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Complex numbers
1. Ability to perform simple arithmetic in cartesian form, including calculation of conjugate and modulus
2. Ability to represent complex numbers on an Argand Diagram
3. Ability to represent simple straight lines and circles in complex number notation
4. Ability to calculate with the polar form
5. Ability to use de Moivre's Theorem to calculate powers
6. Ability to use Euler's formula to find simple roots and fractional powers |
a mathematical modeling course in a civil/environmental engineering program
This book has a dual objective: first, to introduce the reader to some of the most important and widespread environmental issues of the day; and second, to illustrate the vital role played by mathematical models in investigating these issues. The environmental issues addressed include: ground-water contamination, air pollution, and hazardous material emergencies. These issues are presented in their full real-world context, not as scientific or mathematical abstractions; and for background readers are invited to investigate their presence in their own communities.
The first part of the book leads the reader through relatively elementary modeling of these phenomena, including simple algebraic equations for ground water, slightly more complex algebraic equations (preferably implemented on a spreadsheet or other computerized framework) for air pollution, and a fully computerized modeling package for hazardous materials incident analysis. The interplay between physical intuition and mathematical analysis is emphasized.
The second part of the book returns to the same three subjects but with a higher level of mathematical sophistication (adjustable to the preparation of the reader by selection of subsections.) Many important classical mathematical themes are developed through this context, examples coming from single and multivariable calculus, differential equations, numerical analysis, linear algebra, and probability. The material is presented in such a way as to minimize the required background and to encourage the subsequent study of some of these fields.
An elementary course for a general audience could be based entirely on Part I, and a higher level mathematics, science, or engineering course could move quickly to Part 2. The exercises in both parts tend to be quite thought-provoking and considerable course time might be well devoted to discussing their solutions, perhaps even in a seminar format. The emphasis throughout is on fundamental principles and concepts, not on achieving technical mastery of state-of-the-art-models.
The author of this book is particularly well suited to writing about the subject. Starting off as a mathematics professor, he spent 13 years as an environmental consultant before returning to the classroom. Thus, many of the examples, experiences, and insights in the book are realistic and convincing. Read the full review. |
FIRST COURSE IN PROBABILITY leader is written as an elementary introduction to the mathematical theory of probability for readers in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus.
A major thrust of the Fifth Edition has been to make the book more accessible to today's readers. The exercise sets have been revised to include more simple, "mechanical" problems and new section of Self-test Problems, with fully worked out solutions, conclude each chapter. In addition many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, packaged with each copy of the book, provides an easy to use tool to derive probabilities for binomial, Poisson, and normal random variables. It also illustrates and explores the central limit theorem, works with the strong law of large numbers, and more. |
The book covers the basic aspects of linear single loop feedback control theory. Explanations of the mathematical concepts used in classical control such as root loci, frequency response and stability methods are explained by making use of MATLAB plots but omitting the detailed mathematics found in many textbooks. There is a chapter on PID control and two chapters provide brief coverage of state... |
Advanced Algebra is an in-depth study of topics covered in Algebra I. A good understanding of Algebra I topics is required. Other topics include the study of roots, rational and irrational numbers, conics, solving and graphing quadratic functions, and an introduction to exponential and logarithmic functions. Students are introduced to the graphing calculator and learn how it is used in problem solving situations. |
Algebra I A, the first course in a two-semester series, guides students through units of study that allow them to gain practical mastery in reading, writing, and evaluating mathematical expressions. Students will study topics including numbers, expressions, and equations. In the final first semester unit, students learn to solve functions and linear |
Algebra I For Dummies
Factor fearlessly, conquer the quadratic formula, and solve linear equations. There!. Now with 25% new and revised content, this easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems with confidence. You'll understand how to factor fearlessly, conquer the quadratic formula, and solve linear equations. =: Includes revised and updated examples and practice problems; Provides explanations and practical examples that mirror today's teaching methods; Other titles by Sterling: Algebra II For Dummies and Algebra Workbook For Dummies. Whether you're currently enrolled in a high school or college algebra course or are just looking to brush-up your skills, Algebra I For Dummies, 2nd Edition gives you friendly and comprehensible guidance on this often difficult-to-grasp subject.
Customer Reviews:
NOT for beginners.
By J. Meriwether - January 12, 2011
I picked this up at my local bookstore so that I could re-learn the Algebra I'd forgotten from high school. At three chapters in, I am already frustrated with the writing style of the book and the lack of proper editing. (I have the newest edition as of 2011, released for the spring semester.)
~*~
First off, the first chapter of the workbook does not coincide with the first chapter of the textbook. It appears the rest of the chapters might match up.
~*~
Secondly, the math is not taught in the order it needs to be for you to work the equations. (Ex: The ability to multiply fractions is needed to solve many of the problems in WB chapter 2, but multiplying fractions is not introduced until Chapter 3 of the textbook and workbook.)
THE AUTHOR ACTUALLY STATES IN THE BOOK THAT YOU CAN GO THROUGH THE CHAPTERS IN ANY ORDER. ANYONE WHO'S TAKEN ANY MATH AT ALL KNOWS THERE IS AN ORDER YOU MUST LEARN IT IN. (This is why there is Algebra 1 THEN... read more
Editor -- proofread with someone who knows math, first.
By Neilton - October 24, 2010
I'm shocked. I've been impressed with the series but not this time.
I have three children, all in Algebra and all needing help. I went shopping for a supplemental text. I took a look at "Algebra I for Dummies" as a possible choice. I have other "for Dummies" books and like that this one comes with workbook.
I opened up the book to a random page and started reading. The page was on the greatest integer function. Their description was correct (greatest integer less than or equal to the value); however, the figures show the wrong result for a positive value ([3.8] = 4 if I remember correctly). I thought this was a simple typo until I noticed that the text attempts to justify it (BTW [3.8] = 3, not 4).
It would have been nice for the editor to send the book to someone who knows basic math. I tolerate typographic errors but not conceptual errors. I can't trust a tutorial that gets concepts wrong, even just one. I assume where one, many.
Good for my purposes
By Richard Stone - July 19, 2010
I needed a quick refresher because I am job hunting and this sometimes comes up on interviews due to my occupation. I havent had to use this type of math for quite a while though. I dont disagree however with some reviewers who have complained that the material is not really written for beginners. I had to struggle with much of the book and had to go over certain chapters more than once. Also, there isn't nearly enough explanation of certain key concepts. You are expected, for example, to accept that a complicated equation is an equation with a power no greater than 2 in which the equation is set to equal zero. However the accompanying workbook was a great help; in fact, there is just enough explanation of each concept in each chapter of the workbook that I could almost recommend buying the workbook as well as the main textbook. In the end, though it was a struggle at times, I was able to teach myself algebra from this book, and was able to take my placement exam with a passing... read more |
Powerful mathematical calculation program that specializes in algebraic computation.
Unlike numeric computation applications like MATLAB or Scilab that use approximate real values to perform the mathematical operations, the symbolic mathematics programs allow to perform the calculations using the numbers exact value, because they make use of what's called symbolic computation.
Some of the best known symbolic mathematics applications are Mathematica, Maple andDerive. This last one, is one of the most used in university environments due to its ease of use. It is a powerful mathematics program developed to operate with symbolic notation, even though it also allows numeric computation.
Derive is capable of solving, derivatives, integrals, limits, series, vector and matrix operations, polynomes, algebraic fraction,... What's more, it has various options for graphical representation of bidimensional and tridimensional functions. The result of the operations performed with Derive will be an exact value, expressed with a finite number of decimals, with the precision that the user chose.
If you are looking for an intuitive application to learn Mathematics, downloadDerive.
Requirements and additional information:
It works on Windows Vista or earlier.
The trial period lasts for 30 days. |
Books on Mathematics
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Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than...... more
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About the Book : Designed for undergraduate and postgraduate students of mathematics, the book can also be used by those preparing for various competitive examinations. The text starts with a brief introduction to results from Set Theory and Number Theory. It then goes on to cover Groups, Rings, Vector spaces... more
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About the Book : A Simplified Approach For Beginners Can you multiply 231072 by 110649 and get the answer in just a single line? Can you find the cube root of 262144 or 704969 in two seconds? Can you predict the birth-date of a person without him telling you? Can... more
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About the Book : This completely revised Fourth Edition of the book, appropriate for all engineering under-graduate students, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications. The book focuses clearly on teaching students numerical methods and in helping them to... more
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Contemporary Abstract Algebra 7e, written by Joseph Gallian, a well-known active researcher and award-winning teacher upholds the text's reputation for providing students a solid introduction to traditional abstract algebra topics. The text includes concepts and methodologies used by working mathematicians, computer scientists, physicists and chemists. Contemporary Abstract Algebra 7/e provides... more
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Based on the authors' three decades of teaching experience, Advanced Engineering Mathematics presents the fundamentals and theoretical concepts of the subject in an intelligible and easy-to-understand style. The carefully planned chapters make this book an effective tool for teaching the application of mathematics to engineering and scientific problems. The book... more
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The tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the... more
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Criminal mastermind Artemis Fowl returns for a much anticipated 7th adventure, and the scene is set for another fast, furious and thoroughly entertaining ride. Something has happened to Artemis; he's }nice{. The fairies diagnose Atlantis Complex - a multiple personality disorder, caused by dabbling in magic. Because he's }nice{ he... more
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A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of... more
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This clear, concise and highly readable text is designed for a first course in linear algebra and is intended for undergraduate courses in mathematics. It focusses throughout on geometric explanations to make the student perceive that linear algebra is nothing but analytic geometry of n dimensions. From the very start,... more
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Fully Revised, The New Fourth Edition Of An Introduction To Formal Languages And Automata Provides An Accessible, Student-Friendly Presentation Of All Material Essential To An Introductory Theory Of Computation Course. The Text Was Designed To Familiarize Students With The Foundations And Principles Of Computer Science And To Strengthen The Students'... more
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Expanding on the highly successful formula of the first edition, this book now serves as the primary textbook of choice for any algorithm design course while maintaining its status as the premier practical reference guide to algorithms. This expanded and updated second edition of a classic bestseller continues to take... more
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About the Book : The book introduces engineers, computer scientists, and physicists to advanced math topics as they relate to practical problems. The material is arranged into seven independent parts: ODE; Linear Algebra, Vector calculus; Fourier Analysis and Partial Differential Equations; Complex Analysis; Numerical methods; Optimization, graphs; Probability and Statistics.... more
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"A magnificent exploration of the role that chance plays in our lives. Often historical, occasionally hysterical, and consistently smart and funny, this book challenges everything we think we know--Daniel Gilbert, author of "Stumbling on Happiness." Leonard Mlodinow reveals the psychological illusions that prevent us understanding everything from stock-picking to wine-tasting,...2 new & used from sellers starting at 2,539 In Stock.Ships Free to India in
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Contents : DivisibilityCongruencesQuadratic Reciprocity and Quadratic FormsSome Functions of Number TheorySome Diophantine EquationsFarey Fractions and Irrational NumbersSimple Continued FractionsPrimes and Multiplicative Number TheoryAlgebraic NumbersThe Partition FunctionThe Density of Sequences of IntegersAppendicesGeneral ReferencesHintsAnswersIndex... more
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About The Author GEORGE F. SIMMONS has academic degree from the CAlifornia Institute of Technology, the university of chicago, and Yale University. He taught at several colleges and universities before joining the faculty of Colorado college in 1962, where he is a professor of mathematics. He is also the author... more |
This new book clarifies, extends, and unifies concepts discussed in basic high school geometry courses. It gives readers a comprehensive introduction to plane geometry in a h [more]
This new book clarifies, extends, and unifies concepts discussed in basic high school geometry courses. It gives readers a comprehensive introduction to plane geometry in a historical context. Chapter topics include axiomatic sy.[less] |
Offering students support for the Edexcel GCSE modular specification, this book provides an easy-to-follow course structure, extra practice questions and revision exercises tailored to each module. Page numbers for the Edexcel GCSE mathematics student books are given for reference |
1. Discuss and apply combinatorial properties of sets as well as objects constructed from them (e.g., pigeonhole principle, number of functions of a certain type between two finite sets).
2. Relate the study and properties of graphs to computational applications.
3. Discuss, apply and prove the correctness of various algorithms and results on graphs.
4. Discuss the application of appropriate algebraic operations to properties of graphs as well as the extension of applications by suitable interpretation of algebraic operations (various interpretations of matrix multiplication). |
The book consists of two parts. The first part contains the presentation of the foundation of the theory of Bessel functions, the second part contains the applications. \par The first part is divided into two chapters. In the first chapter, the main properties of solutions of the homogeneous Bessel functions, which are based on the representation of the solutions as series in increasing powers of the argument, are considered. Then, the Bessel integral, the Poisson integral and some of their generalizations are presented. The Neumann addition theorems and the foundations of the theory of products of Bessel functions are considered. Questions concerning differential equations which can be reduced to the Bessel equation and the inhomogeneous Bessel equations are discussed in detail. In particular, functions contiguous to the Bessel functions are considered. \par The second chapter contains the theory of definite and improper integrals as well as elements of the theory of dual integral equations. The representation of functions by the series of Fourier-Bessel, Dini, and Schlömilch is presented. Consideration of problems concerning homogeneous Bessel equations which are more complicated than those considered in the first chapter leads to Lommel functions in two variables. Partial cylindrical functions and asymptotic expansions of Bessel functions are discussed. \par The second part is also devoted to applications and consists of two chapters. In the first chapter, problems about plates and shells of rotation including problems on the oscillations of a circular plate and the equilibrium of a plate on a Winkler-type foundation are considered, as well as problems which can be solved by the method of compensating loadings. The method of initial parameters is considered in detail in the framework of the problem of axially symmetrical deformation of a circular conic shell. \par In the second chapter, comparatively different problems of oscillation theory, hydrodynamics, heat theory, etc. are collected. In Section 11, the boundary-value problems whose solution can be reduced to singular equations are considered. Formally, the author considers plates and membranes; however, the solution has a more general nature and is less connected with concrete applications. [E. V. Pankrat'ev (Moskva)] |
BUS 170: Mathematics for Business Decisions
A focus on organizing, interpreting, assessing and communication mathematical data for quantitative decision making in the business environment. The problem solving, reasoning, and communication requirements in this course will help students make better decisions associated with common business functions such as: payroll and taxes; accounting; banking; both electronic and store-front retailing; insurance, and finance. The course will stress critical and logical thinking skills, number sense and estimation, evaluating and producing statistical information, basic financial decision making, some fundamentals of probability, and an overview of the important social implications underlying any numerical data. Prerequisite: Eligibility for MTH 095 and one of the following: CSI 111 or BUS 115 or BUS 215... more »
Credits:3
Overall Rating:3 Stars
A+
Thanks, enjoy the course! Come back and let us know how you like it by writing a review.
,"Business 170 at HCC is Business Mathematics. This class was very easy. It was almost a review of the math that I had learned in highschool. You learn all of the basics about addition, division, percentages, etc. along with some taxation subjects. It was a good refresher class." |
Maths Skills for Health Science
These pages will allow you to learn about or revise the maths topics covered
in the Numeracy Diagnostic Questions presented on the Public Health 1A MyUni site. Pages relating to each question are listed below.
Follow the links labelled with any diagnostic questions you found difficult.
There are also some "tips" you might find useful and some reference
pages describing topics that will come up during your studies. Please feel free
to access these at any time you like and don't forget that The Maths Drop-In Centre
is open 10am to 4pm Monday to Friday during the semester if you's like to discuss
anything with a tutor. |
Humble Precalculus
...Student are taught how to set of and solve elementary word problems. Algebra 2 basically introduces the notion of a function, and it extends this notion to a variety of different types of functions. We see polynomial, exponential, logarithmic functons and more. |
Matrices are challenging, but they are really important in applied mathematics – they are a critical STEM topic. Engineers and scientists use matrices to solve challenging problems in many, many dimensions. Mathcad's matrix and graphing tools offer capabilities that can help students' explore matrices early in their school experience so that they are both prepared to use and aware of the importance of matrices. With currently available technologies matrices can be used, explored, and visualized effectively in Algebra 1 class. Systems of equations in three variables need not be avoided any longer. Matrices can be an efficient and powerful way to solve systems, with increased clarity now that we have tools to graph 3D plots.... (Show more)(Show less)
New to Mathcad Prime? This brief video illustrates how to leverage the resources on Mathcad's Getting Started tab to learn Mathcad by exploring Help and Tutorials to garner the information required for Just-in-Time learning. ... (Show more)(Show less)
Mathcad 15.0's live math capabilities provide students with timely feedback as they plot graphs, solve equations, or model data. This demonstration illustrates some useful techniques for using Mathcad to help your students be more active in directing their own learning and gain deeper understanding of mathematical concepts.... (Show more)(Show less)
Mathcad offers great features for communicating measurements, calculations, and design intent. This demonstration shows how students can use Mathcad to document and illustrate designs or solve problems in math or engineering. ... |
Differential Equations: An Introduction to Modern Methods and Applications, 2nd Edition
The modern landscape of technology and industry demands an equally modern approach to differential equations in the classroom. Designed for a first course in differential equations, the second edition of Brannan/Boyce's Differential Equations: An Introduction to Modern Methods and Applications is consistent with the way engineers and scientists use mathematics in their daily work. The focus on fundamental skills, careful application of technology, and practice in modeling complex systems prepares students for the realities of the new millennium, providing the building blocks to be successful problem-solvers in today's workplace.
The text 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. Section exercises throughout the text provide hands-on experience in modeling, analysis, and computer experimentation. Projects at the end of each chapter provide additional opportunities for students to explore the role played by differential equations in the sciences and engineering.
Brannan/Boyce's Differential Equations 2eis available with WileyPLUS, an online teaching and learning environment initially developed for Calculus and Differential Equations courses. WileyPLUS integrates the complete digital textbook, incorporating robust student and instructor resources with online auto-graded homework to create a singular online learning suite so powerful and effective that no course is complete without it.
Clarity of Applications: Based on the advice of first-edition users and others, the authors have reorganized some topics to make key ideas stand out more clearly, and have added applications that will motivate students by catching their interest and will help to build their skills in modeling with differential equations.
User Friendliness: The 2nd edition is designed to be more student-friendly by adjusting the level and strengthening the emphasis on applications, modeling and the use of computers.
Additional Problems and Exercises: New exercises, projects, and problems invite the student to make conjectures or reach conclusions about complex situations based on computer-generated data and graphs, rather than closed-form solutions.
Stressed Topics: The important link between linear second-order equations and linear systems of dimension two is strengthened in the second edition.
Real-World Applications: New introduction to two-dimensional systems of first-order differential equations in Chapter 3. The author demonstrates the usefulness of eigenvalues in the context of a timely application involving solar energy transfer and storage in a greenhouse.
Reorganization: Sections 4.2 through 4.4 reorganized into two sections. The sections are streamlined and simplified, with optional advanced material moved to exercise sets.
Flexible Organization: Organization of chapters, sections, and projects allows for a variety of course configurations depending on desired course goals, topics, and depth of coverage.
Numerous and Varied Problems: Throughout the text, section exercises of varying levels of difficulty give students hands-on experience in modeling, analysis, and computer experimentation.
Emphasis on Systems: Systems of first order equations, a central and unifying theme of the text, are introduced early, in Chapter 3, and are used frequently thereafter.
Linear Algebra and Matrix Methods: Two-dimensional linear algebra sufficient for the study of two first order equations, taken up in Chapter 3, is presented in Section 3.1. Linear algebra and matrix methods required for the study of linear systems of dimension n (Chapter 6) are treated in Appendix A.
Contemporary Project Applications: Optional projects at the end of Chapters 2 through 10 integrate subject matter in the context of exciting, contemporary applications in science and engineering, such as controlling the attitude of a satellite, ray theory of wave propagation, uniformly distributing points on a sphere, and vibration analysis of tall buildings.
Computing Exercises: In most cases, problems requiring computer generated solutions and graphics are indicated by an icon.
Visual Elements: In addition to a large number of illustrations and graphs within the text, physical representations of dynamical systems and interactive animations available in WileyPLUS provide students with a strong visual component to the subject.
Control Theory: Ideas and methods from the important application area of control theory are introduced in some examples and projects, and in the last section on Laplace Transforms, all of which are optional.
Recurring Themes and Applications: Important themes and applications, such as dynamical system formulation, phase portraits, linearization, stability of equilibrium solutions, vibrating systems, and frequency response are revisited and reexamined in different applications and mathematical settings.
Chapter Summaries: A summary at the end of each chapter provides students and instructors with a birds-eye view of the most important ideas in the chapter.
Available Versions
Differential Equations: An Introduction to Modern Methods and Applications, 2nd Edition |
Probability : An Introduction - 87 edition
Summary: Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, and other key concepts and methods essential to a thorough understanding of probability. Designed for use by math or statistics departments offering a first course in probability. 360 illustrative problems with answers for half. Only high school algebra needed. Chap...show moreter bibliographies |
Colmar Excel Algebra II:
Algebra 2 is a course designed to build on algebraic and geometric concepts. It develops advanced algebra skills such as systems of equations, advanced polynomials,......The students needed to share pencils and paper in order to frugally use the school?s scant supplies. However, most amazingly, the school had no textbooks (a fact that most teachers complained about), but she had each student make his or her own textbook; therefore, the class had forty-some textb... |
This is a beginning Algebra through Intermediate Algebra course. This course is intended to develop student proficiency and confidence in basic algebraic skills. Topics include integer and rational exponents, simplification of algebraic expressions, linear and quadratic equations, linear inequalities, factoring, simplification of rational and radical expressions. This course prepares students for College Algebra as well as satisfies the general education basic algebra requirement. (03.0 crs)
This course is intended for students who have a good background in elementary and intermediate algebra. Topics include a review of the topics in Math 0001, the Cartesian plane and graphing, systems of equations, and linear, quadratic, exponential, and logarithmic functions. This course can be used to prepare students for Pre-Calculus and Business Calculus as well as to satisfy the general education mathematics quantitative reasoning requirement. Prerequisite: Math 0001. The prerequisite can be met by placement. (03.0 crs)
MATH 0004 - PRE-CALCULUS: FUNCTIONS & TRIGONOMETRY
This course provides the necessary background for Math 0221. Topics include an extension of the topics in Math 0002, polynomial and rational functions and their behavior, analytic and calculator graphing, and trigonometry. Prerequisite: Math 0002. The prerequisite can be met by placement. (04.0 crs)
MATH 0071 - STRUCTURE OF THE REAL NUMBER SYSTEM
This course begins with the counting numbers and gradually builds the real number system. The structure of the real number system is explored through problem solving with a focus on number operations and properties, as well as set theory and number theory. Prerequisite: Math 0001. The prerequisite can be met by placement. (03.0 crs)
MATH 0080 – FUNDAMENTALS OF MODERN MATHEMATICS
This course is designed primarily for students whose interests lie outside the natural sciences. It emphasizes problem solving approaches common to many mathematical areas. Topics include geometry, measurement, probability, and statistics. Prerequisite: Math 0001. The prerequisite can be met by placement. (03.0 crs)
MATH 0121 - BUSINESS CALCULUS
This course is designed for students in business, economics, and other social sciences. It introduces the basic concepts of limits, continuity, differentiation, integration, and optimization. Applications to the social sciences, especially business and economics, are emphasized. Prerequisite: Math 0002. The prerequisite can be met by placement. (04.0 crs)
MATH 0212 - INTRODUCTION TO BIOSTATISTICS
In this course the beginning biology student learns the concepts of probability and statistical inference from a non-calculus point of view. Applications are emphasized. Topics include probability distributions, sampling distributions, confidence intervals, hypothesis testing, and analysis of variance. Further topics such as correlation and regression analysis may be covered if time permits. Students must register for both the lecture and the lab to receive credit. Prerequiste: Math 0004. (04.0 crs)
MATH 0221 - ANALYTIC GEOMETRY AND CALCULUS 1
This is the first of a sequence of three basic calculus courses intended for all mathematics, engineering, computer science, and natural science students. Topics include the derivative and integral of functions of one variable and their applications. Trigonometric functions are included. Prerequisite: Math 0004. The prerequisite can be met by placement. (04.0 crs)
MATH 0231 - ANALYTIC GEOMETRY AND CALCULUS 2
This is the second of a sequence of three basic calculus courses intended for mathematics, engineering, computer science, and natural science students. Topics include the calculus of transcendental functions, techniques of integration, sequences, and series. Prerequisite: Math 0221. (04.0 crs)
MATH 0241 - ANALYTIC GEOMETRY AND CALCULUS 3
This is the third of a sequence of three basic calculus courses intended for mathematics, engineering, computer science, and natural science students. Topics include vectors and surfaces in space, the calculus of functions of several variables including partial derivatives and multiple integrals, conic sections, parametric curves, and polar coordinates. Theorems of Green and Stokes may be covered. Prerequisite: Math 0231. (04.0 crs)
MATH 0401 - DISCRETE MATHEMATICAL STRUCTURES
This course is intended for students contemplating a major in mathematics or computer science. Topics include the basic concepts of set theory, logic, combinatorics, Boolean algebra, and graph theory with an emphasis on applications. Prerequisite: Math 0001. The prerequisite can be met by placement. (03.0 crs)
MATH 1012 - INTRODUCTION TO THEORETICAL MATHEMATICS
This course is an introduction to the theoretical treatment of logic, sets, functions, relations, partitions, compositions, and inverses. Classwork and homework will concentrate on the writing and understanding of proofs of theorems. Prerequisite: Math 0401 and Math 0221. (03.0 crs)
MATH 1019 - TECHNICAL SPEAKING IN MATHEMATICS
The course is designed to teach oral presentation theories and techniques specific to situations involving mathematics. Content includes audience analysis, organization, delivery, presenting mathematical material to non-expert and technical audiences, and the use of visuals. Computer software to give oral presentations will be used in some of the speeches. Students will be required not only to give excellent presentations but also to analyze their own and other presentations based on the theories learned in this course. Prerequisite: Math 1012. (03.0 crs)
MATH 1035 - DIFFERENTIAL EQUATIONS WITH MATRIX THEORY
This course is intended for Engineering Technology students. Topics include matrix methods, first and higher order ordinary differential equations, Laplace transformations, series solutions of differential equations, and systems of differential equations. Credit may be received for only one: Ordinary Differential Equations (1271) or Differential Equations with Matrix Theory (1035). Prerequisite: Math 0241. (04.0 crs)
This course is an introduction to numerical analysis at the advanced undergraduate level. Topics include interpolation, numerical differentiation and integration, solution of non-linear equations, numerical solutions of ordinary differential equations, and additional topics as time permits. Emphasis is on understanding the algorithms rather than on detailed coding, although some programming will be required. As a prerequisite, Math 0241 and at least one "1000-level" mathematics course such as 1181, 1271, 1012, or permission of instructor is needed. (03.0 crs)
MATH 1117 - HISTORY OF MATHEMATICS
This course traces the history of mathematics from primitive number concepts through the beginnings of calculus. It emphasizes a "hands-on" approach to significant mathematical discoveries while discussing the lives and contributions of great mathematicians within their cultural settings. Required for Secondary Education Mathematics majors. Prerequisite: Math 0231 and Math 1012. (03.0 crs)
This course is intended for Secondary Education Mathematics majors, and includes topics which are not typically covered in Probability and Statistics 1. Topics include elementary functions of random variables, sampling, distributions, basic estimation theory, and hypothesis testing. (This course cannot be taken if a student has received credit for, or is enrolled in Math 1154) Prerequisite: Math 1153. (01.0 crs)
MATH 1163 - MATHEMATICS SEMINAR 1
This course introduces students to a variety of mathematics specific technology.Topics include computational and algebraic manipulator software and mathematical typesetting programs at the instructor's discretion (01.0 crs)
MATH 1164 - MATHEMATICS SEMINAR 2
Utilizing exams previously given by the Society of Actuaries and readily available study guides, this course examines material typically included in Probability and Statistics. Through careful investigation of these problems, students will gain familiarity with the material pertinent to Actuarial Exam P and will develop problem solving strategies. Prerequisite: Math 1154. (01.0 crs)
MATH 1175 - TOPICS IN APPLIED MATHEMATICS
This course is designed to enhance the student's understanding of how mathematics may be applied in the real world. Possible topics include game theory, cryptography, partial differential equations, complex variables, stochastic processes, the calculus of variation, control theory, and the application of such topics to a particular discipline. Prerequisite: Math 0241 and Math 1012 or premission of instructor. (03.0 crs)
This course is intended as an introduction to linear algebra. The course stresses the computational methods of linear algebra and covers the theoretical development of matrix algebra and vector spaces. Topics include systems of linear equations, matrices, matrix algebra, determinants, vector spaces, linear dependence and independence, spanning sets of vectors, bases, orthogonality, inner product spaces, Gram-Schmidt process, Eigenvalues, Eigenvectors, characteristic equations, and diagonalization. Other topics will be covered as time permits. Prerequisite: Math 0241. (03.0 crs)
MATH 1271 - ORDINARY DIFFERENTIAL EQUATIONS
This course covers methods of solving ordinary differential equations which are frequently encountered in applications. General methods will be taught for single nth order equations, and systems of first order nonlinear equations. These will include phase plane methods and stability analysis. Computer experimentation will be used to illustrate the behavior of solutions of various equations. Credit may be received for only one: Ordinary Differential Equations (1271) or Differential Equations with Matrix Theory (1035). Prerequisite: Math 0241. (03.0 crs)
MATH 1291 - TOPICS IN GEOMETRY
This course is intended to give a "modern" view of geometry. Possible approaches include the exploration of geometric properties on various surfaces, the axiomatic development of finite geometries, the deductive, synthetic development of Euclidean and non-Euclidean geometry, and the connection of geometries to abstract algebraic systems. Required for Secondary Education Mathematics majors. Prerequisite: Math 0241 and Math 1012. (03.0 crs)
This course contains a rigorous development of the calculus of functions of a single variable, including compactness on the real line, continuity, differentiability, integration, and the uniform convergence of sequences and series of functions. Other topics may be included, such as the notion of limits and continuity in metric spaces. Prerequisite: Math 0241 and Math 1012. (03.0 crs)
This course may include some topics from Point-set Topology such as topological spaces, metric spaces, connectedness, compactness, and countability axioms. The course may also include some topics from Algebraic-Combinatorial Topology such as simplicial complexes, the fundamental group, Jordan Curve Theorem, Euler characteristic, classification theorem of compact surfaces, homology groups, homotopy groups, vector fields, and fixed points. Prerequisite: Math 0241 and Math 1012. (03.0 crs)
MATH 1901 - INTERNSHIP
Under faculty supervision the student participates in a mathematics related experience, project, or job. (01.0 TO 03.0 crs)
MATH 1903 - DIRECTED STUDY
Under the direction of a faculty member, a student studies a mutually agreed upon topic in mathematics. (01.0 TO 03.0 crs)
Topics typically chosen represent areas of mathematics that are not covered in any of our regular courses--though exceptions can be made. Such topics have included Number Theory, Graph Theory and Game Theory. |
Mathematics Courses
Note: Your ability to read and understand English may
significantly affect your understanding of the mathematics
covered in certain classes. Eligibility for ENG 101 is highly
recommended.
MAT 073 Number Sense and Pre-Algebra, Foundation
Refer to Developmental Studies
MAT 075 Pre-Algebra – Number Sense, Geometry
formerly MAT 098 Basic Mathematics
Refer to Developmental Studies
MAT 094 Introductory Algebra
formerly MAT 099 Introductory Algebra
Refer to Developmental Studies
MAT 121 Applications for Business & Other Careers
Prerequisite: MAT 094 or appropriate placement test scores.
3 credits
Includes a study of mathematical techniques as
applied to problems in business and the
contemporary world. The primary focus will be
on algebraic, graphing and statistical techniques. (Not recommended for science or math majors.)
MAT 136 Intermediate Algebra
Prerequisite: MAT 094 with a grade of C- or
higher or appropriate placement test score.
4 credits
Includes a study of functions, relations, and
graphs; applications; linear functions and
inequalities; quadratic and other polynomial
functions; exponents and radical expressions;
rational expressions and equations; and systems
of equations. Students must earn a C- or higher
to move to the next level course.
MAT 145* Math for Elementary Teachers I
Prerequisite: MAT 136 or appropriate test score.
4 credits
This course must be passed with a minimum grade of C.
A mathematics course designed for and required
of students preparing to teach in the elementary
schools. Topics include number systems and
their properties, problem-solving, developing
mathematically correct and clear explanations
of mathematical ideas, applications, and
diagnosis of student error patterns. Computer
component to the course.
MAT 146* Math for the Liberal Arts
Prerequisite: MAT 136 or appropriate test score.
3 credits
The goals of the course are to develop, as fully
as possible, the mathematical and quantitative
capabilities of the student; to enable them to
understand a variety of applications of
mathematics; to prepare them to think logically
in subsequent courses and situations in which
mathematics occurs; and to increase their
confidence in their ability to reason mathematically.
Topics that could be included in the
course: applications of everyday mathematics,
symmetry, transformations, voting strategies,
circuits & pathways. This course transfers
easily to most four-year institutions.
MAT 147* Math for Elementary Teachers II
Prerequisite: MAT 145.
4 credits
This course must be passed with a minimum
grade of C. Designed for and required of
students preparing to teach in the elementary
schools. Topics include rational numbers and
their properties, problem solving, geometry and
measurement, probability and statistics, and
transformations.
MAT 172* College Algebra
Prerequisite: MAT 136 with a grade of C- or higher or appropriate placement test score.
3 credits
Topics include concepts of functions; numeric,
algebraic, and graphic techniques as applied to
the following functions: polynomial, piecewise,
rational, radical, exponential, logarithmic;
complex numbers; applications; and systems of
equations. Topics that might be included are
recursively defined functions and topics in
analytic geometry. Students must earn a C- or
higher to move to the next level course. TI
graphing calculator may be required.
MAT 190* Calculus for Business & Social Science I
Prerequisite: MAT 172 or equivalent.
3 credits
Topics include function review; limits and
continuity; the derivative; techniques of
differentiation; optimization problems;
exponential and logarithmic functions and their
derivatives; anti-derivatives and the Fundamental
Theorem of Calculus; techniques of
integration; applications pertaining to business
and the social sciences. TI graphing calculator
required.
MAT 272* Linear Algebra
Prerequisite: Math 256.
3 credits
This course involves a comprehensive
introduction to the theory and applications of
solving systems. Topics included are linear
equations, vector and matrix algebra, determinants,
eigenvectors and eigenvalues,
orthogonality, least squares, symmetry,
quadratic forms, and practical applications.
Technology is a major component of the course,
both computer and calculator work is utilized. |
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Math230 Take home quiz No. 6, Oct.20, Name:, StudentID:(1) ( 2 points) Find the first partial derivative$ of the function:(2) ( 3 p oints) Find the equation of the tangent plane to the given surface a t the specified point.
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Solutions to quiz 4.1. Write a class to describe a rational number, i.e., a ratio of two integers. Name the class RationalNumber and include two instance variables called numerator and denominator. Include a constructor that initializes the two inst
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CS 2605Online Quiz 6: Polymorphism in C+Instructions: This homework assignment covers the basics of inheritance and polymorphism in C+. The answers may be determined from the posted CS 2704 notes and lecture. All inheritance relationships below a |
PRACTICAL MATH APPLICATIONS, 3E offers users math skills needed for business and personal applications. The text begins with a comprehensive review of the basic math functions (addition, subtraction, multiplication, and division) and progresses to fractions and decimals. Once the students have mastered the basics, they are introduced to practical applications that develop critical thinking skills. These applications include bank records, purchasing and pricing merchandise, payroll, taxes, insurance, consumer credit, and interest (simple and compound). This easy-to-follow, step-by-step approach allows students to work at their own pace. Numerous self-help tips, practice activities, and self-assessments are provided so that each student feels competent in their newly acquired skill before moving on to the next.
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Just the math skills you need to excel in the study or practice of engineering
Good math skills are indispensable for all engineers regardless of their specialty, yet only a relatively small portion of the math that engineering students study in college mathematics courses is used on a frequent basis in the study or practice of engineering. That's why Essential Math Skills for Engineers focuses on only these few critically essential math skills that students need in order to advance in their engineering studies and excel in engineering practice.
Essential Math Skills for Engineers features concise, easy-to-follow explanations that quickly bring readers up to speed on all the essential core math skills used in the daily study and practice of engineering. These fundamental and essential skills are logically grouped into categories that make them easy to learn while also promoting their long-term retention. Among the key areas covered are:
With the thorough understanding of essential math skills gained from this text, readers will have mastered a key component of the knowledge needed to become successful students of engineering. In addition, this text is highly recommended for practicing engineers who want to refresh their math skills in order to tackle problems in engineering with confidence.
The EPUB format of this title may not be compatible for use on all handheld devices.
Details
ISBN: 9781118211106
Publisher: John Wiley & Sons, Ltd.
Imprint: Wiley-IEEE Press
Date: Sept 2011
Creators
Author: Clayton R. Paul
Reviews
"Summarizing, this is a very nice textbook, covering many interesting topics and written in a very digestible manner, which can be warmly recommended to students in natural sciences, computer science, and all branches of engineering." - |
Math
Students must complete three credits math in grades 9 through 11. Most students take four or five credits of math, a significant number of whom reach Calculus or a higher level of math.
Department Philosophy
It is the belief of the Math Department that a qualified student who gives the appropriate amount of effort can find success in our program. We do not track students but encourage them to continually challenge themselves to become proficient in the subject area that best matches their ability. Thus a student in a regular class who meets the requirements may be promoted to an advanced class the following year, while a student who is not succeeding in the rigorous environment of an advanced or regular class may be moved into a B-level class.
The Math Department endorses and incorporates the National Council of Teachers of Mathematics standards and philosophies regarding math instruction. Through the course of a Westtown math education, a student will be exposed to many different ways of defining and framing problems, as well as solving them. Collaborative work, in-depth exploratory projects, and an emphasis on thinking skills pervade our curriculum as we seek more creative ways to help our students learn. Technology is used, depending on student needs and teacher interest, while still maintaining a rigorous grounding in writing clear, analytical mathematics. Traditional concerns about organizing students' work and knowledge motivate us to encourage the neatness, thoroughness, and clarity of thought and expression necessary for success in math and across the disciplines. The Math Department is also committed to furthering equity in its active encouragement of both male and female students, weaker and stronger students, as well as those from all cultural backgrounds. We believe that math is not just a cornerstone of intellectual development but also essential to effective participation as citizens in our democracy and in the world.
The goals of the mathematics curriculum:
To identify mathematical questions, to generalize from particular examples, and to use abstract reasoning
To analyze data, represent it graphically, and gain experience creating mathematical models for the systems generating the data
To expose students to a rigorous, theoretical development of math systems both algebraic and geometric
To gain experience in using calculators, programming languages and applications software
Distinguishing Features:
Flexibility of the curriculum: many paths and different paces are possible.
Curriculum is able to meet a wide variety of student interests and background preparation, very responsive to individual student's needs. We challenge all students at an appropriate level
The graphing calculator has been integrated as an educational tool.
Faculty stay abreast of and respond to the latest developments in research, pedagogy, technology, and curriculum.
Math Lab is staffed by current teachers offering help daily in the Learning Resource Center. |
specific... read moreFundamental Concepts of Geometry by Bruce E. Meserve Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
A Vector Space Approach to Geometry by Melvin Hausner This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965Invitation to Geometry by Z. A. Melzak Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
Advanced Euclidean Geometry by Roger A. Johnson This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
A Course in the Geometry of n Dimensions by M. G. Kendall This text provides a foundation for resolving proofs dependent on n-dimensional systems. The author takes a concise approach, setting out that part of the subject with statistical applications and briefly sketching them. 1961 edition.
Elementary Mathematics from an Advanced Standpoint: Geometry by Felix Klein This comprehensive treatment features analytic formulas, enabling precise formulation of geometric facts, and it covers geometric manifolds and transformations, concluding with a systematic discussion of fundamentals. 1939 edition. Includes 141 figures.
Euclidean Geometry and Transformations by Clayton W. Dodge This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
The Beauty of Geometry: Twelve Essays by H. S. M. Coxeter Absorbing essays demonstrate the charms of mathematics. Stimulating and thought-provoking treatment of geometry's crucial role in a wide range of mathematical applications, for students and mathematicians.
Challenging Problems in Geometry by Alfred S. Posamentier, Charles T. Salkind Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and more. Arranged in order of difficulty. Detailed solutions.
Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene F. Krause Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problemsA Modern View of Geometry by Leonard M. Blumenthal Elegant exposition of the postulation geometry of planes, including coordination of affine and projective planes. Historical background, set theory, propositional calculus, affine planes with Desargues and Pappus properties, much more. Includes 56 figures.
Product Description:
specifics of the axiomatic method. Well-written and accessible, the text begins by acquainting students with the axiomatic method as well as a general pattern of thought. Subsequent chapters present in-depth coverage of Euclidean geometry, including the geometry of four dimensions, plane hyperbolic geometry, and a Euclidean model of the hyperbolic plane. Detailed definitions, corollaries, theorems, and postulates are explained incrementally and illustrated by numerous figures. Each chapter concludes with multiple exercises that test and reinforce students' understanding of the material.
Bonus Editorial Feature:
Clarence Raymond Wylie, Jr., had a long career as a writer of mathematics and engineering textbooks. His Advanced Engineering Mathematics was the standard text in that field starting in the 1950s and for many decades thereafter. He also wrote widely used textbooks on geometry directed at students preparing to become secondary school teachers, which also serve as very useful reviews for college undergraduates even today. Dover reprinted two of these books in recent years, Introduction to Projective Geometry in 2008 and Foundations ofGeometry in 2009.
The author is important to our program for another reason, as well. In 1957, when Dover was publishing very few original books of any kind, we published Wylie's original manuscript 101 Puzzles in Thought and Logic. The book is still going strong after 55 years, and the gap between its first appearance in 1957 and Introduction to Projective Geometry in 2008 may be the longest period of time between the publication of two books by the same author in the history of the Dover mathematics program. Wylie's 1957 book launched the Dover category of intriguing logic puzzles, which has seen the appearance of many books by some of the most popular authors in the field including Martin Gardner and, more recently, Raymond Smullyan.
Here's a quick one from 101 Puzzles in Thought and Logic:
If it takes twice as long for a passenger train to pass a freight train after it first overtakes it as it takes the two trains to pass when going in opposite directions, how many times faster than the freight train is the passenger train?
Answer: The passenger train is three times as fast as the freight train |
College Algebra covers all of the topics generally taught in a one-term college algebra course. It is completely Web-based, and is presented in a format that is optimal for online learning, whether you teach a fully online, hybrid, or traditional course.
Student Guide and Syllabus
The Student Guide clearly explains how the course content is organized so that students can focus on learning, not on trying to figure out where to find information.
Instructors customize the syllabus to fit their course, adding information such as a class schedule with important dates, any additional requirements or resources, and grading policies.
Chapter Pretests
Students take a pretest prior to beginning each chapter in order to self-assess their current knowledge of the chapter topics and help determine where to focus their efforts as they go through the chapter. Feedback pointing students to the relevant section for each question is provided. The pretest is delivered through and graded by the course management system.
Lessons, Animations with Audio, Interactive Exercises, Practice Problems, Videos and Section Quizzes
Each chapter is broken into sections. Within each section are lessons that contain animations with audio, interactive exercises, practice problem and answer sets, videos, and quizzes.
Each section begins with a list of specific learning objectives. Lessons give students a thorough, straightforward presentation of the material, broken into small "chunks" of content. There is no extraneous information, allowing students to focus on the key elements of the specific concepts being conveyed. Equivalent to a traditional textbook explanation and lecture presentation, lessons allow students to set their own pace as they move through the material.
Within lessons, extensive use of animation helps students visualize difficult concepts and problem-solving steps. Some lessons also contain interactive examples that guide students step-by-step through problem solving, with hints for completing each step. Students are able to consider each step before requesting a hint.
Many sections contain interactive exercises (Java applets) that help students take their learning one step further.
Problem solving tutorial videos (with audio) for every section allow students to watch an instructor hand-write and explain the solution to selected practice problems.
Practice problems and a complete answer set are provided for each section. Students work through problems related to the lesson. Answers are available, most with step-by-step solutions, for students to self-assess their progress and identify areas of difficulty.
NEW! Algorithmically generated problems with hints and full solutions are provided for each section.
Automatically-graded homework problems are assigned for each section. This allows the instructor to monitor individual student progress on a regular basis. It is delivered through and graded by the course management system.
Posttests
A cumulative posttest is provided for students' self-assessment, allowing them to seek help where needed before the chapter exam. Feedback pointing students to the relevant section for review is provided for each question. It is delivered through and graded by the course management system.
Chapter Exams
Two versions of a comprehensive end-of-chapter exam are available and delivered through and graded by the course management system. Also, a NEW algorithmic testing option is available for chapter, midterm, and final exams.
Test Banks
In addition to two versions of a Chapter Exam for each module, test banks are provided for each chapter. You can use these test banks to modify existing assessments, and/or to create midterm and final exams.
Course Management
We have partnered with BlackboardTM, eCollegeTM, and AngelTM, the leading content management systems in higher education, to provide you with the best assessment, communication, and classroom management tools widely available. |
The purpose of this tutorial is to introduce basic graph theory terminology and concepts.
To begin, a graph is a collection of vertices that are connected by edges. Graphs can be weighted so that there is a cost to go from one vertex to another across an edge, or unweighted so that there is no cost. They can also be directed so that travel is only possible from one vertex to another, but not necessarily bidirectional; or they can be undirected so travel is bidirectional across all edges.
Simple Graphs, Multigraphs, and Hypergraphs
There are three major types of graphs to be familiar with: simple graphs, multigraphs, hypergraphs. When referring to graphs in general, simple graphs are generally being referenced. Simple graphs are unweighted, undirected, and have no loops (vertices with edges pointing to the same vertex on both ends) or multiple edges which point to the same pair of vertices. A simple graph is displayed below:
Multigraphs are graphs which have one or more pairs of vertices with multiple edges connecting the same two vertices. Various academics are conflicted as to whether or not multigraphs can contain loops. This ambiguity leaves a lot of discretion up to the individual. Below is an example of a multigraph:
Hypergraphs have edges, called hyperedges, which can connect more than two vertices together. When displaying them visually, they can quickly get messy. A good, clean example of a hypergraph, however, is a circuit diagram, as shown below. Any resistors, batteries, capacitors, etc., are all considered vertices; and the wires connecting are the edges.
Basic Classes of Graphs
In addition to simple graphs, multigraphs, and hypergraphs, there are a number of other types of graphs, described based on the relations of the vertices to each other. In this tutorial, the following types of graphs will be introduced: cyclic grahps, wheels, complete graphs, bipartite graphs, and cubes.
Cyclic graphs are, as the name suggests, simply circuits. They are denoted by a Cn, with n being the number of vertices. In Cyclic graphs, n is also the number of edges. The cyclic graph C6 is displayed below.
Wheels are similar to cyclic graphs, and actually contain a cyclic graph. The main difference is that wheels have a central vertex that connects to the rest of the vertices in the graph. A wheel is denoted by Wn, where n is the number of vertices in the graph, and Wn contains Cn-1. There are 2(n-1) edges contained in any wheel. Some examples of wheels are displayed below.
Complete graphs are a type of graph where all the vertices are connected to each other. They are denoted by Kn, where n is the number of vertices. Complete graphs have n(n-1)/2 edges. The K5 graph is displayed below as an example of complete grahps.
Bipartite graphs are best defined using set theory. They are graphs such that there are two sets of vertices, where the vertices in the first set only have edges to vertices in the second set, and vertices in the second set only have edges connecting to vertices in the first set. In other words, vertices in the same set are not connected. It could also be described as a disjoint set data structure. Both the cyclic and complete graphs can be bipartite. In order for a cyclic graph to be considered bipartite, it must have an even number of vertices. Otherwise, there will be a vertex that is connected to vertices in both of the sets, violating the bipartite property.
Complete bipartite graphs are slightly different than normal complete graphs. In a complete bipartite graph, the vertices are still in disjoint sets, but all the vertices in the first set connect to all the vertices in the second set, and vice versa. Complete bipartite graphs are noted by Ka,b, where a is the number of vertices in the first set, and b is the number of vertices in the second set.
Below is an example of a bipartite graph, specifically K3,3.
The last type of graph covered in this tutorial is a cube. These graphs are also bipartite, and are denoted with the notation Qn, where n is the number of vertices. Cubes have 2n vertices and n * 2n-1 edges. Looking back at Calculus, this looks exactly like a derivative for xn. In order to determine which vertices are connected, each vertex is given a binary number n digits long ranging from n 0's to n 1's. Only vertices whose binary indices differ by a single digit are connected. So for example, in Q3, there are 8 vertices labeled: 000, 001, 010, 011, 100, 101, 110, 111. Vertex 000 is connected to vertices 001, 010, and 100 exclusively. |
MATHEMATICS LEARNING OVERVIEW 2010-2011
AUTUMN TERM 1
6th September-22nd October
AUTUMN TERM 2
1st November-17th December
During the 1st term Foundation students will study
Area and perimeter of 2 D shapes (e.g. trapezium, parallelogram and triangles) and compound shapes and transformations. They will revisit areas such as simplifying, factorising and linear graphs in algebra.
Higher students will study Graphs of different functions; solve equations using trial and error method.
At end of each topic students are assessed on a 60 minute end of chapter test.
Foundation students will study probability, Ratio and proportion, equations & inequalities and
Transformation.
Higher students will cover topics such as Indices, Standard form and surds, Probability, Constructions, loci and congruence, circle theorems.
There will be some early entries in November.
At the end of each topic all students are assessed on a 60 minute end of chapter test.
1st week in December students will sit for a mock Exam.
SPRING TERM 1
5th January-18th February
SPRING TERM 2
28th February-8th April
Foundation students will study Properties of 3D shapes, Constructions and loci under shapes.
They learn index notation, trial and error method, Substitution into expressions and formulae under Algebra.
Higher students will cover topics such as further factorising, simplifying, rational expressions under algebra.
They will study how to estimate mean of group data of statistics.
At end of each topic students are assessed on a 60 minute end of chapter test.
Foundation students will learn how to analysis and draw scatter graphs under data, Pythagoras theorem and 3-D coordinates
Higher students will study topics such as Pythagoras theorem in 3-D and further trigonometry, solving quadratic
simultaneous equations under Algebra, Similarity, similar shapes and
Vectors.
At end of each topic students are assessed on a 60 minute end of chapter test.
Students will sit for a second mock Exam.
SUMMER TERM 1
25th April-27th May
SUMMER TERM 2
6th June-22nd July
Students in foundation groups will start revision on ALEBRA, DATA, NUMBER AND GEOMERY
Most students will practise exam questions and do past papers.
Higher students will study transformation of functions. Once they complete this topic higher students will start their revision on number, shapes, data and algebra and answer exam questions using past exam papers. |
The following mini quizzes are an indicator of only a few of the skills which you are expected to have at the beginning of
a particular
course.The course itself will
offer little or no time for a formal review… assuming that you are truly
prepared right from the beginning of class.Do not use these problems as a personal study guide thinking that they
will adequately prepare you for the course.These particular problems represent just some of the more important
examples from a much larger body of needed objectives, which are taught in the
prerequisite courses.
If
you do well on the quiz, see a math instructor or start at the appropriate level on the college
placement test which should give you your correct placement.
The answers are
found at the bottom of each page.
Click
on the level of quiz that you wish to take. For a course
description, go back to the math homepage. Quizzes are available for Math
20-95. |
In this college level Calculus learning exercise, students use the ratio test to determine if a series converges or diverges. The one page learning exercise contains six problems. Solutions are not provided.
Students analyze geometric series in detail. They determine convergence and sum of geometric series, identify a series that satisfies the alternating series test and utilize a graphing handheld to approximate the sum of a series.
In this calculus learning exercise, students find the limit using the Limit Comparison Test and solve problems with series based on the p-series. They tell whether an equation will converge or diverge. There are 7 problems.
In this Calculus worksheet, students assess their understanding of various topics, including the derivatives of trigonometric functions, evaluating integrals, sigma notation, and convergent and divergent series. The one page interactive worksheet contains fifty-two problems. Answers are not provided.
Students investigate sequences and series numerically, graphically, and symbolically. In this sequences and series lesson, students use their Ti-89 to determine if a series is convergent. Students |
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This is an introduction to Galois Theory along the lines of Galois's Memoir on the Conditions for Solvability of Equations by Radicals. It puts Galois's ideas into historical perspective by tracing their antecedents in the works of Gauss, Lagrange, Newton, and even the ancient Babylonians. It also explains the modern formulation of the theory. It includes many exercises, with their answers, and an English translation of Galois's memoir |
Numerical analysis, algorithms and computation Murphy J., Ridout D., McShane B., Halsted Press, New York, NY, 1988.Type: Book (9789780470212141) Numerical analysis and computation are widely recognized as important parts of the mathematical modeling of real systems. Given the enormous development and widespread use of computer technology, a new introductory textbook on the numerical... |
Stewart's CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.
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The Place of Functions in the School Mathematics Curriculum
Functions are used in every branch of mathematics, as algebraic operations on numbers,
transformations on points in the plane or in space, intersection and union of pairs of sets, and
so forth. Function is a unifying concept in all mathematics. Relationships among phenomena in
everyday life, such as the relationship between the speed of a car and the distance travelled, are
functions. The concept of function has an important part in the school mathematics curriculum;
yet, many countries today are concerned with how to structure the curriculum. The first part of
this brief provides a short background about the historical development of function in
mathematics and its introduction into the school curriculum, explicating the 'identity crisis'
many countries are facing today. We then elaborate more on the goals for including functions in
the school curriculum and on the learning about functions. We conclude this brief with
challenges that policy makers, curriculum developers and teachers face and possibilities for
meeting these challenges.
Introduction
The concept of function has undergone an interesting evolution. Developments in mathematics have changed the
concept of function from a curve described by a motion (17th century) to an analytic expression made up of
variables and constants representing the relation between two or more variables with its graph having no "sharp
corners" (18th century). In the 19th and 20th centuries, new discoveries and fresh emphasis on rigour led to the
modern conception of a function as a univalent correspondence between two sets. More formally, a function ƒ
from A to B is defined as any subset of the Cartesian product of A and B, such that for every a ∈ A there is
exactly one b ∈ B such that (a, b) ∈ ƒ.
As the discipline of mathematics has grown, function has become one of the most important and fundamental
mathematical concepts as a way to organize and characterize mathematical relationships. The development of
the concept of function in mathematics influenced the way function entered and was presented in school
mathematics. The function concept appeared in secondary mathematics curriculum at the beginning of the 20th
century, amplified by the creation of the International Commission on Mathematical Instruction (ICMI) in 1908.
The term 'function' was used then in a way similar to Euler's definition from the 18th century. Function, in the
modern sense, was introduced to the school curriculum in many countries during the 'new math' reform of the
1950s-1960s, often using the function concept as an organizing theme for the secondary mathematics
curriculum. Today, the modern concept of function appears in many school mathematics curricula. A common
expectation is that at the end of high school, students will know the function concept in general and be familiar
with specific types of functions, including linear, quadratic, general polynomial, reciprocal, power, step,
exponential, logarithmic, trigonometric, and piece-wise functions in different representations. Yet, numerous
studies reveal that students have difficulties learning the concept of function. And, although function is often
defined in textbooks in a modern sense, students tend to hold a restricted image of function, similar to the one
from the 18th century when function was a dependent variable or an analytic expression whose graph has no
'sharp points'.
In addition to the problems arising from students' restricted images of the range of the notion of function, there
is evidence that the different representations of functions often stand and are treated in isolation, without the
connections that make them representations of a common core concept. Moreover, there seems to be a growing
uncertainty amongst curriculum designers, textbook authors, teachers and others about the purposes and goals of
the study of functions, in particular as regards the relative emphasis on intra-mathematical goals and goals
related to applications and modelling. All this gives rise to what we would like to call an 'identity crisis' in the
teaching and learning of functions in school.
The term 'curriculum' has multiple meanings. In this brief, we use it in a broader sense to include the rationale,
goals and intentions, principles and standards, the syllabus, course outlines, textbooks, teacher guides, and other
learning, teaching and assessment materials, the mathematical content studied, the teaching and assessment
methods. So, for us, curriculum includes what is taught as well as how it is taught; how what is taught is assessed
and for what purposes. We also note that the official curriculum is not identical to how intentions are translated
and expressed in curriculum materials (e.g., textbooks and teacher guides), in tests and examinations, or in what
actually happens in classrooms.
Some countries or states have an official curriculum whereas others do not. Yet, even in countries that do have
an official national mathematics curriculum, the goals of the curriculum may be different for different groups of
students.
Goals for functions
There are several different purposes for including functions in the curriculum. While the first three purposes are
internal to mathematics, we note that the fourth is a different kind of purpose.
• Include function as a mathematical topic that is perceived as an intrinsic part of mathematics in its own
right. For some students this may be because functions are likely to occur in their later studies.
• Introduce the concept of function as a unifying concept across the entire mathematical curriculum. For
instance geometric transformations of the plane can be perceived and investigated as functions. The
same is true of arithmetic operations, some solution sets to equations, formulae used in mensuration
(length, area, and volume), probabilities, regression functions, recursive definition of objects, etc.
• Use functions as a vehicle for clarifying mathematical thinking and reasoning, as a tool for proving
statements, and suchlike.
• Use functions to provide a means for extra-mathematical ends, in particular to represent, describe and
deal with (i.e., to model) phenomena, situations, or problems outside of mathematics itself. In some
countries and states, this purpose is a key driver of the curriculum, provoking the identity crisis referred
to above.
We believe it is essential for curriculum designers, textbook authors, teachers, teacher educators, and others, to
clarify which of these purposes are to be pursued in a given programme or teaching context, as the purposes are
going to shape and influence in a crucial manner what is taking place in teaching and learning. In particular it is
important to consider whether the needs of different groups of students should give rise to the pursuit of different
purposes for these groups.
When looking at the current state and development of upper secondary curricula around the world, it seems that
a dichotomy is emerging between the adoption and pursuit of a modelling purpose, on the one hand, and an
intrinsically mathematical purpose, on the other hand, for the study of functions. We believe that such a
dichotomy is unfortunate and can be avoided. Therefore, efforts should be made to strike a proper balance
between the two kinds of purposes.
Learning about functions
Once goals are chosen, decisions need to be made about the structure of teaching and learning and phasing
activities over the years of secondary school in order to achieve them. School curricula around the world have
taken different approaches to including functions in the curriculum. Key decisions that need to be made concern
the way in which functions are defined formally, when this occurs in a developmental sequence and the variety
of ways in which students encounter functions, consistent with the goals chosen.
It is clear that the term 'function' has a range of meanings in everyday speech, differing from culture to culture,
often not compatible with and at any rate much less precise than a mathematical definition. Examples of these
include function as purpose: "The function of the brake is to stop the car", function as event: "The function to
celebrate the school's sporting victory will be held on Wednesday", function as role: "His function on the
committee was to take notes", and function as mechanism: "The function of the switch is to turn on the light."
Such everyday meanings of the term may impede students' development of the specific mathematical meanings.
In some languages, the term 'function' may not appear at all.
The relationship between the definition of function and the mental image students develop of function is
important and has been studied by researchers (e.g., Vinner 1983). There are at least three possible approaches to
the inclusion of functions in the school curriculum, all of which have been used in various countries over the past
few decades:
• Students are provided with experiences with classes of functions (such as linear, quadratic (polynomial),
reciprocal, exponential, logarithmic). This experience is then drawn upon to construct a general
definition, later in secondary school.
• Students are given a general definition of the concept of a function, so that later experiences of classes of
functions can be interpreted as special cases of the function concept.
• Students are given experiences with various classes of functions as important objects in their own right,
but a general definition of the concept is not provided at all in secondary school.
While each of these approaches has advantages and enthusiastic supporters, there are also some pitfalls for each
that have been recognised in practice and in research. For example, the first approach above may lead to students
acquiring a very limited concept image for function, such as one that is restricted to continuous functions that are
easily expressed in algebraic symbols or for which there is a two-dimensional graph. A pitfall of the second
approach is that students may have at first such little experience of the concept of a function that the definition
does not have much meaning for them and is not used to interpret their later work. The third approach runs a risk
that students have too little opportunity to see the general concept of a function, unless it has been drawn to their
attention in some way, although some would argue that this is not problematic for some students (such as those
who do not continue studying mathematics beyond secondary school).
Irrespective of the approach that is chosen, it is important to note that the seeds of the secondary school work on
functions are laid in the first several years of school. An example of this is the study of patterns in elementary
schools, where students are helped to observe and describe relationships between quantities.
There are various notations for functions, and it seems important for students to eventually be comfortable with
most of these, rather than being restricted to only one. Indeed, students who understand functions with only one
form of notation are unlikely to have an adequately inclusive concept image. Nevertheless, in some places, a
preference might be expressed for a single notation in order to avoid any confusion for students. Common
notations include:
• f(x) = x2 + 1
• y = x2 + 1
• y = f(x) = x2 + 1
• f: x → x2 + 1
• (x,y) ∈ {y = x2 + 1}
The first of these draws attention to the functional nature of the relationship, while the second supports a
graphical interpretation in the plane. The third notation emphasises the functional character of the graph, while
the fourth is consistent with the idea of a mapping from one set to another, and the fifth emphasises the idea of a
set of points. Over the course of secondary school, students might progressively encounter this variety of
notations.
As well as notations, students' concept images are influenced by the representations of functions that they
experience. To develop a rich concept image—which seems important to develop a rich meaning for and use of
the concept—students ought to encounter functions in different representations and make connections between
these (Thompson, 1994). Some representations support particular ways of thinking about functions especially
well. Among the representations that seem important to include and which students might progressively
encounter are:
• Symbolic (e.g. an algebraic rule such as G(a) = 3a – 1)
• Graphic (e.g. a graph of the quadratic function y = 3 – x2)
• Diagrammatic (e.g., a mapping diagram)
• Verbal (e.g. a description such as "$40 initial charge and $60 per hour" for the labour fee for a plumber.)
• Tabular (e.g. a table showing the population of Chile each year)
• Implicit (e.g., functions emerging from parameterising solution sets of equations)
The study of functions at school allows for the later development of functions as tools for more advanced study
of mathematics. Some of the more sophisticated uses of functions to support advanced mathematical thinking
are included in school curricula in various countries, but there is not space here to elaborate on the details. Some
of these more sophisticated ideas related to functions include: operations with functions, composition of
functions, inversion, differentiation, integration and differential equations and properties of functions (such as
montonicity, injectivity, boundedness, covariance and optimisation). Typically, these are addressed in the final
years of secondary school, if at all, or left to the early undergraduate years.
Teaching of functions
While there is a potential identity crisis for functions in the curriculum, teachers in classrooms still have to make
decisions on what to do. Such decisions are always complex and challenging and are made more difficult when
the goals for including functions in the curriculum are not clear. Thus there are many challenges to be addressed
by teachers.
One challenge is that textbook writers do not present the notion of function in ways that connect function to the
rest of the curriculum, leaving this task to the teacher. The teacher has to ensure that eventually students develop
a concept image that matches a comprehensive definition of function. Another challenge is that students tend not
to make connections among different representations and are unable to extract the underlying core concept. Yet
another challenge for teachers is to take the time to allow students to explore and develop deep and rich
understanding of function. While the use of technology can help, even then the optimal allocation of classroom
time provides a difficult challenge.
No royal road has been identified internationally as the best way for teaching and presenting function to students,
but all successful methods address the various challenges in a conscious well-thought and systematic manner.
Good teachers provide rich environments, emphasizing making connections among different representations, and
allow students to take the time to develop such understanding. Some countries or places do not adopt such a
thoughtful approach, yet, there are quite a few countries and places that do that.
A perennial challenge for teachers everywhere involves motivating students, and the teaching of functions is no
different in that respect. Not all students are alike, so some may be motivated by seeing that functions are
everywhere, in and outside of mathematics; others may be motivated by working on challenging tasks or in
seeing surprising connections. Indeed, it seems likely that one of the reasons for the widespread popularity of a
'modelling approach' to teaching functions is that such an approach helps students appreciate that mathematics
has some practical application in the everyday world.
In recent years, the role of technology has been explored in a number of ways, depending on the facilities
available to teachers. It seems clear that technology provides good opportunities to support student learning
about functions, and it seems likely that this will continue to be an area of some promise for teachers. Many of
these opportunities involve students in exploring functional ideas for themselves. Some potential benefits and
opportunities include:
• The use of multiple representations of functions on computers and calculators
• Facilitation of the use of functions for modelling purposes
• Software platforms for explorations of properties of functions
• Software platforms for consolidating function as object (e.g., families of functions)
• Manipulative tools, including computer algebra systems, to avoid tedious and extensive symbolic
manipulation
• Environments, such as dynamic geometry environments, for exploring other kinds of functions: such as
those mapping R2→ R2 (Hazzan & Goldenberg, 1994)
There are also some pitfalls associated with the use of technology identified by researchers and practitioners.
These include at least
• Concept images can be restricted by technology, which can often best represent functions with distinctly
numerical features.
• A balance of human activity and understanding and use of computers is needed to avoid technology
being used as a 'black box'.
• It takes time for students to learn the software tools, and time is always in short supply in classrooms.
These and other aspects of the use of technology in the teaching and learning of functions are treated in more
detail in a companion brief (PCMI International Seminar, 2009).
Especially in countries with high-stakes examinations, many teachers and researchers have reported on the
powerful backlash effects of examinations on teacher decisions in the classroom. For example, when students are
not permitted to use technology tools in exams, it seems unlikely that they will be widely used in teaching, and
thus schools will have limited motivation to find the necessary resources. Even when technology is permitted or
provided, it seems that it is not always used by teachers and schools; however, this effect is not by itself
sufficient to explain the limited role technology plays in many curricula. By their nature, examinations
frequently focus on a small range of predictable activities, often of a semi-routine nature, which may also have
the effect of narrowing student experience and thus their concept images. Similarly, the reluctance to permit
technology use in examinations may discourage more adventurous and helpful use of technology in classrooms.
Conclusion
Although functions appear in all school curricula in the secondary years, clarity of purpose for this continues to
be needed, so that explicit advice can help teachers in their choices about what to teach and why. Decisions need
to be made regarding the relative importance of the formal definition of a function and the practical applications
of functions for modelling, as well as how to phase this work over the secondary years. The present situation in
many countries has resulted in a kind of identity crisis for the place of functions, and it would be helpful if this
were to be resolved. While technology holds some promise to support teaching and learning, it is no panacea,
and care is needed to ensure that it is used productively, consistent with available facilities in different contexts,
and further that the intentions for including functions in the curriculum are not unwittingly undermined by
assessment practices.
References
Akkoç, H., & Tall, D. (2005). A mismatch between curriculum design and student learning: the case of the
function concept. In D. Hewitt & A. Noyes (Eds), Proceedings of the Sixth British Congress of Mathematics
Education held at the University of Warwick, pp. 1-8. Available from
Hazzan, O., & Goldenberg, E.P. (1997). Students' understanding of the notion of function in dynamic geometry
environments, International Journal of Computers for Mathematical Learning, 1, 263-291.
PCMI International Seminar Brief. (2009). Assets and Pitfalls in Using Technology in Teaching and Learning
Functions.
Thompson, P. W. (1994), Students, functions, and the undergraduate curriculum. In Issues in
Mathematics Education, (4), 21 - 44. Washington DC: College Board on Mathematical Sciences.
Vinner, S. (1983) Concept definition, concept image and the notion of function, International Journal for
Mathematical Education in Science and Technology, 14(3), 293-305. |
The mathematics requirement for all students is the satisfactory completion of four years of mathematical study. Approximately 60% of Freshmen begin with Algebra I. The remaining students begin with Geometry with the exception of a few who begin with Algebra II. Several course sequence possibilities are given.
Readiness for the Strake Jesuit Mathematics Curriculum
We have found that students are well prepared for Algebra I if they:
• know the subsets of the real numbers
• are able to add, subtract, multiply and divide integral values mentally and accurately without calculators.
• know the rules for operating (calculating) with fractions, decimals and percents.
• know the properties of addition and multiplication and appreciate the value of these properties in calculation.
Calculator Policy
Certainly, calculators have a place; unfortunately, many students have been led to believe that having access to the calculator means they no longer have to understand fundamental mathematical concepts. We expect students to have calculators, and we will encourage their use when appropriate. On the other hand, we will strongly oppose their use when unnecessary or ill advised. Calculators are not permitted in Algebra I. A scientific calculator is sufficient for Geometry, Algebra II, and Pre-calculus. Graphing calculators are required for Calculus, AP Calculus, and AP Statistics.
Note: AC designates a more demanding work load with greater GPA value. AP means college credit might be earned by taking an Advanced Placement test at the completion of the course. AP Calculus and AP Statistics are also AC courses.
Placement into the Geometry section as a Freshman requires having completed Algebra I by the end of 8th grade and passing an Algebra test at 80% or higher. This test will be administered in May. Only students with Algebra I on their middle school transcript should take this test. Students who do not score 80% or better will be expected to take Algebra I in their freshman year.
Placement in AC courses is an option only for students who excel in mathematics the preceding year. These placements are made each summer in consultation with the student's former teacher, guidance counselors, the mathematics department chairman, and the academic assistant principal.
Trigonometry and analytic geometry are taught in the Algebra II courses, and reinforced in the Introductory Analysis and Pre-Calculus courses. The Calculus courses presume these materials. |
The analytic art: Nine studies in algebra, geometry, and trigonometry from the Opus restitutae mathematicae an
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Text: English, Latin (translation)
Learning from Japanese Middle School Math Teachers by Nancy C. Whitman
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Tiny book exploring ways to improve Math education.
Collegiate Business Math
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Collegiate Business Mathematics-Seventh Edition has been written for those students in four-year universities, community colleges, adult schools, private business schools, trade and vocational schools, continuing education, and employee t
Mathmania=Puzzlemania + Math
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Set of 11 50 page math exercise books.
Capitalism and Arithmetic: The New Math of the 15th Century, Including the Full Text of the Treviso Arithmetic
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Text: English, Italian (translation)
Reviewed by a reader
The advent of Hindu/Arabic numbers in Europe made possible "algorithmic" calculation. Math schools were established where parents sent their sons to prepare for jobs with merchants, where ability to calculate was a requirement.
Math Wise!: Hands-On Activities and Investigations for Elementary Students
Editorial review
This generous collection includes more than 100 enjoyable activities that help students master basic math concepts. Each activity is complete and ready to use. Many are accompanied by reproducible handouts. This book is a valuable supplem |
...
Show More time. Furthermore, math teachers and math textbooks simply try to cover too much material, the bulk of which, has no impact on a student's successful completion of math up through calculus in high school. Second, Math Is Easy, So Easy, tries to provide clarity of instruction for a few problems which cover the important aspects of the essential topics. Contrary to most math teacher instruction, it is more important and beneficial to know a few key problems well, than to try to cover many problems only superficially. If you are the parent of a student who is struggling in math, you know how frustrating it can be to get to the bottom of what your student really needs to know to survive and persist in math up through calculus in high school. You also know how important it is that your student stay in math as long as possible in high school, so that they are better prepared to enter and succeed in college. You also, no doubt, know how seemingly unreasonable your struggling student's math teacher can be in terms of communicating with you and your student. As a math teacher for many years now, Max wrote this book to help you and your struggling math student survive math with as few, "I hate math," outbursts as possible. Lastly, Max has personally witnessed many students who struggle in math in high school who then go on to mature into great engineers and scientists. This book will help your student to stay in math longer and be more successful. There is a separate book for each of six math classes: 7th Grade Math, Algebra I, Geometry I, Algebra II, Math Analysis and Calculus. There is a single "Combo" book with all six books in one. Make sure you get the right book for your needs. Nathaniel Max Rock, an engineer by training, has taught math in middle school and high school including math classes: 7th Grade Math, Algebra I, Geometry I, Algebra II, Math Analysis and AP Calculus. Max has been documenting his math curricula since 2002 in various forms, some of which can be found on MathForEveryone.com, StandardsDrivenMath.com and MathIsEasySoEasy.com. Max is also an AVID elective teacher and the lead teacher for the Academy of Engineering at his high school |
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2005
Abstract:
Cossondra George, a Michigan teacher, reviews Kenney's book about helping math students by guiding them through the layout of a math textbook, understanding the unique use of certain words (difference, mode) in math, and using writing to accompany algorithmic responses.
This small book is packed with useful information about how to better serve students in a math classroom by simply thinking differently about the language of mathematics and how you as a teacher use that language to develop understanding of concepts by your students.
The chapter "Reading in the Mathematics Classroom" begins with an idea to help students better understand math that had never occurred to me. The author gives a detailed description of how a math text differs in structure from all other texts. This had never seemed important to me, but I could now see how students who have been taught how to read a typical textbook would find the math book's organization confusing. Not only does a math text contain numeric and non-numeric symbols the reader must decode, the layout is not the standard left-to-right layout students have come to expect. The text, the graphics, the examples, are often jumbled across the pages, with unrelated sidebars and pictures. It does not get any easier when the student reaches the problems to solve at the end of the lesson, which are often mixed with review of previously learned skills, enrichment questions, or other tangential material. By simply teaching students the layout of the text, this problem is easily overcome.
This chapter also addresses other reading difficulties—for example, irregularities between the way we use words in day to day life and the specific meanings they have in mathematics. Words like difference, operation, similar, and mode all have meanings unique to math class. Other words like of and off can cause students great confusion if specific care is not taken to assure their understanding of the word, its meaning and usage in the particular mathematical context.
Another particularly engaging chapter was "Writing in the Mathematics Classroom." This chapter gives an in-depth analysis of how we expect students to show their understanding of a mathematical solution. Examples of how teachers might encourage students to actually demonstrate their understanding through writing—rather than just giving an algorithmic answer—are shown in detail. Kenney also provides assessment guides, along with sample student solutions. The chapter summary starts with "Writing in mathematics helps students think." This one line tells it all. We cannot make assumptions about the level of understanding our students have on a topic simply by looking at a number written in an answer blank. Instead, we must train them (and ourselves) to delve deeper into the problem by thinking and writing about the why's and how's of math.
Other chapters are titled: "Mathematics as Language," "Graphic Representation in the Mathematics Classroom," "Discourse in the Mathematics Classroom," and "Creating Mathematical Metis" (defined in this book as something that cannot be taught or memorized, rather something that can only be imparted and acquired). Each chapter gives the math teacher much food for thought-not only about the way they teach, but more importantly, the way they assess student learning in the classroom. Kenney offers many examples of easy-to-implement strategies, with enough variety that any teacher looking to improve the mathematical understanding in their classroom will find something they can put to use.
This book will stay on the top of the pile on my desk. It's given me much to think about as I work to continually improve my own day-to-day practice.
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Robert Marzano's extensive research into effective classroom practices has won him a national following. In this article, he identifies research-based classroom management strategies that combine "appropriate levels of dominance and cooperation and an awareness of student needs." Marzano and his wife Jana looked at more than 100 studies and found that "the quality of teacher-student relationships is the keystone for all other aspects of classroom management. In fact, our meta-analysis indicates that on average, teachers who had high-quality relationships with their students had 31 percent fewer discipline problems, rule violations, and related problems over a year's time than did teachers who did not...." (Educational Leadership, September 2003)Citation: Marzano, R. (2003). Building Classroom Relationships. Retrieved June 5, 2007, from Educational Leadership. Web site:
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Carol Patterson, a North Carolina teacher, uses the term "golden pages" to describe Overmeyer's book about strategies for when writing workshops fall short of engaging students, such as having them make lists and interview one another.
Full Text:
I have never met Mark Overmeyer and I feel quite certain that he has not visited my classroom. Yet, as I read his When Writing Workshop Isn't Working, I thought he was speaking directly to me.
I was sure somehow he knew the problems I had this year with Ms. Lucy's Writer's Workshop. Lucy Calkins has a terrific program, and I do give her credit for that, but really, no program is perfect. So what could I do when my writing workshop had kinks?
Well, Mark Overmeyer stepped right in and answered my questions! He saw that little guy in MY classroom staring out into space while the other students were at least trying to write something. When I stooped down by his desk to see if I could help, he just looked at me with a puzzled expression. He didn't know where to begin or what to write.
In his second chapter, Mark Overmeyer told me (because I AM sure he wrote this book just for me!) ways to help my little fellow—simple ideas like making lists, having interviews with a partner, and using "anchor writing experiences." I use the word "simple" because Overmeyer's "answers to ten tough questions" are user-friendly.
This little book has become a treasure in the few weeks I have owned it. It's my new reference book for any problem that rears its ugly head during writer's workshop. Inside these golden pages, you'll find writing solutions for ELL students, managing conferences, writing rubrics, preparing students for standardized tests, and lots more. It's the next best thing to having Mark Overmeyer visit our classroom — and he is always welcome!
Thank you, Mark, for making writer's workshop easy for the children and the teacher as well.
I probably should divulge upfront that I like middle schoolers. I like them so much that after teaching elementary students for 15 years I'm determined to return to middle school next year.
I've been warned about how their hormones and changes in their brains make them mentally unstable. My own wonderful daughter's middle school years were, how should I put it, educational. I've observed the mixed look of horror and pity on the faces of elementary and high school teachers when I tell them my plans. I've also heard the much greater level of applause in teacher gatherings when a group of middle school teachers are introduced, a level usually reserved for military heroes. I've even read Yes, Your Teen is Crazy by Michael J. Bradley.
However, a little picture book like Mr. DeVore's Do-Over helps explain why middle school teachers continue to teach at that level and why I want to do so again. A pair of middle school teachers that I shared the book with teared up a little afterward, and said that they loved how it showed a teacher reaching out to an individual student. One of them had even had a similar experience.
The narrator, a seventh grader named Donald, begins the book with "When it comes to school, I've always been a failure! I never could do anything well." The typical clutzy kid disasters befall him daily. He hears that Mr. DeVore is the "hardest teacher in the whole school," and learns that he has him for Social Studies this year. But because of Mr. DeVore's faith and encouragement and the "do-overs", Donald's self-confidence is re-established, and his grades in all subjects improve.
But then one day, late in the year, Mr. DeVore has a bad day with the class, the kids aren't attentive, there are interruptions, and Mr. DeVore is obviously discouraged. Donald reaches out to him (I won't ruin it and tell you how, but it's very touching). Moments like that can fuel us teachers for a long time. Even vicariously experiencing it through a book can help us carry on, so I recommend copies of this for every middle school teacher you care about.
Of course, if that doesn't help, there's always Yes, Your Teen is Crazy!
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2005
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Kathy Renfrew, a Vermont NBCT, shares highlights from this book, such as the use of Backward Design, discussion of the "with-it-ness" middle-level teachers must have, looking carefully at student work, and more.
Full Text:
by David Puckett 2005 (208 pp; paperback) National Middle School Association ISBN: 1-56090-184-5 $28.00 ($19.99 if you order online)
Reviewed by:
Kathy Renfrew, NBCT Grades 5/6 Peacham (VT) Elementary School
Inside-Outside in the Middle was a great read. David Puckett's book draws, in part, on conversations that have taken place online over a number of years as part of the MiddleWeb virtual community of middle school educators. It was truly awesome to read and reflect on many things we have discussed on Middleweb since its start-up in 1999.
I made a connection with David when he talks about the "with-it-ness" of teachers who teach in the middle grades. This age level is not for everyone. This was brought home to me this winter when we hired a permanent substitute for me. The teacher is great. She had actually taught some of these students as 2nd and 3 rd graders. What we all discovered is that what worked then, doesn't necessarily work now with these kids and it is no one's fault. It has been a learning experience for all of us.
David makes so many great points as he reflects on his own teaching that I fear this review will be too lengthy as I discuss the points that were most salient for me. But let's begin!
He notes that movement is extremely important to this age student. They need more time to move than a younger elementary student. Their bodies are growing and changing all the time. This need for movement can and should be planned for. It can be intentionally addressed and incorporated as part of rigorous, engaging instruction.
Another high point in the book for me was the importance of how we plan instruction. David spends time discussing the work of Grant Wiggins and Backward curriculum design. It is a very different way of thinking about our teaching. In Backwards Design you begin with "what we want our kids to know and be able to do" at the end of our unit. From there we design a few essential questions to keep us focused. The next step is for us to decide how we are going to assess our students. How will we know they have learned what we wanted them to learn?
The final piece is designing instructional activities that will bring our students to where we want them to be at the end of the unit. This final piece is the biggest change for many teachers, including myself. I always started with the activities and hoped my students learned what I need them to learn. I am really trying to use a Backwards Design format as often as possible.
The next point that I personally think is very important and worthwhile is the idea of looking at student work. We can learn so much from carefully looking at our assignments and looking at how our students responded to them. In the book, David talks about a protocol I am familiar with called "tuning." This is one of many organized tools that teachers can use as a common lens to look at and discuss the work of our students together in gatherings of "critical friends."
Time was a large issue reflected upon in the book. One of the crucial issues is to make sure we make time for kids. We are teaching children, not a curriculum. David reinforced this for me. As I work with 5th & 6th graders, I am constantly reminded that these students are still little girls and boys, and they need my individual attention.
Another piece David views as important (as do other middle school teacher/authors like Rick Wormeli) is David Sousa's research on Retention During a Learning Episode, and how crucial those first ten and last ten minutes of class are. That time needs to be used to set up and bring closure to a lesson. The middle of the period is the time to review and do the more mundane tasks that are necessary each day. I am going to think thorough how I can apply this research in my own self contained elementary classroom.
Did I mention that David Puckett began teaching from a wheelchair fairly late in his teaching career, after his childhood polio began to recur? The final chapter in the book brought real synthesis for me as a reader. I was totally engrossed in the analogies David made between the learning he did with his wheelchair and the teaching he did at the middle school level.
This was a great book for me to read. It brought to the forefront things I knew but needed to refresh. I recommend this book for every middle school teacher.
strategies
Publication Type:
Authors:
Year of Publication:
2006
Abstract:
Donna
C. White, a literacy coach in North Carolina, introduces this book by saying,
"Imagine sitting around a kitchen table drinking coffee with a few of your
favorite literacy experts." The "daily five" are reading to oneself, reading to
someone, listening to reading, working with writing, and spelling/word work.
Full Text:
Imagine sitting around a kitchen table drinking coffee with a few
of your favorite literacy experts, along with two enthusiastic
sisters who are both teachers and nationally recognized consultants
in literacy and "creating beautiful spaces for learning."
That is the feeling that emerged as I read The Daily Five:
Fostering Literacy Independence in the Elementary Grades
by Gail Boushey and Joan Moser. Grounded in the work of authorities
such as Regie Routman, Richard Allington, Lucy Calkins, and
Irene Fountas and Gay Su Pinnell, among many others, The
Daily Five provides a systematic structure for helping
students become independent and successful readers and writers.
Boushey and Moser begin with a reflection of their own evolution in
reading and writing instruction. This proves to be a wonderful
"stroll down memory lane" for those of us who have been teaching
long enough to remember a time when the classroom was "MY"
classroom and the materials were "MINE." This was a time when
"I" made the rules, and students who could not behave would
have to "flip a card" and miss recess. During this time, literacy
instruction was either delivered entirely in whole group or
entirely in small groups. Students who were not working with
the teacher had plenty of worksheets, "board work," and projects
to keep them busy and quiet!
At the end of the day, we had mountains of papers to grade and
even more to "run off" for tomorrow. Still we were perplexed
when our students did not make the progress that we felt they
should. We knew there had to be a better way, but we did not
have the time or energy to figure it out.
The Daily Five approach transforms the literacy block to a time
for students to benefit from both whole group and small group
instruction with explicit, focused teaching. The students
also participate in activities that actively engage them in
purposeful practice and application of the skills that they
are developing. These activities comprise the Daily Five:
•
Read to Self
• Read to Someone
• Listening to Reading
• Working on Writing
• Spelling/Word Work
The foundation for the Daily Five is achieved through a student
driven management structure that is put into place from the
very first day of school. Based on principles of trust, choice,
community, and stamina, Boushey and Moser thoroughly explain
the steps necessary to establish an environment that simultaneously
conveys warmth and caring as well as a respect for the seriousness
of the literacy tasks at hand.
The authors clearly realize that this type of environment does
not magically happen. Teachers are given the specific steps
to take to ensure that each component of the Daily Five is
explicitly defined, taught, practiced with appropriate feedback,
and reviewed until the routines become a habit for every student.
Ultimately, the students learn the rationale behind the Daily
Five through discussions about a "sense of urgency" and work
with the teacher to create "I" charts that will help them
be independent as they develop the stamina to become successful
readers and writers.
Boushey and Moser have anticipated just about every possible scenario
and provided tips on how they might be addressed. For example,
many teachers use paired reading with their students. It is
not too difficult to use this technique when the students
are sharing a book or when they each have their own copy of
the same book. However, Boushey and Moser give practical strategies
to use when the partners are reading two different books of
differing reading levels. They even give step by step instruction
on how to teach the students to "ignore the teacher." While
at first glance, a teacher may not see why his/her students
would benefit from this instruction, it can be distracting
for students when a teacher is conferencing with an individual
student or a small group of students. Learning when and how
to ignore the teacher at appropriate times is definitely a
worthwhile skill!
The Daily Five: Fostering Literacy Independence in the Elementary
Grades is a great book to read just before the beginning
of a new school year. It gives many practice strategies for
starting the school year in a way that will ensure that the
reading and writing proficiency of students will soar. However,
by following the steps outlined by Boushey and Moser, the
framework can be implemented at any time during the school
year.
I look forward to using this book as I facilitate a book study
when my colleagues return to school in just a few weeks.
While we will not be able to gather around the kitchen table
with coffee and literacy experts, we will have the benefit
of the wisdom and practical advice of two very knowledgeable
and talented sisters! I look forward to implementing the
Daily Five so that each of our students will become proficient
readers and writers with the stamina and independence they
will need to become lifelong learners.
Publication Type:
Authors:
Year of Publication:
2006
Abstract:
Carolann
Wade, a North Carolina teacher, reviews Ben-Hur's book, which discusses the
importances of giving genuine feedback, not just marking errors, and applying
the term "preconception" to student understanding, not "misconception." Wade
says that Ben-Hur "does a job of combining effective teaching strategies and
tying them specifically to mathematics instruction."
Full Text:
Concept-Rich Mathematics Instruction by Meir Ben-Hur is about quality
mathematics instruction, and teachers of mathematics from
PreK to college could benefit from reading this book. Some
prior understanding of higher level mathematics content
is needed to understand some of the examples presented.
Links to the theories of Vygotsky and Brunner are made with recommendations
for providing learning opportunities rich in communication
and conducting authentic formative assessment to drive a spiraled
instruction. As in Vygotsky's Zone of Proximal Development
theory, the recommendation is made that math teachers should
instruct students "just beyond" their current levels
of understanding to challenge them—but take care not
to instruct too far beyond students' current levels of understanding
so as not frustrate them. Many familiar teaching strategies
such as wait time and effective questioning are presented
as valuable in mathematics instruction. A
focus of this book is the importance of teachers looking carefully
at student errors and using the errors to plan instruction.
Teachers often correct student work in mathematics by marking
errors and do not give any feedback. Instead of just marking
errors to generate grades with no feedback or further instruction,
teachers should use student errors to help deepen student
understanding and to clear misconceptions. Standardized testing
and formal assessment only measure the products of mathematical
understanding, not the processes. For students to grow, they
need authentic assessment with feedback. A
term Ben-Hur uses is preconception, as opposed to the
term misconception, to describe early mathematical
understandings that, with proper teacher guidance, will be
replaced eventually by mathematical truths. Instead of thinking
of student errors as just carelessness, laziness, or misconceptions
in need correction, Ben-Hur argues that errors can be viewed
as preconceptions or early understandings that will evolve
with guidance and practice. (An example used in the book is
that young students often think of the equal sign as what
comes before the answer in an equation rather than as a symbol
meaning equality.)
Six notable instructional principles for conceptual remediation
are explained in detail in the book:
Reciprocity–It is important to create a trusting, safe environment
for students to take risks in communicating understanding
and discussing solving problems.
Flexibility–Teachers should alter instruction methods and time spent
on math concepts as needed by students.
Meta-Cognitive Awareness– Written or oral student reflection
in articulating mathematical understanding helps students
make sense of it all. This can also help teachers understand
how students are thinking.
Appropriate Communication– Teachers need to help students
learn to use formal math language.
Constructive Interaction Among Learners– Peer
dialogue and communication of ideas among students is
critical in developing mathematical understanding.
This book is full of familiar theory but Ben-Hur does a nice job
of combining effective teaching strategies and tying them
specifically to mathematics instruction. Teachers of upper
elementary students and above may find the information in
this book more applicable than teachers in the lower grades. |
Differential Equations
Spring 2008
Homework Write-Ups
Problem write-ups are your permanent record of your understanding
of the material covered. This is especially true in a course such as
this where there are no exams.
Solutions should be clearly and logically presented. This means
that:
Your method should always be clear. It should be easy to figure
out what you're doing and why.
Use a lot of space. I recommend skipping some lines if you use
lined paper.
Equations should usually be accompanied by prose. Before plunging
into algebra, state what it is you're solving for. If there are any
non-obvious steps in a calculation, explain them.
Write equations in a logical order.
Most of the problems in this course are not short plug-ins. They
will require you to work through a multiple-step process, often
devising and testing a mathematical model along the way. It is
absolutely essential in such problems that you explain your reasoning
clearly. For these sort of problems, the explanation and narrative
is the solution.
Solutions should stand on their own; they should be understandable
to someone who hasn't read the problem. This means that you should
paraphrase the question before writing your response.
For many problems you will find yourself using Maple. For all but
the simplest Maple calculations you should include a printout of your
Maple worksheet.
I will not give numerical grades on HW assignments. Instead, I
will give a letter grade and try to include as many comments as I
can. I'm mainly interested in seeing that you thoughtfully attacked
the problem and wrote it up in a clear and coherent way.
Finally, a few minor requests:
On the top of the homework, please write the assignment number.
If you don't have a stapler, that's ok. But please don't mangle
and fold over the corner in an attempt to get the pages to stick
together. Just write your name or initials on all pages and I'll
gladly staple them together.
Please don't hand in problems on paper that has been torn out of a
spiral notebook. |
Advanced Placement Calculus
AP Calculus is a one-year long class that is equivalent to one semester of college calculus. The three main areas of emphasis are limits, derivatives, and antiderivatives. Students taking this class are expected to take the AP test.
The course's specific goals and objectives are to develop a higher level of confidence and competence in mathematical problem solving, to appreciate real world applications of calculus, to prepare to take and pass the AP Calculus test in May, to learn a variety of methods to solve academically challenging problems, to demonstrate understanding of mathematical concepts through written & verbal communications, to learn to work collaboratively, to understand when the use of a scientific or graphing calculator is appropriate and become proficient at using the calculator to solve problems efficiently.
For this class students will be required to create a binder. This binder will serve as a study tool in preparation for the AP test. In the binder students will keep notes, homework, group work, journal entries, projects, practice AP test questions, as well as information regarding the AP test. |
Other materials: Students are required to have a scientific or a graphing
calculator. You are not
allowed to use a cell phone as a calculator. Calculators are allowed for all
assignments except the
first Test.
Course & MML Structure: The four main required structural components of
this course are:
• In-class lectures with a strong emphasis on student engagement.
• The text.
• In-class assessments.
In-Class
Student engagement during class is critical. The lecture material will be
presented in bite-size
chunks and frequently punctuated with paper and pencil work and the use of
worksheets to keep
you engaged and to give you real-time feedback for you to assess your
understanding of the current
material. Power Point slides will also be used for further reinforcement.
Text
The text provides for each section an abundant collection of worked-out
problems, additional prob-
lems located on the sides of relevant discussions with answers, and an extensive
set of homework
problems. Each chapter ends with a chapter review set of exercises, a chapter
test and a cumulative
test that covers material from previous chapters. The text is also available in
an e-book version
that is accessible once you complete your MML registration.
MML & Online Assignments
The rationale for including MML is to enrich your experience learning algebra
both inside and
outside of the classroom and to give you every possible opportunity to do well.
MML provides
you with a wonderful tool to support your learning on a 24/7 basis. It is always
there for you no
matter what your schedule. It is there to help you to reinforce concepts
introduced in the class-
room. Consider MML as your virtual tutor. Online class work, homework and
quizzes/tests will
be assigned throughout this course. You will get immediate feedback on each
homework problem,
and incorrectly worked problems can be repeated (with a new version of the
problem provided by
the computer) until a correct solution is obtained. Tips and examples are
available online for each
problem, in addition to the help available from your instructor and the Tutoring
Center. Online As-
signments may be done at any location with an internet access. Do not wait till
the last hour to start
and complete online assignments because a computer glitch may prevent you from
accessing your
account. Emergency access to homework assignments
MML Resources
• Video lectures to reinforce the lecture material.
• Power Point presentations to reinforce the lecture material
• Immediate grading and feedback to students and instructors for each
completed MML assign-
ment.
• Student study plan to assist them in improving their identified weak
areas.
• Access to tutors. They can be reached at 1-888-777-0463 .
You are limited to 15 minutes per call. Tutoring is available in Spanish. Tutors
are available
Monday - Friday from 8 AM to 8 PM and on Sunday from 5 PM - 12 PM.
• Access to technical assistance. They can be reached at 1-800-677-6337.
Credit Hours: 4 credit hours. Course Objectives:
1. Understand and make connections between real numbers and expressions.
2. Develop the algebraic skills necessary for problem solving.
3. Develop the ability to model linear relations,
including the use of graphing techniques as tools,
for the purpose of solving contextual problems.
4. Manipulate and apply literal equations for the purposes of solving contextual
problems.
5. Writing and communicating the results of problem solving appropriately.
Student Learning Outcomes:
Upon satisfactory completion of the course, students will be able to:
• The student demonstrates the ability to work independently. (Gen. Ed.
Goal 6)
Class Operation:
1. On-Line Class Work Practice: Each class period will utilize a small set of
problems to reinforce
the material being covered during the class. The students will work these
problems on their
lab computer, and if necessary, complete them outside the lab. You can take each
of these
assignments as many times as you want. On-line "Help" is available. Each
assignment will be
open for one week after the section is completed.
2. On-Line Homework: There is a homework assessment for each section of the six
chapters cov-
ered. The homework comprises. Your lowest homework score will be dropped. The
homework
is found at our MML web site. You can take each of these assignments as many
times as you
want. Each homework assignment will be open for one week after the section is
completed.
There is no help on-line for those assignments.
3. On-Line Quizzes: 5 online quizzes will be given. You may take each quiz up to
two times and
your highest grade will be used. Each assignment will be open for one week after
the section
is completed. There is no help on-line for those assignments. The quizzes cannot
be made up.
4. In-Class Quizzes & Classroom Activities: Throughout the semester, we will
have at least 10
quizzes & classroom activities. In-Class quizzes or classroom activities cannot
be made up.
There are no exceptions. As a result, I will drop the lowest two
quizzes/classroom activities.
We will not have
5. Tests: There will be 4 tests during the semester in addition to the final
exam. The final exam
is also cumulative and it will be given during the last week of the semester.
6. COMPASS Test: All exiting Math 98 students must take the COMPASS test during
the fif-
teenth week of the semester. This test will count 5% of the final exam score.
Policies:
• Participation policy: Class participation is mandatory. You are expected
to attend most of
the class sessions. If you have any question, be ready to ask it at the
beginning the class.
The average student should plan two hours of out of class time for each hour of
class. Some
students need more time than this. |
My Advice to a New Math 175 Student:
My advice to a new Math 175 student would be to remain calm.
Having
not
taken even an algebra course for 3 years, I was a little bit worried
about
this class in the beginning. It really helped me though to do the
Review
Chapter in the front of the textbook. So that is where I would start.
I was
always the type of student who hated doing homework and usually waited
until
the day before the test before I began to study. However, I learned in
this
class that my old habits would not get me by this time. So even though
nobody likes to do homework, I advise you to work on ALL the assigned
problems every night before class or at least the night after the
lecture.
It is really important not to fall too far behind in this class. I
would
also not be afraid to ask questions from the homework in class and when
you
need extra help, I suggest going to talk to your professor. Dr. Hoar
helped
me on numerous occasions. I found it easier to understand the material
when
I went in to his office and we worked on them one on one.
So just remember to keep up with the homework, go over as many
different
problems as you can until you feel you are familiar with them, and also
go
and get help from either the professor or the tutor labs. The tutor
labs are
good, although I found it more beneficial to get help from Dr. Hoar. I
know
that these suggestions may sound generic but they are really necessary
if you
want to succeed in this class. Trust me! Good luck people! |
Textbooks for PDE between "Strauss and Folland" |
Read carefully the text, consulting the lecture notes,
and write down questions about
everything
that is not clear.
The notation will be a substantial difficulty.
Make a reference list of all symbols that are unfamiliar.
Find out the meaning (you may ask me) and write down the explanation.
Record the subsection (and the page number) which was the source of difficulty.
By the time you finish the reading, you will have the answers
to some of the questions.
Read again the same portion of text, this time with a pen and paper.
Write down the proofs and the solutions of the examples in the text.
This will help you get inside the reasoning thread and become more familiar with the notation.
Hopefully during the second reading/writing your understanding of the material
will improve,
and maybe the number of the questions
will be reduced.
Take the list of questions and read them, consulting the
textbook.
Think of possible answers to each question.
Send me the questions and what you think might be a possible answer. |
The Bedside Book of Algebra
The Bedside Book of Algebra
A fun and interactive introduction to algebra and the way in which it affects the world around us.
The book features clear and concise explanations of key concepts to demonstrate the principles of the various disciplines at work in the real world. There are exercises that challenge the reader to consider the concepts presented and help them learn how they relate to common experiences. The book profiles key figures throughout history and presents dozens of fun facts in each discipline and it is written by specialists in their field in an accessible and fun style that will appeal to both the expert and the layperson. |
Portfolios
Mathematical Portfolios
The purpose of the portfolio
The purpose of the portfolio is to provide students with opportunities to be rewarded for mathematics carried out under ordinary conditions, that is, without the time limitations and pressure associated with written examinations. Consequently, the emphasis should be on good mathematical writing and
thoughtful reflection. The portfolio is also intended to provide students with opportunities to increase their understanding of mathematical concepts and processes. It is hoped that, by doing portfolio work, students benefit from
these mathematical activities and find them both stimulating and rewarding.
The specific purposes of portfolio work are to:
develop students' personal insight into the nature of mathematics and to develop their ability to ask their own questions about mathematics.
provide opportunities for students to complete extended pieces of mathematical work without the time constraints of an examination.
enable students to develop individual skills and techniques, and to allow them to experience the satisfaction of applying mathematical processes on their own.
provide students with the opportunity to experience for themselves the beauty, power and usefulness of mathematics.
provide students with the opportunity to discover, use and appreciate the power of a calculator or computer as a tool for doing mathematics.
enable students to develop the qualities of patience and persistence, and to reflect on the significance of the results they obtain.
provide opportunities for students to show, with confidence, what they know and what they can do. |
Math Models
Mathematical Models with Applications 1A
Mathematical Models with Applications1A is a one-semester course designed to help students to build on their knowledge of algebra and expand their understanding through mathematical experiences. Students use interactive media and content to develop an understanding of real-life applied problems involving money, data, chance, patterns, design, and science.
Scope and Sequence |
This is one of the mathematics question of Singapore's PLSE 2009 (which is standard 6 UPSR in Malaysia, though the quality is not comparable.)Algebra? I remembered that algebra is only taught in middle school in Malaysia, and it has been about 10 years ago for me. And can you answer the question above? If you cant, then you failed the Singaporean's standard 6 exam.
And also go to google books and search the title:
How Chinese learn mathematics: perspectives from insiders
Mathematics curriculum in Pacific rim countries--China, Japan, Korea, and Singapore
To really success in mathematics:
1. hardworking - no need explanation for this word
2. good teacher - teachers in malaysia? how many of them can answer your question directly and instantly?
3. syllabus - syllabus in malaysia really [muted]
I have my friends, also top students, studying higher education at singapore. They say those chinese (who really come from China) in their schools always score full marks, if not then highest marks in the exams, and those chinese seldom study mathematics in school (in singapore). Can you see the differences?(S/2) - 12 : (C/2) = 1 : 7
(S/2) : (C/2) - 18 = 1 : 4
Use one of the equations to get C in term of S and use it in the second equation to get the value of S.
But damn, if this was in my UPSR, I wonder if I would be able to answer itI agree with you to a huge extent. Copy and pasting what I have wrote on this topic in another discussion:
Quote:
I am not sure how much better we could have done.
I am pretty sure the derivation from the first principle is taught in A-Level and would in fact be test-able (at least that's the case in Malaysia's SPM syllabus). The fact that this student couldn't do it from prompting either mean that he has not learned it very well, or did not have the capacity to fully take it to heart and reproduce it without prompting.
The thing with mathematical education is that we ought to recognise that a lot of people, while perfectly capable to understand first principles given enough time and effort, will soon forget them as soon as life's other woes overwhelm their memory. I believe that everyone in this group [current and past members of Malaysia IMO team] would be able to remember the first principle even if you aren't doing maths-related things, and in fact even though I haven't done any advanced maths for the last 8 years, when I read about the derivation by first principle in the blog post, I was able to recall [f(x+h)-f(h)]/h because my understanding remained solid even without day-to-day use. I think we are a group of privileged people with brain wiring more capable of deep and indelible understanding of logical truths, but the same is not necessarily true for many high school kids. Yes spend enough time explaining fundamental principles and they will understand it eventually, but invariably they will forget themYes, bro i agree with you...Mind you, i even had a Physics lecturer who was so dumbstrucked with a question and its' answer, and he couldn't even explain why that was the answer. In the end, he asked us to memorized the answers. Btw, most of the time, when he couldnt explain the concepts properly, or at the least make physics sounds a tad bit interesting rather than making it SO mundane for him and his students, he will just tell us to memorize the concepts, formulas and even the derivations. What kind of Physics learning is this?? I was utterly disappointed that this happen during My A Level, whatmore at a so called Tier 6 college in Malaysia.
For Mathematics, all i could remember in primary, was if we got one damn question wrong, i was caned until i had bruises. And later i was forced to do corrections and memorized the methods of deriving the answers. In Form Four mathematics, i had a stand-in teacher, so called an "intern" from UITM to teach us for 3 months as part of her course, she could not even speak proper English, and the medium for mathematics is in English. She could only answers my classmates' questions vaguely and sometimes even totally unsure of her answer |
Numerical Analysis - Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to numerical analysis: the study of methods of computing numerical data. In many problems this implies producing a sequence of approximations; thus the questions involve the rate of
convergence, the accuracy (or even validity) of the answer, and the completeness of the response. Since many problems across mathematics can be reduced to linear algebra, this too is studied numerically; here there are significant problems with the amount of time necessary to process the initial data. Numerical solutions to differential equations require the determination not of a few
numbers but of an entire function; in particular, convergence must be judged by some global criterion. Other topics include numerical simulation, optimization, and graphical analysis, and the development of robust working code. Numerical linear algebra topics: solutions of linear systems AX = B, eigenvalues and eigenvectors, matrix factorizations. Calculus topics: numerical differentiation and integration, interpolation, solutions of nonlinear equations f(x) = 0. Statistical topics: polynomial approximation, curve fitting. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.
more>>
Numerical Analysis - Math Forum
Links to some of the best Internet resources for numerical analysis: Web sites, software, Internet projects, publications, and public forums for discussion.
more>>
alt.math.undergrad - Math Forum
An unmoderated discussion forum for issues and problems pertaining to college undergraduate mathematics. Read and search archived messages; and register to post to the discussions.
...more>>
Arizona Mathematical Software
A collection of approximately 60 educational programs that are designed for use by instructors and students in classroom, laboratory, and home environments. Software falls into four categories: Are You Ready?; Slide Shows; Teacher Aids; Toolkits. It runs
...more>>
BigPrimes.net - BigPrimes.net
An archive of primes, plus information on each prime, and on prime numbers in general, number systems, types of numbers, and universal constants. The number cruncher will tell you facts about numbers you submit.
...more>>
DigiArea Group - Helen Golovina
Makers of atlas™, a Maple package for differential geometry calculations that works with manifolds, mappings, embeddings, submersions, p-forms, and tensor fields; and LdeApprox™, a toolbox for Maple or Mathematica that finds analytical polynomial
...more>>
Elsevier Science
"Information Provider to the World." Elsevier's mission is "to advance science, technology and medical science by fulfilling, on a sound commercial basis, the communication needs specific to the international community of scientists, engineers and associated
...more>>
Finite Element Mesh Generation - Robert Schneiders
Mesh generation is an interdisciplinary area within numerical analysis that includes mathematicians, computer scientists, and engineers from many disciplines. This page is intended to build a bridge between theory and applications. People and research
...more>>
Floating-Point Number Tutorial - Joseph L. Zachary
A tutorial designed to help you understand the significance of mantissa size and exponent range and the meaning of underflow, overflow, and roundoff error. Includes a Java applet in a separate window for use alongside the tutorial. From a Computer Science
...more>>
Foundations of Computational Mathematics
The FoCM's primary aim is to further the understanding of the deep relationships between mathematical analysis, topology, geometry and algebra and the computational process as they are evolving together with the modern computer. The meetings are unifiedGallery of Mathematical Models - Arthur Sherman
"Gold standard" versions of published models, given as input files for xpp but also human-readable ASCII files adaptable for use with other programs. Beta-Cell Models: Generic, CRAC Models I and II, Smolen-Keizer, Keizer-Smolen, Sherman-Keizer-Rinzel
...more>>
GNU Octave Repository
Custom scripts, functions and extensions to GNU Octave. Site includes alphabetical list of functions available for download and a related mailing list, with archives.
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Guy Kindler - The Official Site - Guy Kindler
A mathematics Ph.D. student at Tel Aviv University. Math puzzles are ranked from easy to tough. A paper on approximation and various resources for a seminar on computational models may be downloaded in PostScript format. Related PowerPoint presentations
...more>> |
Now
All book demonstrates how mathematics applies to various fields of study. The text is packed with real data and real-life applications to business, economics, social and life sciences.
show more show less
Linear Equations
Lines
Pairs of Lines
Applications to Business and Economics
Scatter Diagrams; Linear Curve Fitting
Chapter Review
Chapter Project
Systems of Linear Equations
Systems of Linear Equations: Substitution; Elimination
Systems of Linear Equations: Gauss-Jordan Method
Systems of m Linear Equations Containing n Variables
Chapter Review
Chapter Project
Matrices
Matrix Algebra
Multiplication of Matrices
The Inverse of a Matrix
Applications in Economics (the Leontief Model), Accounting, and
Statistics (the Method of Least Squares)
Chapter Review
Chapter Project
Linear Programming with Two Variables
Systems of Linear Inequalities
A Geometric Approach to Linear Programming Problems
Chapter Review
Chapter Project
Linear Programming: Simplex Method
The Simplex Tableau; Pivoting
The Simplex Method; Solving Maximum Problems in Standard Form
Solving Minimum Problems Using the Daily Principle
The Simplex Method for Problems Not in Standard Form
Chapter Review
Chapter Project
Finance
Interest
Compound Interest
Annuities; Sinking Funds
Present Value of an Annuity; Amortization
Annuities and Amortization Using Recursive Sequences
Chapter Review
Chapter Project
Probability
Sets
The Number of Elements in a Set
The Multiplication Principle
Sample Spaces and the Assignment of Probabilities
Properties of the Probability of an Event
Expected Value
Chapter Review
Chapter Project
Bayes' Theorem; The Binomial Probability Model
Conditional Probability
Independent Events
Bayes' Theorem
Permutations
Combinations
The Binomial Probability Model
Chapter Review
Chapter Project
Statistics
Introduction to Statistics: Data and Sampling
Representing Qualitative Data Graphically: Bar Graphs; Pie Charts
Organizing and Displaying Quantitative Data
Measures of Central Tendency
Measures of Dispersion
The Normal Distribution
Chapter Review
Chapter Project
Markov Chains; Games
Markov Chains and Transition Matrices
Regular Markov Chains
Absorbing Markov Chains
Two-Person Games
Mixed Strategies
Optimal Strategy in Two-Person Zero-Sum Games with 2. X 2. Matrices
Chapter Review
Chapter Project
Logic
Propositions
Truth Tables
Implications; The Biconditional Connective; Tautologies
Arguments
Logic Circuits
Chapter Review
Chapter Project
Review
Real Numbers
Algebra Essentials
Exponents and Logarithms
Recursive Defined Sequences: Geometric Sequences
Using LINDO to Solve Linear Programming Problems
Graphing Utilities
The Viewing Rectangle
Using a Graphing Utility to Graph Equations
Square Screens
Using a Graphing Utility to Graph Inequalities
Answers to Odd-Numbered Problems
Photo Credits
Index
List price:
$190.95
Edition:
11th 2011
Publisher:
John Wiley & Sons, Incorporated
Binding:
Trade Cloth
Pages:
864
Size:
8.25" wide x 10.25" long x 1.25" tall
Weight:
3 |
range's tag archives
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Too many students end their study of mathematics before ever taking an algebra course. Others attempt to study algebra, but are unprepared and cannot keep up. "Key to Algebra" was developed with the belief that anyone can learn basic algebra if the subject is presented in a friendly, non-threatening manner and someone is available to help when needed. Some teachers find that their students benefit by working through these books before enrolling in a regular algebra course--thus greatly enhancing their chances of success. Others use "Key to Algebra" as the basic text for an individualized algebra course, while still others use it as a supplement to their regular hardbound text. Allow students to work at their own pace. The "Key to Algebra" books are informal and self-directing. The authors suggest that you allow the student to proceed at his or her own pace. In Books 5-7 of "Key to Algebra" operations on fractions are taught as students study rational algebraic expressions. This Answer Key provides brief notes to the teacher and gives the answers to all the problems in the workbooks KTA Answers Notes, Books #5-7
Review 1 for KTA Answers Notes, Books #5-7
Overall Rating:
5out of5
Date:September 30, 2008
Jessica Fry
Must have for the Algebra student books. Easy to use. I just wish they would combine all the answer keys into one book. |
Mathematics
To be an informed individual requires the ability to reason, to solve problems, and to have the tools necessary to be productive in our technological society. To become mathematically literate an individual must develop the ability to analyze, explore, conjecture, reason, use quantitative and spatial information and use mathematical tools to solve problems and make decisions. They must also develop self-confidence in their abilities and to understand and appreciate the role of math in everyday life.
DEPARTMENT GOALS:
To meet the BC Mathematics Curriculum and the New Western Consortium Mathematics Curriculum
To provide students with opportunity to take a mathematics course that reflects their abilities and meets their needs.
To provide students with mathematical skills and tools to help them achieve their academic and/or career choice
To help students to confidently use numeracy and problem solving/reasoning skills and tools in everyday life.
REMINDERS/DATES:
Pascal, Cayley and Fermat Contests for grade 8 to 11 students will take place in February. Date: TBA.
Students are asked to speak to their math teachers about registering for these contests and receiving practice materials.
Euclid Contest for grade 12 students will take place in April. Date: TBA
Students who have signed up to participate or are wishing to register are asked to see Ms. Martins.
COURSES AVAILABLE:
STA Math Department offers the following courses:
Math 8 / Math 9 / Math 10 courses are undergoing changes and will be updated shortly Principles of Math 11 Principles of Math 11 Honours Essentials of Math 11 Principles of Math 12 Changes are being made to Math 11 and 12 courses for the school year 2011-12 |
The study of mathematics forms the basis of logical thought and problem solving. In an increasingly technological world, the knowledge of how mathematics is applied to present day problems is as important as the skill to apply these mathematics. Math courses are intended to show the student the variety and depth of the topics where mathematics has made a significant impact in our present day world and to give them an appreciation for the power of mathematics as a problem-solving tool. The following core values are fundamental to all math courses:
Appreciating the usefulness of mathematics in understanding the real world.
Recognizing the application of mathematics to other fields of study.
The Math Department's Curriculum includes: Algebra I, Algebra II and Honors Algebra II, Geometry and Honors Geometry, Pre-Calculus and Honors Pre-Calculus, Calculus and AP Calculus, Statistics and Honors Statistics, and Discrete Mathematics. This curriculum provides all cadets with a solid mathematics foundation to pursue their college degree of choice whether it be the math intense programs found at our nation's service academies which several of our graduates attend or the diverse offerings found throughout the prestigious colleges in Virginia that are well attended by our graduates.
Algebra I
Level I consists of the application of the properties of real numbers to algebraic expressions and equations. Emphasis is placed on solving and graphing linear equations and inequalities, factoring and its applications, and developing and applying the properties of exponents and radical expressions. Students are taught to develop and use visual aids to problem solving, including charts, tables, graphs, and diagrams. Quadratic functions are introduced.
Geometry
Primary emphasis of this course is placed on traditional plane geometry with formal proofs. The course also includes an introduction to solid and coordinate geometries.
Prerequisite: Algebra I Credits: 1
Geometry (Honors)
In addition to the course prescribed for regular geometry, this course covers more extensive work with areas and volumes of solids; and coordinate geometry. The course is designed to offer challenging and thought-provoking discussions and problems for the math-oriented student.
Prerequisites: B+ in Algebra II and teacher recommendation Credits: 1
Algebra II and Honors Algebra II
In Level II, the skills and concepts of Algebra I are strengthened and expanded to include complex numbers. Additional emphasis is placed on the properties of exponents and roots, quadratic equations and functions, conics and polynomial functions. Logarithms are introduced. An honors section is available for strong math students.
Prerequisite: Algebra I Prerequisites for honors: B+ in Algebra I; A standardized math score in the 85%tile on the SSAT, or a passing score on the Algebra I SOL test, or a passing score on the Diocesan Algebra I test, is recommended for ninth graders placed in the honors level. Credits: 1
Algebra Functions and Data Analysis
In this course students will investigate, graph and analyze function families and their characteristics; collect data and determine the curve of best fit to predict outcomes: determine optimal values in problem situations using linear programming: explore exponential, logarithmetic and polynomial functions and explore, graph and apply trigonometric and circular functions.
Prerequisite: Algebra II Credits: 1
Statistics including Algebra II Credits: 1
Statistics (Honors) with B+ or higher in Algebra II, and teacher recommendation Credits: 1
Pre-Calculus
This course is designed to provide a solid foundation for those who wish to continue their study of mathematics. It covers a wide variety of topics, including algebraic, exponential and logarithmic functions; systems of equations, matrices and determinants; sequences; trigonometric functions and graphs.
Pre-Calculus (Honors)
This course is designed to prepare the student to perform well in Calculus and all college-level mathematics. The course covers a wide variety of topics, including algebraic, exponential and logarithmic functions; systems of equations, matrices and determinants; sequences; trigonometric functions and graphs. A pre-test test is required.
Calculus
This is an introductory course in Calculus and is designed to prepare the student to perform well throughout the calculus sequence in college. The course covers limits and continuity, differential and integral calculus with applications, logarithmic and exponential functions, calculus of trigonometric functions and integration techniques.
AP Calculus (AB)
This course is designed to prepare students for the AP Calculus AB test and to perform well throughout the calculus sequence in college. The students cover limits and continuity, differential and integral calculus with applications, logarithmic and exponential functions, calculus of trigonometric functions, advanced integration techniques and, if time permits, sequences and series. |
Self-Education] Statistics & Game Theory
I'm a few weeks into my first semester of college and I'm beginning to miss math (two years of high school calculus fulfilled my requirements).
I never took a stats class in high school, and though I'll likely be taking one next semester, I want to learn more about it now. I feel like I'm missing out on a vital part of being an educated individual.
So I'm looking for books that provide a basic overview of statistics, as well as books that serve as an introduction to game theory (I'm an evolutionary biology major). I'm not intimidated by lots of math, but I don't know any real statistical terminology beyond the extreme basics (mean, standard deviation, etc).
Posts
Depending on your university, some math classes may also double as computer science classes. Maybe you can take something and have it count as other than math. For example, back in 04 I enrolled in "Number Theory and Cryptography." Awesome, I thought, we'll learn how to write code that does math on huge prime composites and stuff. Nope. Math class. There were currently-employed high school math teachers in the row behind me. X__X
Be warned, as math tends toward junior, senior, and grad level, there's a LOT more proofs. Math starts being a lot less about computation (i.e. can you remember the right transformation rules for a given situation, and apply the transformations correctly?) and a lot more about proofs (i.e. why is this true? Can you prove it's true for ALL situations?)
To clear up the confusion, I'm not looking for suggestions on what classes to take (I'm already planning to take stats next semester) but books about the subject I can read now. Something to read in my free time.
I'm going to check out that Cartoon Guide. I need a refresher on statistics for my next job and I think that will be a fun book to have on my desk.
Not to hijack the thread but any similar recommendations for math? I would be looking for a book that covers Algebra to Calculus. It's been about 8 years since I've seen a calculus book. I may have traded in my college calc book for a candy bar (thanks new edition!)My experience with biology has been that if you take an active interest in the subject outside of class, you end up learning more in class and having a richer, fuller understanding of the subject.
Coming from someone who works as a Student Aid Peer Math Reviewer (Read: Math Tutor - Pay) at a Community College and as someone majoring in Statistics, I can recommend Essentials of Statistics. It teaches the class quite well, and does a good job of ramping up off of mean/meadian/std dev/ etc. The third edition has its occasional wobbles (Right around a third of the way through the book it has an identity crisis on how you should deal with with/without replacement and giant sample sizes that can be kind of annoying if you're already struggling in that area), but overall it's a rather good book. |
Follows Saxon's Algebra 1, 3rd edition text. Includes lectures and visual instruction for each and every Saxon lesson. Arithmetic and evaluation of expressions involving signed numbers, exponents,...
More about Algebra 1 (3rd ed) Dive Into Math CD
A supplemental compact disc that is designed to be used in conjunction with Saxon's Algebra 1/2 - 2nd edition textbook. Includes lectures and visual instruction for each and every Saxon lesson. ...
More about Algebra 1/2 (2nd ed) Dive Into Math CD
Follows Saxon's 3rd edition textbook. Includes lectures and visual instruction for each each and every Saxon lesson. Fractions, decimals, signed numbers and their arithmetic operations, translating...
More about Algebra 1/2 (3rd ed) Dive Into Math CD
For use with Saxon Algebra 2, 2nd edition textbook. Includes lectures and visual instruction for each and every Saxon lesson. Graphical solutions of simultaneous equations; scientific notation;...
More about Algebra 2 (2nd ed) Dive Into Math CD
The new Online Algebra 1 Placement Test (APT) covers nineteen key concepts essential for success in Algebra 1. It is a quick, easy, and inexpensive way to see if your...
More about Algebra Placement Test
A supplemental CD that may be used in conjunction with the Saxon Calculus, (1st edition) text. Includes lectures and visual instruction for each and every Saxon lesson. Covers all material...
More about Calculus (1st ed) Dive Into Math CD
A collection of word problems with Catholic themes written by the Seton Staff and designed for students using level D of MCP Mathematics. More than thirty separate lessons with 10 Catholic...
More about Catholic Word Problems Level D
A collection of word problems with Catholic themes written by the Seton Staff and designed for students using level E of MCP Mathematics. 15 separate lessons with 10 Catholic word problems...
More about Catholic Word Problems Level E
Counting with Numbers introduces the child to the practice of neatness in all work, carefulness in the use of books, and following directions. It continues the presentation of recognition of shapes...
More about Counting with Numbers
E-Z Grader is a hand-held manual computer. It helps make your homeschooling just a little bit easier. It saves time and effort otherwise needed to compute grades. Gives you freedom to use any number...
More about E-Z Grader
NEW from Dive Into Math, this Interactive CD is for use with the new Saxon Geometry 1st edition textbook. The DIVE CD-ROM teaches each of the 120 lessons and 12 Investigations, plus...
More about Geometry (1st ed) DIVE Into Math CD |
Book Description
Release date: August 5, 2008 | Age Range: 11 and upEditorial Reviews
About the Author
Best known for her roles on The Wonder Years and The West Wing, Danica McKellar is also an internationally recognized mathematician. She was chosen as ABC World News Tonight's "Person of the Week" for writing Math Doesn't Suck and has recently been featured in Newsweek and The New York Times, and on the CBS Early Show, and NPR's Science Friday.
--This text refers to an out of print or unavailable edition of this titleThis funny math book teaches girls that it's OK to be smart, and that they are perfectly capable of kicking a little pre-algebra butt.
McKellar takes a lightweight approach to math, but is deadly serious about it. In the prologue, she writes that "lots of people change their majors and abandon their dreams just to avoid a couple of math classes in college." Girls in particular, she emphasizes, often use their fear of math to keep them from learning the skills they'll need to succeed in life, and they start backing away from the subject in middle school.
And it's not just fear. Girls often don't see how they'll use math once they get out of school. Testimonials in Kiss My Math fight this. Stephanie Perry, the finance director for Essence magazine, explains how she uses algebraic formulas to stay on top of the magazine's financial performance. Jane Davis, financial strategist at Polo Ralph Lauren, was hired as an assistant buyer because of her facility with math. She describes determining inventory over time by finding the mean of a list of numbers.
McKellar -- famous for playing Winnie Cooper in the "The Wonder Years" but also a summa cum laude math graduate from UCLA -- uses simple language and lots of illustrations to teach pre-algebra. Each chapter covers a single topic, such as the distributive property or exponents. She clearly explains each topic, and includes problems for the reader to solve (answers are in the back). The author is generous with helpful notes and shortcuts.
A lively, breezy writing style makes it seem as if McKellar is sitting next to the reader. She uses examples girls can relate to, like clothes shopping, working on the school play, blind dates, parties, kissing and breath mints. It's like having the perfect math tutor. (I'm not a middle school girl, of course, but I just got finished having one. My daughter is starting high school this month.)
Especially good are the entries called Danica's Diary, which are true stories from the author's life as a student, actress and mathematician. One is titled: Dumbing Ourselves Down for Guys: Why is it so Tempting? McKellar gives practical advice on how girls can avoid this common pitfall.
I can't think of a better book to buy for a girl taking pre-algebra.
Here's the chapter list:
Part 1: Number Stuff Chapter 1: Breath Mint, Anyone? Adding and Subtracting Integers (Including Negative Numbers). Chapter 2: The Popular Crowd. The Associative and Commutative Properties. Chapter 3: Mirror, Mirror, on the Wall... Multiplying and Dividing Integers (Including Negative Numbers!) Chapter 4: A Relaxing Day at the Spa. Intro to Absolute Value. Chapter 5: Long-Distance Relationships: Are They Worth It? Mean, Median, Mode. You Said: Most Embarrassing Moments in School Poll: What Guys Really Think... About Smart Girls Quiz: Are You a Stress Case?
Part 2: Variable Stuff Chapter 6: The Blind Date. Getting Cozy with Variables. Chapter 7: Backpack Too Heavy? Adding and Subtracting with Variables. Chapter 8: Something Just Went "Squish." Multiplying and Dividing with Variables. Chapter 9: Do You Like Him Like Him? Combining Like Terms. Chapter 10: The Costume Party. The Distributive Property. Chapter 11: Didn't That Guy Say He Was Going to Call? Using Variables to Translate Word Problems. More Than 20 Ways to Beat Stress Math... In Jobs You Might Never Expect!
Part 3: Solving for X Chapter 12: The Art of Gift Wrapping. Solving Equations. Chapter 13: Nope, She Never Gets Off the Phone. Word Problems and Variable Substitution. Chapter 14: Can a Guy Be Too Cute? Intro to Solving and Graphing Inequalities. You Said: Your Horror Stories About Procrastination Poll: What Guys Really Think... About Talented Girls Quiz: Do You Pick Truly Supportive Friends?
Part 4: All About Exponents Chapter 15: Champagne and Caviar. Intro to Exponents. Chapter 16: Excuse Me, Have We Met Before? Intro to Variables with Exponents. You Said: Well... That Didn't Work! Do You Sudoku?
I am a mother that went back to college later in life. One of my classes was algebra. I had math anxiety and tried to find way to wiggle my way out of this class. The algebra class was very difficult for me. I could not understand the instructor or the book. I went to tutors,family members and friends and I could not get algebra. I failed the class. I was embarrassed and angry with my myself. I needed something right away. So my boyfriend and I went to Barnes & Nobles and purchased Kiss My Math & Math Doesn't suck. (I do suggest that you purchase both). So I had a six week break before I had to take the algebra class again. I am happy to say that I passed the algebra class with a B and I am looking forward to starting MATH 209 which is the second part of algebra. Danica was easy to understand and the experiences from other young ladies helped a great deal too. Thanks Danica!
Danica McKellar is a beautiful actress who is probably very well off and successful. So why did she go to UCLA to study math after being a very successful child star on the wonder years and then bother to write a book entitled Math Doesn't Suck. Well it is because she wanted to prove she was more than just a good looking actress. She had a brain and could handle math. The attitude that math is not for the ladies was a horrible prejudice in my high school years and even in this enlightened age we haven't quite gotten over it and many a capable young lady lacks the confidence and courage to try to do math. Danica is a rol model who proves that they can. Her first book was so successful and helped young middle school girls overcome their fears and lkearn that math is not really hard and can be fun and interesting whenit is approached in the riht way. So math does not suck! But in addition to convincing young girls and boys that they can learn it she became encouraged to write another book based on the encouraging emails from young ladies who benefitted from the book. Well love of math should not end with middle school and algebra, geometry and calculus are very different form the kind of math you learn in the elementary and middle schools that a good series of lectures in pre-algebra is needed to help those who become discouraged again in high school. It bothers Danica to see a girlfriend of hers give up on medical school just because calculus is required. So in the same interesting style as her first book Danica interest the high schoolers with concepts like negative numbers, mathematical inequalities, exponential functions and much more. By uncovering the mysteries of pre-algebra Danica unlocks the door to advanced levels of mathematics that students in high school need. This book is good for high school teachers and anyone else with an interest in mathematics. But it is aimed at and can help most high school girls who are capable of doing well in math and nedd it for the careers they seek, like med school. |
Advanced Mathematical Methods for Scientists and Engineers: Asymptotic, by Bender
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
This text serves as an introduction to the programming language Java for scientists and engineers, as well as experienced programmers wishing to learn Java as an additional language. The authors have ... |
Instructions for Submitted Work
When
preparing solutions for marking please note the following points.
Not attempting a solution is generally unacceptable.
Set out your solution as a coherent narrative explaining any
principles used. The final solution should be underlined, or a
reasonable gap left in the text so the end of the question is obvious.
In general solve problems algebraically before inserting values.
In multiple part questions, identify all the answers being asked for
and present a solution that answers them all. Counting the things asked
for in a problem, and matching this to the number of underlined results
in your manuscript, can ensure this.
Do not use different notation from that used in the question. Define
any new variables you introduce.
Write legibly. If you struggle to do this in first draft then rewrite
your solutions when complete.
Solutions should be presented on 1 side of the paper and stapled at
the top left hand corner (or otherwise held together).
Obeying these rules is good practice and will pay off in exams.
Scripts that fail to respect these rules will be returned to be rewritten. |
The best selling 'Algorithmics' presents the most important, concepts, methods and results that are fundamental to the science of computing. It starts by introducing the basic ideas of algorithms, including their structures and methods of data manipulation. It then goes on to demonstrate...
For departments of computer science offering Sophomore through Junior-level courses in Algorithms or Design and Analysis of Algorithms. This is an introductory-level algorithm text. It includes worked-out examples and detailed proofs. Presents Algorithms by type rather than application.
Designed for use in a variety of courses including Information Visualization, Human—Computer Interaction, Graph Algorithms, Computational Geometry, and Graph Drawing. This book describes fundamental algorithmic techniques for constructing drawings of graphs. Suitable as either a textbook ... |
Constructing and Exploring Composition of Functions with Sketchpad (Intermediate/Advanced)
Composition is hard for students—but the multiple representations shown in this webinar will get them over the rough spots and help them to generalize and master the concept of composition. We'll compose functions both geometrically and symbolically, find the links between different representations, and put the behavior of the variables front and center. We'll show, and make available to attendees, composition activities that are accessible to early-algebra middle-school students and activities that will give high school algebra and pre-calc students new insights. The function dance activities from this webinar (in which the dependent variable dances with the independent variable) are likely to become a favorite for students at all levels.
Presenter
Scott Steketee taught secondary math and computer science in Philadelphia for 18 years and received the district's Teacher of Excellence award. Since 1992 he has worked on Sketchpad software, curriculum, and professional development for Key Curriculum and KCP Technologies. He also teaches Secondary Math Methods in the graduate teacher education program at the University of Pennsylvania. |
Based on your search results and the class
discussion which followed the list of on-line tutorial sites for Precalculus has
been pared down to ten (10) sites.
Your job is to evaluate the 10 sites
in order to determine the 2 best sites that you would recommend for on-line
tutorial sites that could be used by Math 105 and Math 120 students and placed
on the Math Department Web page.
You will report your choices as
follows:
A. The address or URL of each on-line site and the name of the
site. (2 points)
Site 1:
Site 2:
B. Describe the strengths of each site and the
weaknesses or drawbacks of each site. Use complete English sentences with proper
grammar and spelling.
Site 1: Strengths: (2 points)
Site 1: Weaknesses: (2 points)
Site 2: Strenghts: (2 points)
Site 2: Weaknesses: (2 points)
C. Prepare a POSTER that would advertise
your number one choice. The poster should include the name of the site, the URL,
emphasize the strengths you identified above and alert the consumer to some of
the weaknesses of the site. You can be as creative as you want. Be sure you
write down the name of the group members on the back of the poster. (15 points) |
Alina Galindo and Cameron Alves demonstrate their understanding of linear systems by creating a video using stop-animation on the iPad.
Courses
The Mathematics Department is offering 17 courses during the 2012-2013 academic year to meet the mathematics and computer programming needs of Somerville students regardless of their plans after high school. These course offerings are meaningful and have real world applications and connections so that students will be in a position to make themselves more marketable in today's society.
To contact the Head of the Somerville High School Mathematics Department, Marie Foreman, please call 617-625-6600 x6258. Phones are staffed from Monday to Friday from 8:00 AM - 4:00 PM. You can also contact Ms. Foreman by email. |
Competency in College Mathematics, 5th Edition, guarantees coverage of the concepts and skills traditionally expected of a liberal arts student. More than 4,000 exercises are presented with answers, along with numerous solved problems, examples and exercises that allow continuous review. Competency in College Mathematics also features the most complete presentation on logic found in any liberal arts mathematics text. A complete testing battery consisting of multiple forms of each chapter test is included upon adoption.
Competency in College Mathematics thoroughly prepares students for the College-Level Academic Skills Test (CLAST) administered by the state of Florida at the completion of the college sophomore year. The book has been revised to reflect the latest CLAST requirements. The Appendix includes an 130-questions sample exam with explained answers. |
More About
This Textbook
Overview
This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities |
North Wales StatisticsSolve linear equations and inequalities.
10. Solve systems of equations.
11. Solve quadratic equations Most computer-savvy people out there today know that MS Excel is a spreadsheet program that you can use to record data, create charts, and utilize mathematical equations. |
With LIFEPAC Pre-calculus, your student is given a comprehensive study of advanced math, trigonometry, and pre-calculus. Topics are: Relations and Functions; Trigonometric Functions; Circular Functions and Graphs; Quadratic Equations; and Probability. Easy-to-understand, personalized instructions ease anxiety and give student's an assertive, positive attitude toward calculus. Packed with valuable information, this course, which covers functions and identities, is a great preparatory course for college math classes. The LIFEPAC Pre-calculus Set contains ten worktexts and a teacher's guide that may be purchased individually. |
Specification
Aims
experience important mathematical ideas not covered in other first year modules;
develop presentation skills.
Brief Description of the unit
These weekly classes are intended to help students experience a wide range of mathematical topics. The course unit
includes a number of projects to be worked on in groups. The projects are assessed via a written report. Marks will
be awarded for presentation as well as mathematical content to encourage the development of good writing habits.
Future topics requiring this course unit
This course unit is not a formal prerequisite for later courses but the approaches to problem solving with be beneficial in
later Mathematical study.
Content
Week 01: Study skills lecture and teamworking activity.
Week 02: Project 1 Modular Arithmetic.
Week 03: Project 1 Modular Arithmetic.
Week 04: Group presentations
Week 05: Project 2 Conic Sections
Week 06: Mid semester break.
Week 07: Project 2 Conic Sections
Week 08: Project 3 Difference Equations.
Week 09: Project 3 Difference Equations.
Week 10: Project 4 Graph Theory.
Week 11: Project 4 Graph Theory.
Week 12: In class test.
Textbooks
Teaching and learning methods
Three hours contact time per week made up of one hour lecture followed by two hours of problem solving in groups.
In addition students are expected to do at least five hours private study each week on this course unit. |
Goals
The Mathematics department develops critical thinking, quantitative literacy, and problem-solving skills in its students through an integrated mathematics curriculum that emphasizes student-centered teaching methodologies, real world applications, and the appropriate use of technology.
The Mathematics Department will...
...create an active learning environment for all its students through the prevalent use of student-centered discovery exercises and cooperative learning strategies.
... foster a deep understanding of mathematical concepts at each grade level by using computers and graphing calculators to solve problems, analyze data, explore patterns, and communicate results.
...promote quantitative literacy and problem-solving skills by frequently using applications from the natural and social sciences, and requiring at least one research project at each grade level.
...establish objectives, select supportive materials, and design assessment instruments in each math course based on a constructivist-learning model, where students build deep understanding through explanation, interpretation, experimentation, application, and reflection.
...publish an integrated model for the mathematics curriculum that identifies key threads and topics that are developed and extended in a progressive flow through consecutive courses. ...employ a wide variety of methods including tests, homework, class work, research reports and oral presentations to assess student levels of critical thinking, quantitative literacy, and problem-solving skills.
...maintain fair and equitable grading practices by aligning assessment techniques with teaching methodologies, and by clearly specifying how students will be assessed in each mathematics course.
...offer a variety of mathematics courses so that students at every ability level have the opportunity to continue and succeed in their mathematics education.
...encourage its faculty members to attend mathematics conferences, enroll in educational courses, and pursue other professional development opportunities that directly support the department's mission and goals.
...strive continuously to make improvements in its curriculum and teaching methods, and annually assess the effectiveness and suitability of all its programs in achieving institutional and departmental goals. |
Career Opportunities
A degree in mathematics can open the door to a wide range of career opportunities. While most mathematics students seek careers that require them to directly apply their knowledge of mathematics on a daily basis, many others find success in careers that make use of the general problem-solving and logic skills acquired during the study of mathematics.
An excellent resource for mathematical careers is Andrew Serrett's 101 Careers in Mathematics, published by the Mathematical Association of America. This book contains interviews with over one hundred people who have studied mathematics and are now working in a wide variety of areas, including:
Well-known companies such as IBM, FedEx, and L.L. Bean
Government agencies such as the Bureau of the Census and NASA
Legal and medical professions
The field of education at elementary, secondary, and university levels |
If you?re curious about how things work, this fun and intriguing guide will help you find real answers to everyday problems. By using fundamental math and doing simple programming with the Ruby and R languages, you?ll learn how to model a problem and work toward a solution.
All you need is a basic understanding of programming. After a quick introduction... more... |
BEGIN:VCALENDAR
PRODID:-//Microsoft Corporation//Outlook MIMEDIR//EN
VERSION:1.0
BEGIN:VEVENT
DTSTART:20121111T203000Z
DTEND:20121112T000000Z
LOCATION:255-D
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:ABSTRACT: Computer modeling is an essential tool for discovery and innovation in science and engineering. It can also be used as a valuable educational tool, involving students in inquiry-based problems which simultaneously illustrate scientific concepts, their mathematical representation, and the computational techniques used to solve problems. A number of institutions have begun undergraduate computational science minor and certificate programs. One major challenge in such programs is to introduce students from a wide variety of backgrounds to the principles of modeling, the underlying mathematics, and the programming and analytical skills necessary to provide the foundation for more advanced modeling applications in each student's major area. This session will review the organization and course materials from such a course. Participants will use a variety of models that are used to illustrate modeling, mathematical, and scientific principles critical to beginning work in computational science.
SUMMARY:Introducing Computational Science in the Curriculum
PRIORITY:3
END:VEVENT
END:VCALENDAR |
Basic Mathematics - 8th edition
Summary: For the modern student like you--Pat McKeague's BASIC MATHEMATICS, 8E--offers concise writing, continuous review, and contemporary applications to show you how mathematics connects to your modern world. The new edition continues to reflect the author's passion for teaching mathematics by offering guided practice, review, and reinforcement to help you build skills through hundreds of new examples and applications. Use the examples, practice exercises, tutorials, videos, and e-Book sec...show moretions in Enhanced WebAssign to practice your skills and demonstrate your knowledge. ...show less
1133103626 Good condition EXAM COPY / INSTRUCTOR EDITION of Book! May have highlighting and or stickers on front and back cover! All day low prices, buy from us sell to us we do it all!!
$5373.2398.25 |
Place Value and Names for Numbers. Addition with Whole Numbers, and Perimeter. Rounding numbers, Estimating Answers, and Displaying Information. Subtraction with Whole Numbers. Multiplication with Whole Numbers, and Area. Division with Whole Numbers. Exponents and Order of Operations. Summary. Review. Test. Projects.
2. FRACTIONS AND MIXED NUMBERS.
Meaning and Properties of Fractions. Prime Numbers, Factors, and Reducing to Lowest Terms. Multiplication with Fractions, and the Area of a Triangle. Division with Fractions. Addition and Subtraction with Fractions. Mixed-Number Notation. Multiplication and Division with Mixed Numbers. Addition and Subtraction with Mixed Numbers. Combinations of Operations and Complex Fractions. Summary. Review. Cumulative Review. Test. Projects.
softcover teacher edition with all Students content and solutions text only no supplement ship immediately - Expedited shipping not available oversized
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a2zbooks Burgin, KY
Has some markings. Has minor shelf and corner wear. Has minor corner curl and creasing to covers. Has water stain at back of book, does not affect text. Binding is in good condition. Has stickers on s...show morepine and back cover. Quantity Available: 1. Category: Mathematics; Math/Algebra/Trig; ISBN: 0495013919. ISBN/EAN: 9780495013914. Inventory No: 1560788120. 2nd Edition. ...show less
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A2ZBooks Ky Burgin, KY
Pacific Grove, CA 2006 Softcover 2nd Edition Good Condition Has some markings. Has minor shelf and corner wear. Has minor corner curl and creasing to covers. Has water stain at back of book, does no...show moret affect text. Binding is in good condition. Has stickers on spine and back cover. Quantity Available: 1. Category: Mathematics; Math/Algebra/Trig; ISBN: 0495013919. ISBN/EAN: 9780495013914. Inventory No: 1560788120 |
A set for students
that are ready for advanced algebra skills. This series is geared
for high school level students. Topics include: Solve for the Unknown
(Using logs), Solving Inequalities by Adding and Subtracting, Solving
Inequalities by Multiplying and Dividing, Solving Fractional Equations,
Absolute Value Equations, Slope of a Line, Slope and Equation of
Lines, Algebraic solution to linear system, Algebraic Solutions
to Simultaneous Equations, Algebraic Translations |
Trigonometry new 2nd edition of Cynthia Young's Trigonometry continues to bridge the gap between in-class work and homework by helping students overcome common learning barriers and build confidence in their ability to do mathematics. The text features truly unique, strong pedagogy and is written in a clear, single voice that speaks directly to students and mirrors how instructors communicate in lectures.
The new second edition of Cynthia Young's Algebra & Trigonometry continues to bridge the gap between in-class work and homework by helping students overcome common learning barriers and build confidence in their ability to do mathematics.
Now in its 10th edition, Analytic Trigonometry is a book that students can actually read, understand, and enjoy. To gain student interest quickly, the text moves directly into trigonometric concepts and applications and reviews essential material from prerequisite courses only as needed. |
Subscribe now and discover a teaching revolution!
The Alpha Mathematics Teaching Resource CD contains:
A reformatted version of the textbook designed for use with interactive whiteboards or data projectors.
A Teacher Guide version of the textbook.
'User...
Subscribe now and discover a teaching revolution
The Beta Mathematics Interactive Teaching Resource contains:
The contains:
A reformatted version of the textbook designed for use with interactive whiteboards or data projectors.
A Teacher Guide version of th...
Subscribe now and discover a teaching resolution!
The Gamma Mathematics Teaching Resource CD contains:
A reformatted version of both textbooks designed for use with interactive whiteboards or data projectors.
A Teacher Guide version of the textbooks.
...
THE ONLY MATHS RESOURCE INCORPORATING ALL STRANDS OF THE NEW NZ CURRICULUM
Pearson Mathematics Level 3
Pearson Mathematics Level 3 is divided into two books, 3a and 3b. Students working on 3a are expected to be using basic addition and subtraction facts and place value to solve whole number ad...
THE ONLY MATHS RESOURCE INCORPORATING ALL STRANDS OF THE NEW NZ CURRICULUM
Pearson Mathematics Level 3b
Pearson Mathematics Level 3 is divided into two books, 3a and 3b. Students working on 3b are expected to be proficient in using basic addition and subtraction facts and place value to solve whole ... |
The LIFEPAC Math (Geometry) complete set contains all 10 student workbooks for a full year of study plus the comprehensive Teacher's Guide.
Topics covered include:
A Mathematical System
Proofs
Angles and Parallels
Congruency
Similar Polygoms
Circles
Construction and Locus
Area and Volume
Coordinate Geometry
Review1 out of 1100%customers would recommend this product to a friend.
Customer Reviews for Lifepac Math, Grade 10 (Geometry), Complete Set
Review 1 for Lifepac Math, Grade 10 (Geometry), Complete Set
Overall Rating:
5out of5
Good Product
Date:March 5, 2013
mrsdebby
Location:Indiana
Age:45-54
Gender:female
Quality:
5out of5
Value:
4out of5
Meets Expectations:
5out of5
This math is easy to follow and use, for the most part. Some of it is difficult to follow, not explained as well as it could be, but usually can figure out. Lifepac is a good homeschooling curriculumn, and yes, I would recommend it.
Share this review:
0points
0of0voted this as helpful.
Review 2 for Lifepac Math, Grade 10 (Geometry), Complete Set
Overall Rating:
5out of5
Date:September 6, 2010
Melody M.
I love this curriculum. I think it's outstanding and the best explained math I have ever used.
Share this review:
0points
1of2voted this as helpful.
Review 3 for Lifepac Math, Grade 10 (Geometry), Complete Set
Overall Rating:
2out of5
Date:August 25, 2009
Melanie Walsh
Initially I was excited about this product. Each book represented a "do-able" goal and I thought this would be just what we were looking for. Now that my son has really gotten into this course we are sadly disappointed. There is definitely not enough instruction in these lessons. It leaves the student with many questions and no explanations.
Share this review:
+2points
2of2voted this as helpful.
Review 4 for Lifepac Math, Grade 10 (Geometry), Complete Set
Overall Rating:
5out of5
Date:July 6, 2008
Terri Hastings
This is the most well prepared and manageable math program that we have found! The units are well explained and grading is made so easy.
Share this review:
+1point
1of1voted this as helpful.
Review 5 for Lifepac Math, Grade 10 (Geometry), Complete Set
Overall Rating:
5out of5
Date:June 26, 2008
Linda
This was a great course for my child! He completed the vast majority of it independently. It was also great preparation for the SAT.
Share this review:
+1point
1of1voted this as helpful.
Review 6 for Lifepac Math, Grade 10 (Geometry), Complete Set
Overall Rating:
5out of5
Date:April 4, 2008
Jennifer Schueler
I am very pleased with the 10th grade Geometry set. It is making is easier for my daughter to learn how to do the math! I rate this as outstanding!! |
Precalculus - 7th edition
Summary: Get a good grade in your precalculus course with PRECALCULUS, Seventh Edition. Written in a clear, student-friendly style, the book also provides a graphical perspective so you can develop a visual understanding of college algebra and trigonometry. With great examples, exercises, applications, and real-life data--and a range of online study resources--this book provides you with the tools you need to be successful in your course |
233- Knowing the Vocabulary: A Key to Understanding in College Algebra
Thursday, April 14, 2011: 2:00 PM-3:00 PM
143 (Convention Center)
Lead Speaker:
Susan Gay
Co-Speaker:
Ingrid Peterson
We will present students' work that provides insight into college algebra students' understandings about important concepts such as function, equation and domain. Our data on instructors' and students' opinions about the role of vocabulary will be shared. Then, we'll lead a discussion about implications for high school and college classrooms. |
Calculus Teacher Resources
Title
Resource Type
Views
Grade
Rating
Students use the Fundamental Theorem of Calculus to solve problems. In this calculus lesson, students use the TI to solve the graphing porting of the problem. They practice graphing functions and discuss their place in the real world.
Students solve problems using implicit differentiation. In this calculus lesson, students take the derivative to calculate the rate of change. They observe two robots and draw conclusion from the data collected on the two robots.
Math pupils calculate the average rate of change over a specific interval. They represent the average rate of change on a graph and examine the behavior of the graph for decreasing and increasing numerals.
Students explore the concept of minimization. In this minimization worksheet, students determine the least expensive box given specific requirements. Students solve a question from the AP Calculus exam in 1982; the same question from the movie Stand and Deliver. |
Hi, can anyone please help me with my math homework? I am not quite good at math and would be grateful if you could explain how to solve permutations and combinations exercises problems. I also would like to know if there is a good website which can help me prepare well for my upcoming math exam. Thank you!
I possibly could help if you can be more specific and give more details about permutations and combinations exercises. A good program would be ideal rather than a costly algebra tutor. After trying a number of program I found the Algebra Buster to be the best I have so far found. It solves any algebra problem that you may want solved. It also shows all the steps (of the solution). You can just copy it as your homework . However, you should use it to learn math, and simply not use it to copy answers.
I am a regular user of Algebra Buster. It not only helps me complete my homework faster, the detailed explanations offered makes understanding the concepts easier. I advise using it to help improve problem solving skills. |
Mathematical requirements
The Leaving Certificate Technology syllabus does not require a sophisticated knowledge of mathematics--a basic understanding of algebra, arithmetic, geometry and trigonometry will suffice. Students will be expected to understand, use and present numbers expressed in standard form. They will be expected to recognise standard prefixes used with the symbols for physical quantities (see below and opposite).
Students may use an electronic calculator that conforms to examination regulations.
Symbols and Units
Throughout the course, students will be expected to recognise and use the correct symbols and units for physical quantities. The table below shows the most common quantities likely to arise in Technology.
PhysicalQuantity
Symbol
Unit Name
Unit Symbol
Expressed in termsof other units
length
l
metre
m
area
A
square metre
m2
mass
m
kilogram
kg
time
t
second
s
speed
v
metre per second
M s1 or m/s
force
F
newton
N
moment of a force
M
newton metre
N m
torque
T
newton metre
N m
work
W
joule
J
N m
energy
E
joule
J
N m
power
P
watt
W
J s1
temperature
T t
kelvin degree Celsius
K °C
electric charge
Q, q
coulomb
C
electric current
I
ampere
A
potential difference
V
volt
V
capacitance
C
farad
F
C V1
resistance
R
ohm
frequency
f
hertz
Hz
s1
angle
degree
°
The following SI prefixes may also arise in Technology.
Prefix
Symbol
Factor
giga
G
109
mega
M
106
kilo
k
103
centi
c
102
milli
m
103
micro
µ
106
nano
n
109
pico
p
1012
Relationships and Formulas
Students should know and be able to use appropriate relationships and formulas. The derivation of these formulas is not required. Some typical relationships and formulas used in Leaving Certificate Technology are presented below. Others may be found in the Mathematical Tables, copies of which will be available during the examination. |
Trigonometry
Often, trigonometry students leave class believing that they understand a concept but are unable to apply that understanding when they get home and attempt their homework problems. This mainstream yet innovative text is written by an experienced professor who has identified this gap as one of the biggest challenges that trigonometry professors face.
She uses a clear voice that speaks directly to students- similar to how instructors communicate to them in class. Students learning from this text will overcome common barriers to learning trigonometry and will build confidence in their ability to do mathematics.
show more show less
Edition:
N/A
Publisher:
Wiley & Sons, Incorporated, John |
Search Results from Wikipedia for Linea
In mathematics, a linear map (also called a linear mapping, linear transformation, linear operator or, in some contexts, linear function) is a function between two modules (including vector spaces) that preserves (in the sense defined below) the operations of module (or vector) addition and scalar multiplication.
The Lincoln Near-Earth Asteroid Research (LINEAR) project is a collaboration of the United States Air Force, NASA, and the Massachusetts Institute of Technology's Lincoln Laboratory for the systematic discovery and tracking of near-Earth asteroids |
EngCalc is a new calculating software with extended capabilities. It is recommended for use by math, physics and engineering student and teacher. The main advantage of the software is a simple input format even for the most complicated formulas.
SimplexCalc is a multivariable desktop calculator for Windows. It is small and simple to use but with much power and versatility underneath. It can be used as an enhanced elementary, scientific, financial or expression calculator.
Middle-School (grades 5 through 9) math program written to provide skills in context. Students are shown a Cartesian plane across which a small dot moves. Students try to "capture" the dot by typing in its current or anticipDownload free trial version of Do The Math, a Windows desktop program for bi-directional conversion between US measurements and the metric system, International System of Units (SI). Conversion types include length, area, mass volume and temperature |
Math for Meds: Dosages and Solutions, 10th Edition
ISBN10: 1-4283-1095-9
ISBN13: 978-1-4283-1095-7
AUTHORS: Curren
Increase walks you through basic and advanced calculations in detail, including intravenous and pediatric calculations |
No-Nonsense Algebra {Review}
Have you ever said, "I'll NEVER try anything different"? I have. We LOVE our current math curriculum. When the Crew posted requests for Math Essentials No-Nonsense Algebra I figured we'd use the program for review time and return to our regularly scheduled plan. I was wrong.
When I first received the book I thought, "This is it? Really?" Yet, as we delved into learning, I realized the genius of this program.
How it Works
No-Nonsense Algebra consists of 2 components: The student book and the free online video lectures. Each lesson contains five key parts:
Introduction and explanation of topic; easy-to understand. There is not sample problem after sample problem. It's one simple introduction, easy for the student to understand.
Helpful Hints offer bullet point tips that give a further insight into the lesson. They can include tips, formulas or explanations.
Example of Helpful Hints From Lesson 1-7 Exponents
Any number to the power of zero is equal to one. For example n0 = 1 and 50 = 1.
Examples with step-by-step solutions. Simple, easy-to-understand. Even the more advanced lessons. There is NO FLUFF. Just pure math!
Written Exercises: The number of exercises that coordinate with the lesson range from 12 to 20 depending upon the complexity of the lesson. Some concepts will require more practice to master.
Review: Every lesson ends with a set of review problems to ensure that the student is consistently practicing previously learned concepts. There is on average 4 review problems to solve.
Wait…there's more!
The book includes FREE access to online video lessons that correspond with each lesson! The author Richard W Fisher guides you through step-by-step. He is not a "dry" lecturer. The video has audio with a whiteboard. The longest we've found is 11 minutes. It kept a 14-year old boy entertained…need I say more?
Non-Nonsense Algebra is really…No-Nonsense!
A simple book and the videos. No fluffy word problems. Just pure 100% algebra. Math. Simple. Basic. Easy.
How We Used this Program
The book is divided into chapters and lessons with a review at the end of each chapter. There are a total of 10 chapters.
I assigned a lesson per day to The Boy. He began by watching the video upstairs on his computer. After watching the lecture he would read through introduction, tips and examples. Often he would complete the problems & review on his own. As the answers are in the back of the book, I require him to "score" his own work. Any problems missed we go over together.
Occasionally I would find a lesson that I knew The Boy needed further instruction. I would note at the top in red pen *Complete lesson with mom. Watch additional video online. Complete additional worksheet.* If he missed more than 5 problems on a lesson, we would have a review the next day. (Unless of course he just forgets to multiply instead of adding!)
We are consuming the book as a workbook. It may not be reproduced in any manner.
Final Thoughts
My son and I had this conversation.
Me: So, how do you like the Math program.
Boy: I like it. Can I use this for math?
Me: Really? You don't want to continue with XYZ?
Boy: No. I want to use this. You can sell the other program.
Me: Why? Can you tell me what you like?
Boy: It's easy. There are not a lot of problems. I understand the videos…they are better. It's just math. That's all I want.
Me: OK. So would you write a review paragraph for me?
Boy: (arching his eyebrow) Uh, no way mom.
Me: Well, I tried.
We are selling our XYZ program and continuing with this program. I cannot think of any better recommendation than a 14-year old asking to use the program. Way to go Mr. Fisher! Thank you for making my journey into high school homeschooling easier!
Pros
Cons
Affordable
Self-contained program (only one book!)
Flexible
No Fluff!
If a student needs rote-learning, supplementation may be needed
Your child may actually love Algebra.
Additional Review Item
We also received an additional book to review from Math Essentials. We chose Fractions.
This book covers all four operations for fractions. Specific and easy-to-follow instructions ensure that students master the "dreaded" fraction. With consistent, built-in review included in each lesson, students will conquer this topic that gives many students so much difficulty. Each book also contains plenty of practical, real-life problem solving.
Daily drills can be finished in 20 minutes or less! Same simple format as the Algebra book! |
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Summary
Strong Algebra and Trig skills are crucial to success in calculus. This text is designed to bolster these skills while students study calculus. As students make their way through the calculus course, this supplemental text shows them the relevant algebra or trigonometry topics and points out potential problem spots. The table of contents is organized so that the algebra and trigonometry topics are arranged in the order in which they are needed for calculus. |
This program will motivate your students by making many of the fundamentals of algebra easier to understand. Hands-on visual investigations link manipulatives to formal algebra and encourage students to analyze problems and formulate solutions. Students will also learn proper mathematical terms and develop a meaningful understanding of: |
Superb set of resources. There is basically a very comprehensive revision book here. I will be pointing my Year 10s Set 3 to the relevant sections of this booklet as revision practice over half term. I'll also give them the answer booklet - obviously pointing out to them that they need to scroll down to find the relevant section! The proof will be what they do with it!
I use these resources all the time when home-schooling my grandson. I have been using them since he was 11: he will sit his GCSE in 2014. He needs tutorial input but the exercises are very compehensive and the answers are invaluable. |
Math Planet
1998 Math Planet is web site dedicated to the advancement of mathematics. That's good, because today's demanding world requires young people to be equipped with a solid math foundation. Targeted towards high school students, there are many different categories, including Basic Algebra and Geometry, advanced Algebra and Trigonometry, SAT and ACT math preparation courses, and even a chat room for team problem solving. |
Math Skills for Allied Health Careers, CourseSmart eTextbook
Description
Appropriate for Two-year associate in arts health care curriculum
Basic Mathematical Skills for Allied Health Careersprovides allied health students with a solid mathematical foundation because it presents clear explanations of the mathematical concepts required of health care workers. It contains over 1500 problems ranging in level and difficulty, and applies material directly to a variety of allied health careers. Detailed examples are worked through step-by-step and concepts are presented in a non-threatening, yet sophisticated, manner. Unique to this book, it covers a broader range of allied health topics, discusses calculators and manual calculation techniques, and presents multiple methods for determining dosages.
Table of Contents
1. Basic Arithmetic Computations in Health Applications
2. A Review of Algebra
3. Systems of Measurement
4. Medication Labels, Prescriptions, and Syringe Calculations
5. Modeling Health Applications
6. Calculations for Basic IV Therapy
7. The Basics of Statistics
8. Logarithms, Ionic Solutions, and pH |
More About
This Textbook
Overview
Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, series, the derivative, higher derivatives, the integral and more. Each chapter contains a problem set (hints and answers at the end), while a wealth of examples and applications are found throughout the text. Over 340 theorems fully proved. 1973 2005
getting started in math analysis
This book by Shilov covers the fundamentals in beginning analysis(both real and complex). It has in common with Walter Rudin's book (entitled 'Real and Complex Analysis') that it covers both real functions (integration theory and more), as well as Cauchy's theorems for analytic functions. Shilov's book is at an undergraduate level, and it can easily be used for self-study. The Dover edition is affordable. Rudin's book is for the beginning graduate level, and it is widely used in math departments around the world. Both books have stood the test of time. Comparison of Shilov with Rudin: Rudin's 'Real and Complex' has become an institution, and I have to admit I have loved it since I was a student myself, but conventional wisdom will have it that Shilov is a lot gentler on students, and much easier to get started with: It stresses motivation a bit more, the exercises are easier (some of Rudin's exercises are notorious, but I find the challenge charming--not all of my students do though!), and finally Shilov gets to touch upon a few applications; fashionable these days. But that part easily gets dated. I will expect that beginning students will enjoy Shilov's book. Personally, I find that with perseverance, students who keep at it with Rudin's book, will end up with a lot stronger foundation. They are more likely to have proofs in their blood. I guess Shilov can always serve as a leisurely supplementary reading to Rudin. There will never be another book like Rudin's 'Real and Complex', just like there will never be another van Gogh. But the fact that we love van Gogh doesn't prevent us from enjoying other paintings.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
COURSE DESCRIPTIONS
This course is designed to serve as preparation for the study of college algebra, statistics, trigonometry and other college mathematics courses. Topics include a review of the real number system, an introduction to imaginary and complex numbers, the solution of first degree, quadratic and systems of equations, polynomials, rational expressions, exponents and radicals, graphs of functions (both linear and nonlinear) and of relations, and exponential and logarithmic functions.
MATH 104 - TRIGONOMETRY (4 Units):
Topics for this preparatory course for calculus include trigonometric functions and equations, solutions of both right and oblique triangles, trigonometric forms of complex numbers and De Moivre's Theorem. Course content also includes verification of trigonometric identities, inverse trigonometric functions, half and multiple angles, vectors and theit applications, parametric equations, polar coordinates and polar equations.
MATH 105 - COLLEGE ALGEBRA (4 Units):
This course offers a review of real numbers, real number exponents, and factoring polynomials. The course also covers equations and inequalities, solutions to systems of equations and inequalities, solutions to equations and inequalities involving absolute value, graphing relations and functions, matrices, determinants, matrix algebra. Complex numbers, the zeros of exponential, rational and radical functions, the conic sections, sequences, mathematical induction and the binomial theorem are also covered.
MATH 120 - INTRODUCTION TO STATISTICS (4 Units):
This course covers basic statistical techniques, including design and analysis for both parametric and non-parametric data. Descriptive statistics included are measures of central tendency and measures of dispersion. Graphical techniques of illustrating the data are covered. Probability and its application to inferential statistical procedures is covered. Inferential statistics included are estimation and hypothesis testing, chi-square, analysis of variance and regression. Applications are drawn from a variety of fields.
MATH 226 - CALCULUS I (5 Units):
This course offers an introduction to the calculus of single variables. Topics covered include limits, using limits of functions to determine continuity, finding derivatives and integrals of functions, basic properties of derivatives and integrals, the relationship between derivatives and integrals as given by the Fundamental Theorem of Calculus, and applications.
This course covers vectored and the geometry of space, vector-valued functions, the calculus of functions of several variables, multiple integrals, Green's theorem, divergence theorem, Stoke's theorem and applications.
This course covers sets and their application to permutations and combinations, the binomial theorem, correspondence, countability, finite probability measures, and the expectation. Also topics in geometry (Euclidean and non-Euclidean, tessellations and fractals) or beginning calculus (derivative and antiderivative of simple polynomial functions) are covered.
MATH 50 - ELEMENTARY ALGEBRA (4 Units):
This course covers signed number arithmetic, square roots, order of operations, algebraic expressions, solving equations, factoring, graphs of linear equations and solving systems of equations. |
The
goal of this course is to
prepare the students to apply quantitative reasoning in work-setting
decisions.† The 501 course takes a
hands-on approach by using real-life examples to illustrate the use of
quantitative tools from algebra, probability and descriptive statistics in
solving concrete problems. This course helps the students to master the
quantitative tools used routinely in the quantitative methods courses: UST601,
UST602, UST803 and in research.† This
course includes computer sessions where the students will be trained to use the
state of the art software MathCAD to solve problems and visualize data.
TENTATIVE
SCHEDULE
®TU, 7/3,
class organization: syllabus, assessment quiz, algebra
®TH, 7/5,
algebra, Hw.1 due, Computer
Lab#1
®TU, 7/10,algebra, Hw.2 due, Computer Lab#2
®TH, 7/12,algebra, Hw.3 due, Computer Lab#3
®TU, 7/17,algebra, Computer Lab #4
®TH, 7/19,algebra, Hw.4 due, Computer Lab #5
®TU, 7/24,Exam I
®TH, 7/26,probability, Computer Lab #6
last day to drop
®TU, 7/31,probability, Hw.5 due, Computer Lab #7
®TH, 8/2, descriptive statistics, Hw.6
due, Computer Lab #8
®TU, 8/7,
descriptive statistics, Hw.7 due,
Computer worksheets: disk and printouts due
®TH, 8/9, Exam
II
The course includes eight
computer sessions.† The grading of the
computer work is based on the number of projects successfully completed and on
the attendance record. You should save each MathCAD worksheet.† A printout of each worksheet will be
collected on Tuesday 8/7/2001.
Each
student needs a calculator.† No textbook
is required.† There are several books in
the library that you may find helpful in learning the material.† They are located in the Rhodes Tower, on the
4íth floor under QA154.† I will
distribute periodically handouts.
Late
homework will not be accepted but in cases of proven reason.† Exam attendance is obligatory.† Makeup exam will be given only in cases of
proven emergency.† Attendance of classes
is needed for the proper understanding of the material.† Class attendance requirements are listed in
the CSU Bulletin. |
Selected metadata
Identifier:
newtonspmathema00newtrich
Mediatype:
texts
Copyright-evidence-operator:
scanner-gwendolynn-amsbury
Copyright-region:
US
Copyright-evidence:
Evidence reported by scanner-gwendolynn-amsbury for item newtonspmathema00newtrich on Mar 21, 2006; no visible notice of copyright and date found; stated date is 1846; the country of the source library is the United States; not published by the US government. |
If your students search the web for "math homework help", you may be surprised by what they will find. They will find cheat-sites that perform homework assignments for a fee! However, there are lots of free, constructively helpful sites. You should be aware of these sites and be clear with your students about what use of these sites is OK with you. This article summarizes what students will find, and describes one site, in particular.
There are free bulletin-board sites where a student can post or email homework questions and a web-teacher will respond, perhaps within an hour or so. MathGoodies.com is one such site. Of course, in order to be most helpful, the web-teacher needs to know the "context" of the question, such as "what are you learning in class right now." For example, there are lots of methods that can be applied to "factor ".
There are automatic problem solvers on the web, such as quickmath.com and calc101.com. Here, a student can enter an expression or formula and get an answer to polynomial factoring, multiplication, long division, integration, and differentiation. These sites can be helpful to students who want to confirm that they have solved a problem correctly.
Some sites maintain a database of frequently asked questions with associated, tutorial solutions (e.g., Students can search for a problem similar to one they have for homework, in hopes that the tutorial will be relevant to their problem. Similarly, some publishers have sites with practice problems that can be used to prepare for tests.
Also, there is an excellent site with a hyper-linked math textbook (Sosmath.com). Students who couldn't follow the textbook explanation or the teacher lecture can turn here for yet another description of a troublesome concept that may be needed to complete homework.
One site, has tutorial solutions to the odd-numbered homework problems in most of the popular math textbooks used in California. A student clicks on textbook and page number, and selects the troublesome problem number from a list on the screen. The site instantly begins a tutorial, interactive explanation for how to do the actual problem. The student is presented with a self-paced sequence of explained hints and explained steps, right up to the final answer! For many problems, the student is prompted with a question at some point during the solution. The Hotmath tutorial solutions seek to mimic what a tutor or teacher would say if a student asked for help on the problem. Each solution is prepared in the context (methods and vocabulary) of the textbook, chapter and section. Here are a few hints and steps from a sample introductory word problem in algebra 1. Try to imagine each hint and step being shown on an attractively designed screen in an engaging way:
PROBLEM: Find three consecutive odd integers that add up to 105
HINT-1: Consecutive means one after another. For example, 13 and 15 are consecutive odd numbers.
STEP-1: Choose a variable to represent the smallest of the three odd numbers, call it N.
HINT-2: How can the other two odd numbers be represented?
STEP-2: The other two odd numbers can be represented as N+2 and N+4.
And so on. It would be best to visit the site to see for yourself.
Hotmath is intended to be a resource for under-performing students who may not have math help at home or may not have the confidence or motivation to complete homework assignments. The "magic" of our site is that students may come here instead of giving up, while they might not otherwise seek help in the fear that it will be too time-consuming or too embarrassing. What we find is that students start to build confidence as a result of using the site, and can frequently convert from failing students to very successful students. Hotmath is based on over a decade of research that indicates that viewing worked solutions is superior to struggling, especially for under-performing students. The PressRoom page of the Hotmath website has a summary of this research.
Hotmath has been in use now for over two years and has over 100,000 teacher-edited solutions for over 30 popular math textbooks from pre-algebra through calculus. Last year the site was for-pay at $9 per month. This year the site is free, as we decided to try to help as many students as possible (and seek sponsorships to cover costs).
The availability of some of these sites, especially Hotmath, raises some questions. Is it "fair" if homework is graded and one student uses Hotmath and another doesn't? Will students mindlessly rely on Hotmath rather than thinking for themselves? Is it "cheating" if a student relies on a Hotmath solution to complete an assignment? Hotmath only answers odd-numbered problems for most textbooks, so teachers can assign a mix of problems for practice versus assessment and challenges. Virtually every teacher we have spoken with favors Hotmath usage after some classroom experience, and feels that the benefits of Hotmath availability far outweigh the risks.
Another fairness issue is that many students still do not have the Internet at home. These students must be informed about all their options for free Internet use in your community.
Our recommendations for teacher usage of Hotmath are as follows: 1) Use Hotmath in class to reduce prep time for classroom examples. 2) Assign a mix of 2/3 odds and 1/3 evens for homework. 3) Require that each student visits the site so they can see that help is available 24/7 4) Give extra credit for any student who finds an error in a Hotmath solution!
One gratifying aspect of our site is the success we seem to be having with ESL students who may have trouble understanding their teacher or the textbook explanations. We keep our explanations succinct in order to keep students engaged, and this seems to help.
Testimonials submitted to Hotmath are voluminous and unanimous in their message: Hotmath helps students who were previously failing, to earn honor grades. We hear this time and again, and hope you will visit and form your own opinion.
Oh, by the way, I'm involved with Hotmath as you may have guessed by now. |
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