reason may lead the not too young to logic mastery. Mid- and senior- high school mathematics and logic skill development may build on early development to serve the needs of senior high school science and technology courses, and the needs of calculus-based college programs in commerce, science, engineering and technology. Calculus in the first instance consists of calculation of slopes for linear and nonlinear curvers y =f(x). The key role of slopes in calculus explains why slopes and rates of change need to be mastered in earlier studies. Hint, Hint Site volume 3 with its light calculus previews offer a context for the study of slopes, factored polynomials and function maxima and minima may amuse and inform students in courses leading to calculus and in the first weeks of calculus. Students heading for calculus-based, college programs in business, if they avoid demanding high school science courses, will not see senior high school mathematics used before arriving in college. To compensate, long-term value needs to be emphasized - the calculations and logic of college level programs requiring calculus will be more difficult to use and bend to our future requirements with a weak mastery of mathematics. Site volumes 2 and 3 in forming and reforming the views of students and teachers in senior high school mathematics as indicated above may inform and amuse, and in the process provide some context and motivation for the study of slopes, factored polynomials, function maxima and minima, and calculus too. All the ideas described briefly below are explained in more detail in site algebra starter lessons and in site Volume 2, Three Skills and Algebra. The arithmetic related ideas could have been placed with site arithmetic lessons instead. Arithmetic and algebraic expressions are often to complicated to read aloud, term term by term. Diagrams too are better seen than "read aloud". Outside of mathematics, a picture is worth a thousand words. In mathematics, a symbol, an expression or a diagram better seen and grasped in silence may also be worth a hundred to a thousand words. There has been a great silence in arithmetic, algebra, geometry and calculus because mathematical ideas and methods are often better written and drawn in silence instead of being expressed and explained aloud. Yet we may deliberately use more words to introduce skills and concepts clearer, to talking unifying themes, and to improve communication in circumstances where writing or drawing is not possible. While demonstration how appears in site material, we will identify where the greater use of words is possible. There is more to mathematics than be given a formula, and numbers to use in it. But remember, pictures and diagrams too can be employed alone and besides words to make skills and concepts easier to learn and teach. Before and besides the role of letters and symbols in algebra, we may use words and numerical examples to talk about about and show how to calculate totals and products by adding and multipling subtotals and subproducts. We may also talk informally but precisely about counts and measures as being known or not, constant or not, forgotten or not, and variable or not. Many technical terms may be introduced and understood before and besides the letters and symbols. Moreover, to gossip or talk about people, places and activities, we need names, labels and phrases to identify them. In mathematics, names and descriptive phrases such as the compound growth formula, the rectangular area calculation, the distributive law and the Chinese Square Proof of the Pythagorean Theorem allow us to gossip and talk about calculations and further ideas in situations where symbols and diagrams cannot be formed nor read. Most formulas, methods and practices in mathematics and logic are named. For people wanting and able to talk about what they learning with others, learning the names becomes an asset and not a burden. In describing how to calculate averages and how to compute the perimeter of a polygon, word descriptions of how may be simpler or not to understand and explain than formulas. As a first example, the average of a set or sequence of numbers is given by their total divided divided by the number (count) of set or sequence elements. As a second example, the perimeter of a polygon is given by the sum of the lengths of it sides, or more briefly by the instruction: add the sides. As a third example, the total area of a region consisting of non-overlapping subregions is given by a sum of subareas. In early mathematics instruction, how to compute this or that may be easier to understand and explain with words with the use of letters or symbols being more complicated. But for the compound interest or growth formula, for the quadratic formulas and later for the chain rule - do not worry what computations these phrases name or identify, the the letters and symbols in them are worth a thousand words. The greater use of words advocated for earlier instruction here is not possible in later instruction. So the silence will return. Using rules and formulas forwards and backward, and talking about it may end a further silence. Talking and writing about the forward and backward use of rules and formulas provides a unifying verbal theme for the study of logic, mathematics and science in school and college studies. Most if not all rules and formulas are not only used directly in a forward sense but also indirectly or backwards. Determing the constant in a proportionality relation uses the relationship, an equation, backwards. Once it is found, the proportionality relations may then be used or rewritten forwards and backwards to compute or express the value of one number or quantity in terms of others. The example here may not be familar to you if you have not seen them, but by talking about the forward and backward use of rules, formulas and proportionality relations, the backward use will be expected and not be another surprise for students weak and strong of mathematics, logic and science. This forwards and backwards use is common pattern previously met and mastered case by case in silence. Talking and writing about it introduces or extends the oral dimension of skill and concept development. Site algebra starter lessons and the online chapters of Volume 2, Three Skills for Algebra, material, show how to learn and teach skills and concepts with words, forwards and backwards. Algebra starter lessons include a geometric, stick diagram introduction for solving linear equations in a way that visually proves or improves fraction skills and sense. Here fractional operations on stick diagrams are suppose to make the algebraic solution of linear equations easier to grasp. However, in entertaining a group of students during a one hour, substitute teaching assignment, one keen student could not make the transition from solving with stick diagrams to solving algebraically. It was not my place to give him extra instruction. He may have been better served by more stick diagram examples, or by a leap to the algebraic method. I cannot say. Geometry too can help with the introduction of calculus and in providing motivation or context for the study of slopes (remember the domain name is whyslopes.com) and the study of factored polynomials alone and in ratios (rational expressions). See site Volume 3, Why Slopes and More Mathematics, online in full with a fall 1983 why slopes prequel. Volume 3 in a preview of calculus provide geometric motivation for the study of slopes and factored polynomial to the location of maxima and minima of functions. The site introduction of complex numbers is geometric instead of algebraic. It follows or re-invents a path in a 1951 book on Secondary Mathematics (possibilities) by Howard Fuhr, a mathematician who masqueraded as a mathematics education professor at Columbia University and who as part of the NCTM leadership in the 1960s help develop and implement the college-oriented Modern Mathematics Programs for skill and concept development in primary and high school mathematics from counting to calculus. The level of rigour in this geometric introduction of complex numbers is not less than that in the geometric introduction of trigonometry using triangles and/or the unit circles drawn in a Cartesian plane. The big steps in modern mathematics programs were too hard for many to follow. Site material offer smaller steps to compensate. Before modern mathematics programs, instruction had a greater focus on skills and concepts with value for daily and adult life - work, mortgages and investments included. The discussion of ends and values above suggests preparation for daily and adult life as much as possible first and foremost, and on preparation for college second while emphasing anything in the latter that could have take-home value. Site composition was driven by a search to remedy the skill and concept development difficulties stemming from steps too big and steps without clear value for students and their families in earlier programs in mathematics and logic education - programs which aimed for student mastery of selected skills and concepts. In consequence, site lessons and lesson ideas include many expositional innovations to aid skill and concept development. Most, if not all, are mathematically correct, with a few small departures from earlier views to make instruction simpler. In calculus and secondary mathematics, late primary mathematics too, there are many different starting points for instruction. For example, the site development of prime numbers begins with a definition that is not the most general but with a definition that is likely the easiest for students to understand and apply. For a second example, the site essay on what is a variable, by talking or writing about numbers and quantities varying in one sense or another, we provide a prequel to the later, more formal and more algebraically advanced view of what is a variable, a prequel that is easily understood because it is wordy and pre-algebraic. For more examples, see the site geometric development of complex numbers before trig, and see light calculus preview in Volume 3, Why Slopes and More Math, and see, still in Volume 3, the decimal prequel to the epsilon-delta view or definitions of limits and continuity. The choice of starting point need not reflect the conventions of higher mathematics, conventions that may be arbitrary despited being widely accepted. Instead, the choice of starting point may reflect the objective of making skill and concept development simpler for students and their teachers. The harder starting points may be left to advanced studies involving fewer students and teachers. Mathematics Literacy: Since students may leave school early, we need to show them and give them mastery of reading, writing, arithmetic and geometry with actual or potential take-home value for their daily and adult life in local and distant communities. While learning mathematics with comprehension is best, the take-home value of basic and routine skills needed for daily and adult to important to insist upon mastery with comprehension. In this course design and delivery should emphasize the domino effect of errors in multistep methods, numerical or geometric. And in arithmetic, students should be shown how to do and record steps in a manner that their skills can be seen and checked as done or later. In practical, skill-based arts and disciplines from cooking to mathematics, skills needs to be demonstrated to be believed, and indeed to be both taught and mastered. In general, there are too many skills for a student to find them or their refined form by discovery. The challenge for early mathematics instruction is to identify and provide observable and thus verifiable skills with take-home value that serves common or routine needs while seamlessly preparing students for late instruction. Geometry with Proportionality First: To quickly support the common, actual or potential, geometric use of maps, plans and diagrams drawn to scale in daily and adult life, and in precollege trades and professions, the site webvideo exposition of geometry may include SAS, ASA and SSS methods or practices for the construction of similar or proportional triangles, and in general assume that in maps, plans and diagrams drawn to different scales that corresponding angles are equal and corresponding lengths are proportional. So the similarity or proportionality present in maps, plans and diagrams drawn to scale may be exploited to indirectly measure angles and lengths, and quantities computed from them. Trigonometry may then be introduced as a way to calculate angles and lengths instead of obtaining them direct from measurements, actual or of the corresponding angles and lengths on maps, plans and diagrams drawn to scale. The early mastery of common, and easily understood and repreated practices with maps, plans and diagrams drawn to scale provides a context for and even implies the assumptions and axioms of Euclidean Geometry. Geometry with Congruence or Isometery Second: For simpler or more accessible account of Euclidean geometry, the site account does not include a proof of the Pythagorean thereom. The Chinese Square Dissection proof provides a more accessible alternative. The latter is presented online in Volume 2, Three Skills for Algebra. Without the Pythagorean thereom, Euclidean geometry may be easy enough to return to the North American classroom in a way that shows high school or college students how logic in the form of implication rules alone and in direct deductive chains of reason appears in mathematics. Counting and Arithmetic with Decimals: Decimal place value is the key to counting. We assume every set of fewer than 10, 100, 1000 and 10000, etc, can be divided into a group of upto 9 units, a group upto 9 groups of ten, upto 9 groups of 100 and upto 9 groups of 1000 in manner that the count between 0 and 9 of units, 10s, 100s and 1000s are unique, albeit the division of set elements into groups of units, 10s, 100s and 1000s is not unique. The foregoing division or partition gives a unique, multidigit decimal way to write and record the count or number of set elements in which each unit has a place value. The concept of place value leads to and easily justifies arithmetic counting shortcuts involving the addition, comparision, subtraction and multiplication and even division of decimals. The details are given in the site arithmetics section along with North American, metric (or SI) and UK-German methods for writing and reading aloud with words multidigit decimals without and then with a decimal point. Comprehension of operations with decimals enriches early instruction and may help some master these operations. Others, most others perhaps, may find full explanation of why some operations work too complicated for their liking. For them skill and confidence in decimal methods may follow learning how to use the methods to obtain repeatable and reproducible results via steps observable and, if need-be correctable. Counting and Arithmetic with Fractions: The fraction three quarters when written or read aloud means three times a quarter. A quarter ¥ is a unit fraction. Proper and improper fractions with the same denominator all give a number or count of a unit fraction, that associated with the same denominator. With the aid of decimal representations forms of numerators, it is an easy matter to count, add, compare, subtract and even divide multiples of a single unit fraction. It also an easy matter to multiply a multiple of a single fraction by a whole number - to form a multiple of a multiple. By long division and regrouping, each improper fractions is equivalent to a mixed numbers. In primary and secondary school, students may be shown how to add and subtract fractions with unlike denominators by raising terms to convert each fraction to another equivalent fraction, so after conversion, each has a common denominator and so is a multiple of a common unit fraction. Following this, students may be shown how to compare, multiple and divide fractions by rote. Site fraction lessons in contrast show how raising terms to obtain like denominators explains and justifies methods to compare and divide fractions while raising terms to ensure the numerator of the multiplicand is a multiple of the denominator of the multiplier explains and justify methods for fraction multiplication. The justification of arithmetic with fractions sets the stage for the justification of arithmetic with decimal fractions (multiples of one-tenth, one hundredth, one thousandths) that usually denoted by multidigit decimals with digits after and even before a decimal point. Comprehension of operations with fractions agains enriches early instruction and may help some master these operations. Others, most others perhaps, may find full explanation of why some operations work too complicated for their liking. For them skill and confidence in decimal methods may follow learning how to use the methods to obtain repeatable and reproducible results via steps observable and, if need-be correctable. Prime Numbers and Fractions: For algebra alone or as part of calculus, and for operations with complex numbers, students need an efficient command of arithmetic with fractions where the denominators are say less than 200. Prime factorization of whole numbers less than 200 is useful here. The development of prime number factorization methods in the site arithmetic section shows how to use time tables to recognize small primes, and how to use an olde square rule method to quickly and efficiently obtain prime number factorization of whole number less than 289 = 172, and to recognize primes less than 289 as well. The foregoing path as demostrated in site arithmetic section may be easier for people to learn and teach. Prime factorization is also useful for a "simplification" of roots involving whole numbers or their fractions, a simplification often seen in trig and calculus. Mastery of exact arithmetic in high mathematics requires mastery of some cosmetic standards or conventions for the expression of fractions, roots and radicals. Arithmetic with units and denominate Numbers - missing. Units of measure and counting appear directly in daily and adult life, and also in science and technology. Units of measure also appear in the description of speed, acceleration and other first and second order rates - rates that may be described as derivatives in calculus. Modern mathematics programs did not mention nor sanction the use of units and their multiples (denominate numbers) in high school and college studies, albeit this use appear in science courses and in some practical examples met in mathematics courses in trigonometry and before. The site account of arithmetic and fractions with units compensates for this. Albeit, the compensation is given in a do this, do that manner, because of a lack of words on my part to provide greater comprehension. Readers are invited to provide remedies. Early algebra courses today may introduce monomials (products of letters or "variables" to various powers) and operations on them alone and in fractions before students understand the computational significance of monomials and operations on them. Site algebra starter lessons explanation of equivalent computation rules may provide a remedy for that. But before or besides algebra, The same exercises with monomials given by numerical multiple of products of units to various powers may be more meaningful to students, while be a prerequisite to the numerical description of rates and proportionality constants. Algebra Starter Lessons. Showing students how to do and record numerical and algebraic steps in ways that can be seen and checked when done or later makes their mastery of multistep methods observable, and hence verifiable or correctable. Showing should also make students aware of the domino effects of mistakes, and the care needed to avoid or correct such errors. The introduction and assumption of methods to compute totals and products using subtotals and subproducts employs practices that are too complicated in high school instruction to derive from the usual axioms for arithmetic with real numbers. But the assumption of these methods or practices extends the usual axioms and from the perspective of advance mathematics gives a very redundant set of axioms. But the same redundancy is justified as it makes early instruction easier and more effective, and the extra assumptions have immediate take-home value for daily and adult life not present in the usual axioms. Now the usual axioms are best understood besides or after a math-free mastery of logic. The usual axioms for the distributive, commutative and associative law are algebraically described. Many students find the algebraic description too remote or abstract. But if we introduce the concept that each algebraic expression give a unique computation rule, one that that be evaluated on paper or with the aid of a program on a calculator or computer, we may observe from numerical examples that different computation rules appear to be equivalent in the sense that they give the same result. This small step of introducing the concept of equivalent computation rules provides another context, a different starting point, for understanding and explaining distributive, commutative and associative laws in arithmetic with many kinds of numbers, and eventually with numbers being replaced by computation rules - those with numerical values. Arithmetic without Calculators: To be over-prepared is better and less risky than being under-prepared. A written, calculator-free mastery of arithmetic with signs, decimals, fractions; with units of measures; and with number theory practices is needed for a full, traditional, mastery of algebra, trigonometry, complex numbers and calculus. A full mastery of arithmetic with units of counting and measures also has value for adult and daily life, and for further studies in commerce, science, engineering and even mathematics itself. In modern urban life we depend on machines to simplify our daily life. But calculators usage both simplifies and weakens mathematics mastery, or that needed to understand decimals, fractions, algebra, trigonometry and calculus. As a master of my subject with standards for skill and concept development, I see the student who can only do arithmetic with the aid of a calculator as being handicapped from being too spoilt in earlier instruction. Any expectation that quantitative skills and disciplines can be well-taught without a written mastery of arithmetic with decimals and fractions is false. Again, manually learning how to do and record work in steps that can be seen and corrected as done or later may begin with evaluation of arithmetic expressions and algebraic formulas. While calculators are useful, failure to require manual student mastery of arithmetic removes a starting point for observable skill and concept development. In particular, mastery of observable steps that can be seen and confirmed or corrected as done or later is also is key part of showing and demonstrating abilities in problem solving, in writing proofs and employing multistep methods at home, at work and in studies in many arts and disciplines. Mathematics after primary school has been difficult and without immediate value for many generations of students. While some students have parents who did well or who encourage skill and concept development, other students have parents who may say mathematics after arithmetic is a waste of time. High school and college students may attend courses because those courses are required. In high school and college, students who base their efforts only on whether or not their teachers are pleasing have a shallow context and motivation for learning. Students for whom doing well in tests and finals is the only motivation also have shallow reason for learning. Cultural values for learning may appeal to some. But practical ends and values may appeal to more. In primary school, students and their families may see the 4Rs (reading, writing, reasoning and arithmetic) as being useful in adult and daily life. There-in lies content and motivation. But at the junior- and mid-high school level, some mathematics and logic lessons are of actual or potential service to daily and adult life for decision-making and money-matters at home and the work place. Other lessons only have long-term value for college programs that some students may never enter or complete. Instruction may lean to the first kind of lessons initially to provide ends and values easily understood and appreciated by students and their families. Emphasizing the more useful methods and concepts first may help retain student motivation and also help those who have leave school early. But eventually, high school and college mathematics has less and less take-home value besides more and more value for future studies or courses that students may not see. Here again, instruction may focus on the take-home value, when present to provide motivation. At the precalculus level, instruction should focus on two kinds of skills and concepts, those that have actual or potential take-home value for daily & adult life, and for precollege trades and activities; and those that prepare students for a light and then deeper command of calculus. In the former, I would include a set-based development of probability theory. In both streams, I might include matrix operations but not linear programming. The latter can be left to college programs in commerce, science, engineering and technology. I would restrict high school mathematics to computations and proofs that are lead to repeatable and reproducible results, and to the computation of averages useful in small business for estimating demand for products and services being sold. Further elements of descriptive statistics, I would leave to college studies, or to high school courses on critical thinking. The recommended focus may mean fewer topics are taught. For students not heading for calculus-based studies, less with a focus of skills and concepts with take-home value may be best. In the preparation of students for calculus and senior high school mathematics, multiple topics with no short-term value may be met. That short-term value will vary between students. Students in courses required to prepare for calculus who do take mathematically demanding, senior high school courses will see more short-term value. In general, calculus and preparation for calculus is a long demanding path which many find difficult or hard to complete. But, here is a plug, site Volumes 2 and 3, make the path easier and throught calculus preview make calculus and precalculus easier and more appealing. To serve the skill and concept needs of the common person in the street, we need to put first those skills and concepts with actual or potential value for daily and adult life. Then students may attend school and go home with methods that help themselves or their families in money and other matters. Near the end of school coverage of arithmetic, geometric and logic (or reading and writing) skills and concepts with actual or potential service for daily and adult life, more algebra and higher level geometry skills may be introduced to revisit and reinforce the foregoing service while being of service to more trades and activities at the precalculus level, and also being of service or preparation for senior high school science courses and perhaps later studies in calculus. The multiple ends and values in the foregoing need to be balanced. The balance may depend on the local or immediate needs of students and their families, that is, how long students are likely to remain in school; on whether or not, they are likely to see all all ends and values served; and on whether or not, the students are quick or slow learners. The concept and skill development standards and principles for instruction in results-oriented arts and disciplines, as espoused in site material, seek to provide students with an observable and verifiable know-how of the ideas and methods currently forming and characterizing each art or discipline. The latter presents a moving targets as best practices in each may vary over time and place. But in a moving target, concept and skill mastery may be seen or empirically measured by student response to questions. In each such art and discipline, students are expected to retain know-how and build on it in a progressive manner, with regression being a sign of weakness, or absence too long from practice in an art or discipline. Each art or discipline comes with different cultural and practical values, some more important than others in ways that may justify its instruction or not in each school or school system. Morover, course design and delivery needs to acknowledge that there are multiple intelligences in learning and teaching styles. A style that is suitable for instruction in the humanities where conclusions are highly subjective is not suitable for instruction in mathematics and science where the benefits, origins and limitations of ideas and methods need to be indicated and mastered in all or part. In modern mathematics programs for secondary mathematics education, direct instruction aimed at student mastery of given concepts and skills has been uncertain and unreliable due to steps too big or hard for most to follow, and due a college-oriented choice of concepts and skills with value too long-term for students and their families. Those steps too big undermined course design and delivery. However, direct instruction can address its own problems by serving short- and long-term ends and values in the selection and arrangement of course topics, and in offering smaller, more accessible and reliable steps for concept and skill mastery. The key question is whether or not remedies based on the smaller and alternative steps in site lessons and lesson ideas, alone or with the proposed ends and values above, will be effective.. Site lessons and lessons ideas from counting to calculus provide a foundation for college level studies of modern mathematics. Site lessons and lesson idea offer student and their teachers a mastery of concepts and skills with comprehension, if that be wanted, based on a redundant set of practices and axioms, whose redundancy can be explained and removed in college course in or leading to modern mathematics. The ends and value further offer reasons for mathematics and logic mastery that students and their families are more likely to appreciate before preparation for calculus becomes the main focus of instruction at the senior high school level. For calculus, Chapter 14 of site Volume 3, Why Slopes and More Mathematics, offers a decimal, error control development of limit and continuity concepts that may stand alone, or be used to make the epsilon-delta development much easier to understand and explain. Site departures in early instruction from modern mathematics are intended to provide TCPITS an more accessible view, but they are also intended to develop the logical and algebraic maturity needed for college and senior high school students to study modern mathematics if they choose or where it appears in their programs of study. Indirect Instruction Benefits and Limits Indirect instruction has the advantage of enriching skills and concept mastery in classes where there is time for individual and group creativity. But the subjective nature of that enrichment means direct instruction is needed to develop or at least consolidate mastery of core skills and concepts, those on which later methods and ideas stand, Moreover, for student mastery of skills and concepts of importance for their take-home value, or importance for further mastery, direct explanations seem more reliable and certain than indirect ones, and easier to design and provide. When and where direct instruction clear steps or lessons to provide mastery of important skills and concepts, to aid student to follow the steps and lessons as is or in briefer form, teachers may provide circumstances and pose questions to indirectly lead student to formulate ideas and skills and gain the experience on which direct instruction may stand. But where direct instruction lacks those clear steps and lessons, it is doubtful that indirect instruction will provide a practical and clearer path to to student mastery of the given skills and concepts. The ability to explain matters directly is likely a prerequisites to the ability to provide skill and concept mastery indirectly. Each program of instruction aim at mastery of given ideas and methods has varying degrees of success and failure, and of motivation and alienation for students and their families. In the case of modern mathematics programs for secondary and college studies, the very rigour that attract some students repelled many more, and include steps too big and also, I will missing, in course design and materials. Missing steps were missing not only in modern mathematics programs for algebra alone and in advance courses, but also in earlier methods or paths for concept development. The missing steps represent old gaps inherited in the design and redesign of mathematics instruction over many, many decades, if not a century or two. Site material in providing smaller steps allows steps too big to be recognized and gives remedies - full or not - to be tried and tested. Given that students have multiple abilities levels, a situation inherited from nature, how far students may go in mastery of mathematics depends on their will and natural talent. Smaller steps should allow more to go further
A new model for graphing functions of complex numbers 4DLab plots complex functions in an integrated way: the domain and the range of a function are not shown apart. In fact, complex functions are plotted analogously as the real functions are plotted. The traditional graphing procedure —in textbooks and in other plotting software— is to separate the function domain from the function range; this is because the domain is usually a plane region of a plane, and the range is usually a surface. But 4DLab follows the new transcomplex numbers approach, where the complex numbers are extended to 4–dimensional ordered pairs. At last, the graphs of the functions of complex variables are meaningful! The transcomplex numbers system is an extension of the complex numbers system to 4 dimensions. Complex variables are 2–dimensional while transcomplexs are 4–dimensional. There are other four entries numbers systems, like, for example, the quaternions. But only the transcomplexs combine the simplicity of the real numbers with the power of the complex numbers. But where the transcomplexs shine above all the others is in the graphs it produces: visually simple and beautiful; no more abstract "surfaces", no more dual and disintegrated plotting. 4DLab is the software made specially to plot transcomplex surfaces, but since mathematics is an integrated and unified field, 4DLab also follows this model. Thus, in the same way that 3–dimensional surfaces are plotted, the 2–dimensional real functions are also plotted: you use the same equation editor. Just write-in —the editor will check your syntax— and choose the type of rendering you wish. Math can be inspirational! 4DLab was also a program made to produce aesthetically appealing images. There are many choices and parameters to choose or change. So, if you wish, your plots can be done over an appealing background, you can add your name, or the equation involved, etc. 4DLab is a new tool for learning math and a new tool for graphing 3D equations and 2D equations. This free software is a3D and 2D graphing software. Choose a picture —any picture; a texture, a landscape, a photograph— and plot it against a surface and you will visually grasp the concept of one-to-one (1–1) mapping. Complex math can be made simple by bringing some abstract concepts down to the point that it becomes personal. Overall Features of 4DLab: With 4DLab the function domain can be any rectangular shape; not necessarily square. Graphs can also be made of any rectangular sub domain of the main domain. Surfaces can be shown in grid-only mode, or opaque with or without showing the grid mesh. Axes are shown exactly where they belong: intersecting the surface at the exact points. For any function, the domain-to-range relation can be seen instantly by just moving the mouse over the the domain region. The corresponding point of a domain can be seen as a moving point, or as a line connecting the domain with the range. This is an useful tool, especially when a point in the space is relate to another point in the space far away, or not directly above, as with real functions plots. The program incorporates a dedicated calculator to compute the coordinates of any point coordinates for any equation set, be them part of the equation domain or not. The program can maintain a list of your favorite website links with editable comments. You can click on any of the saved links for immediate reference. Decorate any of your math pictures with any background of your preference. The coordinates axes names can be changed to adapt to your needs. So, instead of X, Y, or Z, the axes labels can be named: Ohms, or Degrees, or Distance, etc. Surface or line pictures can be labeled as Fig.1, Fig. 2, etc, or the user can insert, his/her name or a copyright notice. Other labels are available. The notes are saved as part of the pictures. Surfaces or line plots can be rotated and viewed from any angle. The program can show the surface plots intersection with the XY, or iZY planes. Pictures can be resized manually with the mouse, or can be resized exactly to any desired dimension with pixel precision. The center of coordinates can be moved away from the center of the picture frame for better composition of those offset plots.
Kahn Academy Submitted by Howard, from Portland, OR, who is not affiliated with the site. What started out as Sal Kahn making a few algebra videos for his cousins has grown to over 2,100 videos and exercises and assessments covering everything from arithmetic to physics, finance, and history. While there isn't a URL for just the math videos, they are easy to navigate to, with the drop down menu. Includes all levels of math from basic arithmetic to calculus.
Catalog Description: This course is intended to be a one-semester survey of Calculus topics specifically for Biology majors. Topics include limits, derivatives, integration, and their applications, particularly to problems related to the life sciences. The emphasis throughout is more on practical applications and less on theory. Pre-requisite: grade of C in Math 180, or suitable placement score. This course qualifies as a General Education course, G9. Text:Calculus for the Life Sciences, by Bittinger, Brand, and Quintanilla (Pearson-Addison-Wesley, 2006). Note: I have chosen a text that includes a nice collection of problems that are oriented toward applications of calculus to the life sciences. So this course really has two characteristics: (1) it is something of a "Calculus lite", a little less emphasis on theory and proof that the traditional course, and (2) it has a particular emphasis on applications in the life sciences. General Education Core Skill Objectives 1. Thinking Skills: Students engage in the process of inquiry and problem solving, which involves both critical and creative thinking. (a) The student understands the "big problems" in the development of differential calculus, the tangent problem and the area under the curve problem. (b) The student understands the mathematical concept of Limit. (c) The student explores differentiation and works with differentiation formulas for a variety of functions, including exponential and logarithmic functions, and the applications of these methods, especially to problems from the realm of life sciences (d) The student explores integration and a variety of integration techniques, and applications of these techniques to a variety of problems, especially those related to the life sciences. 2. Communication Skills: Students communicate effectively orally and in writing in an appropriate manner both personally and professionally. (a) The student does group work (labs and practice exams) throughout the course, involving both written and oral communication. (b) The student uses technology - graphing calculators and DERIVE in the computer labs - to solve problems and to be able to communicate solutions and explore options. (c) The student will use the language of mathematics accurately and appropriately. (d) The student will present mathematical content and argument in written form. 3. Life Values: Students analyze, evaluate, and respond to ethical issues from informed personal, professional, and social value systems. (a) The student develops an appreciation for the intellectual honesty of deductive reasoning. (b) The student understands the need to do one's own work, to honestly challenge oneself to master the material. 4. Cultural Skills: Students understand their own and other cultural traditions and demonstrate a respect for the diversity of the human experience. (a) The student develops an appreciation of the history of calculus and the role it has played in mathematics and in other disciplines. (b) The student learns to use the language of mathematics - symbolic notation - correctly and appropriately. 5. Technology: (a) The student will demonstrate the basic ability to perform computational and algebraic procedures using a calculator or computer. (b) The student will demonstrate the ability to efficiently and accurately graph functions using a calculator or computer. (c) The student will demonstrate the knowledge of the limitations of technological tools. (d) The student will demonstrate the ability to work effectively with a CAS, such as DERIVE, to do a variety of mathematical work. Required Course Work Your basic work in this course is to learn the material and develop your problem-solving kills so that you can apply the concepts and methods of the calculus to problems you will encounter along the way. It is important that you attend class regularly and especially that you do the homework. The homework may seem "hidden" to you since it will not be graded, but it precisely in that outside-of-class practice that you learn the material. There is a rule of thumb that says college courses require roughly 2 hours outside of class for every hour in class and I think this is not at all an overstatement. It takes discipline to leave class on a Wednesday or Thursday, knowing that you have class again the very next day, and still find a couple hours to practice your calculus, but it is exactly that sort of discipline that is required for success in the course. In short: DO YOUR HOMEWORK! Your grade will be based on two primary factors: (1) Exams; and (2) Group work. There will be a quiz following the review chapter, an exam following each of chapters 2 , 3, and 4, and then a final cumulative exam at the end of the course, following chapter 5. These exams will be done in class subject to the 50 minute time limit (except for the final, of course), but you can use a set of notes you prepare for the exam and you may use a graphing calculator as well. I see exams as a way to see if you as an individual can actually do what the course asks of you. Secondly, there will be two types of groupassignments: (a) Labs; and (b) practice exams. Every so often, roughly once a chapter, I will take a day and have you work in small groups of 2 or 3 students on a set of problems. I will refer to these problem sets as "labs", in the sense that you will be exploring the concepts and trying to apply them to the problems. I like the idea of asking you to occasionally work in groups – I think the opportunity to discuss the mathematical ideas is extremely valuable. After all, mathematics is a language as well as a way of thinking about things. I will also have you take a "practice exam" during the class period just prior to each individual exam. These practice exams will be done in groups like the labs, and must be turned in by the end of the period, as do the labs. This is an attempt on my part to give you an idea of what to expect on the exam. I am also going to try a sort of "oral exam" this semester – let's call it an "interview". After the third exam I will meet individually with each of you and ask a few questions to test your understanding of the material we have been covering. It is also worth mentioning here that because one of our goals is to develop some skills with technological tools, I will be asking you to use DERIVE on a few problems along the way. DERIVE is a computer program created by Texas Instrument, the calculator people, to perform a very wide variety of mathematical procedures. It is a CSA (Computer Algebra System), which means it can perform algebraic manipulations like solving equations or factoring polynomials, as well as graphing functions in 2 or 3 dimensions. It can also perform calculus procedures and we will have a chance to see some of this power. Instructional Methods My general "lecture" style is more of a give-and-take discussion than simply a rote presentation of material. I like to try to see that the class is following what I am doing and so I want feedback along the way. I often will ask a leading question to see that you are ready for what is about to come. One specific strategy I will use is called Think-Pair-Share. In this case I will ask a question and have each of you think about it for a bit, then pair up with a "neighbor" and finally share the answer with the rest of the class. Not every pair will share with the class each time, but I hope as we do this on a regular basis most of you will have an opportunity to speak. I have already mentioned the "Labs" we will do on occasion. I will randomly assign you to a group and give each of you rotating roles within the process; I'll explain the details when we do that first lab on Wednesday, 7 September. I will try to keep the labs reasonably short so that the group can turn in the work at the end of the period. Assessment Strategies The main outcomes I want to see in each of you can basically be listed briefly as: (1) thinking, or problem solving; (2) communicating your mathematical ideas and solutions; and (3) using technology to do some of the work. I will be assessing your ability to do these things throughout the course by grading the labs, the technology assignments, and the exams. I will also be noting your participation in the class room, both in your group work and in general class discussion. Grading System I expect, in sum, that we will have the following possible points during the semester: I will then assign letter grades as follows: 90% of possible points for "A", 80% for a "B", 70% for a "C", and 60% for a "D". By the way, I am aware that the biology program requires a grade of at least a "C" in its support courses, so you needn't tell me that if the going gets "close" later on in the course. I wish this wasn't the case, since it is sometimes stressful on me as well as on you, and I don't like "losing" the possibility of giving a "D" grade – sometimes people pass a course but "just barely". One final note about grading: I will "guarantee" the grade you earn on your final exam! What I mean by this is, regardless of the grade you have earned based on the percentage of total points, if you score a higher grade on the final I will accept this demonstration that you have learned the material at this higher level and will give that grade. Please don't depend on this as a means of getting through the course – most people do not show better performance on the final exam, but it does give you one last chance to improve things. Attendance Policy I think that regular attendance is of paramount importance in any course, but perhaps a mathematics course more than most. There may be the occasional exception, a student who is so mathematically talented that she or he can get the material by just reading the text and doing some problems, but for most students it is important to be in class every day. To encourage this I am going to include attendance in the grading scheme in a simple way: 1 point for each day you are there. I'm not going to engage in deciding whether absence is "excused" – too many subtleties and degrees there - just a point a day when you are there. Disability Statement I want to include taking exams in the learning center under this category; you will need a written request from Wayne Wojciechowski before I will allow you to take exams there.
The asymptotic approximations are not valid for small samples. The ability to perform exact statistical tests frees one from the worries of the quality of asymptotic P-values. `Exact Test` always gives you exact P-values, regardless of your... Are multiplication tables showing up in your kid`s homeworks? MULTIPLEjm will help your kids learn multiplication tables. Trying to beat their high score, they will have fun and will learn their multiplication tables. Dicom is the first ever calculator of its kind that deals with dimensions of physical quantities in mathematical expression. Dicom enables calculations, conversions, and documentations in one place, at absolutely no cost. Free math/graphing program that will allow you to develop and visually analyse mathematical expressions quickly and easily. Boasts a unique graphing module that permits expressions with up to 8 parameters to be plotted directly, such as y=Asin(kx+b). Robot4 (tm) is a Robotic Arm Movement program where the arm is moved from given position to desired position(an Inverse Problem). The program finds the angles necessary for the desired position. Improved Productivity demo do to Calculus programmingMiddle-School (grades 5 through 9) math program written to provide skills in context. Students use coordinate graphing to guide a moving dot through a series of mazes. Think: coordinate graphing pinball. Middle-School (grades 5 through 9) math program written to provide skills in context. Students calculate the probability of three different types of outcomes on a slot machine: three apples, at least one apple, or no apples. Middle-School (grades 5 through 9) math program written to provide skills in context. Students write and solve simple algebra problems, then manipulate the vertices of an on-screen triangle so that it matches given information about its angles. Middle-School (grades 5 through 9) math program written to provide skills in context. Given the radius or diameter of a circle, and the measure of a central angle, students find various areas and lenths correctly CFB Primes is an optimised PalmOS program which can find the prime factors and closest primes of any integer up to one billion (US) in a few seconds or less. The standard edit menu allows you to make use of the results in other applications. The Number Base converter is a tool which converts numbers from one base to another such as binary,decimal,hex,octal. The program is quite simple so even if you are a beginner you can use it without any trouble.
expression can be modified or corrected, and recomputed at will. There ara also unit conversions, physical constants, computer math (binary, octal, hex), and function graphs included. For more advanced users, Kalkulator provides less trivial operations: numerical integration and differentiation, interpolaton (linear or cubic spline), statistics (mean, s.d., histograms, polynomial regression), column operations on stat data, polynomial roots, linear algebra (vector/matrix operations and systems of linear equations). Hard-to-find features: systems of non-linear and differential (ODE) equations, multi-argument function extremum search and point or histogram fitting with an arbitrary function. Most importantly, advanced features don't obstruct the basic ones. You can use as much of Kalkulator's capabilities as you need, without being hampered by the program capabilities you do not need. Disk save/restore, Help file and other niceties are also included. Kalkulator has been evolving on various OS platforms for the last 15 years, being refined and polished through all this time, and its author has more than 25 years of active experience in numerical methods and software development. JMNumerics - JMNumerics is a Numerical Library for .NET. The library is written in pure C#, it has more than 150,000 lines of code with the most advanced algorithms for Linear Algebra, Differential Equations and Optimization problems.JMNumerics is a Numerical... GNU OctOctNature of Equations Video - A video explaining the nature of equations in algebra.A video explaining the nature of equations in algebra.Midget - Tiny calculator with 12 variables, 32 functions, unit conversion, deg/min/sec...A tiny, but very capable numerical calculator for Windows. It differs from others in the way you calculate your expressions: enter the whole expression at a time, like... Mr. Matt - An addictive logic puzzle game for Windows, all agesAn addictive logical puzzle game for Windows, similar to the classic Boulderdash, but with many enhancements and extra touches. Teen to adult age bracket, no gore or violence. You are Mr. Matt,... Statmaster - Many scientific and engineering programs generate numeric output which needs to be presented graphically.Many scientific and engineering programs generate numeric output which needs to be presented graphically. Statmaster is a simple way to do...
Free Science & Mathematics Software Learn about the foundations of mathematics and science with these free software downloads for Microsoft Windows. Scientifical topics range from biology and physics to geometry and statistics. For mathematics, see also: Free Calculators.
(6th Edition),(a) The student does group work (labs and practice exams) throughout the course, involving both written and oral communication. (b) The student uses technology - graphing calculators and DERIVE and Excel in the computer labs - to solve problems and to be able to communicate solutions and explore options.(a) The student develops an appreciation for the intellectual honesty of mathematical reasoning.(a) The student develops an appreciation of the history of linear programming and calculus and the role played by mathematics in business problems. (b) The student learns to use the language of mathematics - symbolic notation - correctly and appropriately. Specific Course Goals: 1. Students will participate in a formal assessment of their algebra skills and do appropriate work to improve their skill level to what this course requires. 2. Students will learn mathematical concepts that apply to business (as determined by the business school). 3. Students will learn how to apply mathematics to various types of business-related problems. 4. Students will improve their problem solving skills. 5. Students will learn to use technology, specifically graphing calculators and computer software, to solve a variety of problems. 6. Students will improve their mathematical reasoning skills. 7. Students will improve their ability to communicate, primarily in writing, mathematical ideas. Attendance: Very few students seem able to learn mathematical material independently, and it is therefore important to attend class and participate actively in these class meetings. I do not use attendance in a formal way as part of the grading process, but part of the commitment to success in the course is regular attendance. I include here a detailed schedule so that if you do have to miss a class you can keep up with the material, but it's not the same – you simply miss out on a key part of the learning process if you miss a class meeting We will also make some use of the Excel spreadsheet program for the linear programming topic. Homework: The homework assignments (by the way, the listed assignments are intended to be done following the material presented on the given day – not to be due that day) are in fact the KEY to learning the material and therefore to success in the course. I cannot overstate this – you cannot learn the material unless you practice. Here's an analogy: if you paid someone to give you piano lessons you would expect to have to practice, and you know that without practice your skills will never develop. Learning mathematics is just like that – Mathematics is NOT a spectator sport! I already know how to solve these problems, but the purpose of the course is not to convince you of that, but rather to put you in a situation in which you can, IF YOU PRACTICE ENOUGH, and if you are adequately prepared, succeed in learning the content and being able to do the problems. The problems I have listed in the daily assignments should give you a basic idea of the types of problems you will be expected to solve. If you can convince yourself that you understand the particular topic well enough to do all the problems listed, you might not have to actually work them, but you should at least work enough to test yourself. The single biggest mistake a math student makes is to look at a problem and say, "I think I can do this," without actually trying it. These are the students who say, "It looks easy when you do them in class, but on the exam I 'blanked'." At each exam you will be expected to show me that you can work problems that are very much like the ones you are supposed to have practiced. I know your program requires a "C" in a support course like this, and I can tell you that while the vast majority of students do earn the credit, there are always a few who don't. You simply will not be successful unless you work at it! My teaching style includes discussion and question-answering. You will only have questions to ask if you have put in the time trying to work the problems. Only then will you specifically know what you don't yet understand. 8 (EIGHT) hours per week to study mathematics. Quizzes: It is extremely important to stay on top of the class work; learning mathematics is something like learning to play the piano – you simply have to practice. To help insure that you do this I will frequently have a little 5-point quiz, based on the homework assignment from the previous class. This also amounts to a way of taking attendance and checking to see that you are doing the homework. I am trying to create a system that places value on class attendance and homework assignments that exam – it's not worth it to cheat, and it is also unethical. The grades will then be assigned on the scale: A = 90%, B = 80%, C = 70%, D = 60%.Disability Statement: If I reserve the right to make adjustments to the schedule and the syllabus in general as we move through the course. This is a new edition of the text and it may turn out that some changes may be necessary.
The ABC's of Nuclear Science The ABC's of Nuclear Science is a brief introduction to Nuclear Science. We look at Antimatter, Beta rays, Cosmic connection and much more. Visit here and learn about radioactivity - alpha, beta and gamma decay. Find out the difference between fission and fusion. Learn about the structure of the atomic nucleus. Learn how elements on the earth were produced. Do you know that you are being bombarded constantly by nuclear radiation from the Cosmos? Discover if there are radioactive products found i Author(s): No creator set License information Related content No related items provided in this feed 05 - Telling a Free Story: Fugitive Slaves and the Underground Railroad in Myth and Reality ProfessorLearning to Think Mathematically Concerned that most students leave college thinking of mathematics as a fixed body of knowledge to be memorized, Cooperstein designed a new course to help students learn to think mathematically for themselves. This website serves as a course portfolio that documents the new class, Introduction to Mathematical Problem Solving. The principal activity in the class involved students working on and discussing novel problems which required them to formulate experiments, work out cases, look for patter Author(s): No creator set License information Related content No related items provided in this feed Essential Physics I Essential Physics 1, is an intensive introduction to classical and special relativity, Newtonian dynamics and gravitation, Einsteinian dynamics and gravitation, and wave motion. Mathematical methods are discussed, as needed; they include: elements of differential geometry, linear operators and matrices, ordinary differential equations, calculus of variations, orthogonal functions and Fourier series, and non-linear equations for chaotic systems. The contents of this book can be taught in one seme Author(s): Frank W. K. Firk License information Related content Rights not set No related items provided in this feed Introduction to Groups, Invariants and Particles Introduction to Groups, Invariants & Particles is a book for Seniors and advanced Juniors who are majoring in the Physical Sciences or Mathematics. The book places the subject matter in its historical context with discussions of Galois groups, algebraic invariants, Lie groups and differential equations, presented at a level that is not the standard fare for students majoring in the Physical Sciences. A sound mathematical basis is thereby provided for the study of special unitary groups and their Author(s): Frank W. K. Firk License information Related content Rights not set No related items provided in this feed License information Related content Rights not set No related items provided in this feed The Structure and Interpretation of Computer Programs This is an introduction se Author(s): Brian Harvey License information Related content Rights not set TeachPhilosophy101 This site presents strategies and resources for faculty members and graduate assistants who are teaching Introduction to Philosophy courses; it also includes material of interest to college faculty generally. The mission of TΦ101 is to provide free, user-friendly resources to the academic community. All of the materials are provided on an open source license. You may also print as many copies as you wish (please print in landscape). TΦ101 carries no advertising. Author(s): No creator set License information Related content No related items provided in this feed Computer Applications for Instruction and Training Introduction to basic computer applications on a Macintosh computer, with special emphasis on software that may be used in instruction and training. In this course, students will orient themselves to the Macintosh environment, get a brief overview of Macintosh-specific software, and learn the fundamental basics of the following tools available to assist in instruction and training: PowerPoint, Photoshop, GoLive, and iMovie. Author(s): No creator set Redistricting Game The Redistricting Game is designed to educate, engage and empower citizens around the issue of political redistricting. Currently, the political system in most states allows the state legislators themselves to draw the lines. This system is subject to a wide range of abuses and manipulations that encourage incumbents to draw districts which protect their seats rather than risk an open contest. By explore how the system works, as well as how open it is to abuse, The Redistricting Game allows play Author(s): No creator set Discovering Information Systems An Exploratory Approach Note: This book was written in 1999 and last updated in 2003. Since then technologies have changed so the non-conceptual and more technical parts of the book may be out of date.Why Yet Another Textbook (WYAT)?There are many excellent introductory information systems (IS) texts on the market. Why then produce our own text? Interestingly enough, when we sat down to critically review the first year Information Systems curriculum, the very last thing that we wanted was to get involved in writing yet Author(s): No creator set License information Related content No related items provided in this feed Calculus I, Summer 2007 This course is an introduction to differential and integral calculus. It begins with a short review of basic concepts surrounding the notion of a function. Then it introduces the important concept of the limit of a function, and use it to study continuity and the tangent problem. The solution to the tangent problem leads to the study of derivatives and their applications. Then it considers the area problem and its solution, the definite integral. The course concludes with the calculus of element Author(s): No creator set
On May 15, 2012, Canaa Lee published a collection of math stories entitled, "Algebra for the Urban Student." She is the daughter of Kathleen D. Lee and the late Travis O. Lee. Canaa has been a teacher for 11 years now and loves algebra. She has watched students struggle in math year after year and wanted to help students wrap their minds around abstract math concepts. Lee is an expert algebra teacher. She also orchestrated a math enrichment program, Project (Educating and Diversifying to Grow Exponentially) EDGE in Garland, TX. Not only do students struggle with math but they also struggling with reading. In addition to Algebra for the Urban Student, Canaa Lee is writing a sequel that is due to be released August 2012. After the release of the sequel to Algebra for the Urban Student, she also plans to write a series of children math books. Please visit The students Lee teaches inspired "Algebra for the Urban Student." The book started off as just a collection of units for her students so she could ensure that were exposed to and master all the topics for the assessments. Parents commented on homework assignments because they could now help their children with their homework because it was easy to understand and and easy to follow without stepping foot in the classroom! For the first time, many students understood their homework and could complete their assignments. Also, students were improving their reading and comprehension skills in both English and algebra! Canaa Lee has written enough units and assessments to write a book. Textbooks are designed for math teachers and professors; "Algebra for the Urban Student" is intended for the common student.
Problems in Solutions. ABSTRACT Whether it has been a fault in the public school system of America or simply a trait more common to certain minds, the matter of simple proportions is—to the average nurse and oftentimes to physicians as well—most confounding. When the student nurse encounters the elementary arithmetic associated with the making of solutions or the primary problems of chemistry, she is generally, in the language of the street, "up against it." Possibly no one has realized it better than Miss Sullivan, who has had broad teaching experience. How much good such a book will do is problematic. In the first place, one who explains these arithmetical problems should have a reader with patience and a certain amount of intelligence. After this step is successfully passed, Miss Sullivan may get her book across. To one, on the other hand, who has even a fair acquaintance with lower mathematics, the book seems unnecessarily
Course Detail Mathematics: Fundamentals of Mathematics MATH 052 Z1(CRN: 60921) Emphasizing proofs, fundamental mathematical concepts and techniques are investigated within the context of number theory and other topics. Credit not given for both MATH 052 and MATH 054. Co-requisite: MATH 021.
Find a Centennial, CO Trigon ...CheersPre-algebra is one of the most important sections in math. It is the basic fundamentals for all high-school and college math. The fundamentals include the following: Operations of real numbers, polynomials, rational expressions, radicals and exponents, equations/functions, area and volume...
Summary: Lecture 1. Real numbers. Constants, variables, and mathematical modeling. In this lecture we briefly sketch the structure of Real numbers and recall properties of addition and subtraction. Then we will discuss the notions of variables and constants and basic ideas of mathematical modeling. 1.1. Real Numbers We will try to sketch the structure of numbers by ranging them by the increase of com- plexity. Most people agree that the simplest are the counting numbers. 1, 2, 3, 4, 5 The next step is the whole numbers (a "zero" element was added) 0, 1, 2, 3, 4, 5 to make whole numbers even more useful the addition and multiplication were invented. The addition and the multiplication were invented in such a way to satisfy commutative properties a + b = b + a a · b = b · a, and the associative properties a + (b + c) = (a + b) + c a · (b · c) = (a · b) · c,

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