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The Matrix Algebra Tutor: Learning by Example DVD Series teaches students about matrices and explains why they're useful in mathematics. This episode teaches students how to solve systems of equations using matrix inverses. Grades 9-College. 32 minutes on DVD.
Customer Reviews for Solving Systems Using Matrix Inverses DVD
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Calculus demystified by Steven G Krantz(
Book
) 24
editions published
between
2002
and
2011
in
English and Spanish
and held by
2,297
libraries
worldwide
Explains how to understand calculus in a more intuitive fashion. Uses practical examples and real data. Covers both differential and integral calculus.
Differential equations demystified by Steven G Krantz(
Book
) 9
editions published
between
2004
and
2005
in
English
and held by
1,121
libraries
worldwide
Here's the perfect self-teaching guide to help anyone master differential equations--a common stumbling block for students looking to progress to advanced topics in both science and math. Covers First Order Equations, Second Order Equations and Higher, Properties, Solutions, Series Solutions, Fourier Series and Orthogonal Systems, Partial Differential Equations and Boundary Value Problems, Numerical Techniques, and more.
Techniques of problem solving by Steven G Krantz(
Book
) 10
editions published
between
1996
and
1999
in
English
and held by
1,018
libraries
worldwide
The purpose of this book is to teach the basic principles of problem solving, including both mathematical and nonmathematical problems. This book will help students to translate verbal discussions into analytical data; learn problem-solving methods for attacking collections of analytical questions or data; build a personal arsenal of solutions and internalized problem-solving techniques; and become "armed problem solvers", ready to battle with a variety of puzzles in different areas of life. Taking a direct and practical approach to the subject matter, Krantz's book stands apart from others like it in that it incorporates exercises throughout the text. After many solved problems are given, a "Challenge Problem" is presented. Additional problems are included for readers to tackle at the end of each chapter. There are more than 350 problems in all. A Solutions Manual to most end-of-chapter exercises is available.
Mathematical apocrypha : stories and anecdotes of mathematicians and the mathematical by Steven G Krantz(
Book
) 4
editions published
in
2002
in
English
and held by
665
libraries
worldwide
With the story of David Hilbert perplexedly asking a colleague, "What is a Hilbert space?' being a typical example, this work presents anecdotes about the practice of mathematics that range in tone from humorous to celebratory. The anecdotes are arranged under sections devoted to great foolishness, great affrontery, great ideas, great failures, great pranks, and great people.
Discrete mathematics demystified by Steven G Krantz(
Book
) 9
editions published
between
2008
and
2009
in
English
and held by
636
libraries
worldwide
"If you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts. Written by award-winning math professor Steven Krantz, Discrete Mathematics Demystified explains this challenging topic in an effective and enlightening way. You will learn about logic, proofs, functions, matrices, sequences, series, and much more. Concise explanations, real-world examples, and worked equations make it easy to understand the material, and end-of-chapter exercises and a final exam help reinforce learning."--P. [4] of cover.
Geometric function theory explorations in complex analysis by Steven G Krantz(
Book
) 15
editions published
between
2005
and
2007
in
English
and held by
421
libraries
worldwide
"This methodologically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis - and also to spark the interest of seasoned workers in the field - the book imparts a solid education both in complex analysis and in how modern mathematics works."--Jacket.
The elements of advanced mathematics by Steven G Krantz(
Book
) 7
editions published
between
1995
and
2002
in
English
and held by
408
libraries
worldwide
"The gap between the rote, calculational learning mode of calculus and ordinary differential equations and the more theoretical learning mode of analysis and abstract algebra grows ever wider and more distinct, and students' need for a well-guided transition grows with it. For more than six years, the bestselling first edition of this classic text has helped them cross the mathematical bridge to more advanced studies in topics such as topology, abstract algebra, and real analysis. Carefully revised, brought thoroughly up to date, and expanded in essential areas, The Elements of Advanced Mathematics, Second Edition now does the job even better. It builds the background, tools, and skills students need to meet the challenges of mathematical rigor, axiomatics, and proofs."--Jacket.
How to teach mathematics by Steven G Krantz(
Book
) 11
editions published
between
1991
and
2000
in
English
and held by
405
libraries
worldwide
"This."--BOOK JACKET. |
Foundations
Fall, 2013
Course Description: This course introduces students to mathematical reasoning and rigor in the
context of set-theoretic questions. The course will cover basic logic and set theory, relations --- including
orderings, functions, and equivalence relations --- and the fundamental aspects of cardinality. Emphasis
will be placed on helping students in reading, writing, and understanding mathematical reasoning. Students
will be actively engaged in creative work in mathematics. Prerequisite: credit for Math 213 or permission
of instructor. |
Describes the guess-and-check method and discusses the advantages of using computers to apply the methods to solve mathematics problems. Provides two examples that use BASIC programs to illustrate the method. (MDH) |
Synopses & Reviews
Publisher Comments:
This is an annotated and indexed translation (from French into English) of Augustin Louis Cauchy's 1821 classic textbook Cours d'analyse. This is the first English translation of a landmark work in mathematics, one of the most influential texts in the history of mathematics. It belongs in every mathematics library, along with Newton's Principia and Euclid's Elements. The authors' style mimics the look and feel of the second French edition. It is an essentially modern textbook style, about 75% narrative and 25% theorems, proofs, corollaries. Despite the extensive narrative, it has an essentially "Euclidean architecture" in its careful ordering of definitions and theorems. It was the first book in analysis to do this. Cauchy's book is essentially a precalculus book, with a rigorous exposition of the topics necessary to learn calculus. Hence, any good quality calculus student can understand the content of the volume. The basic audience is anyone interested in the history of mathematics, especially 19th century analysis. In addition to being an important book, the Cours d'analyse is well-written, packed with unexpected gems, and, in general, a thrill to read. Robert E. Bradley is Professor of Mathematics at Adelphi University. C. Edward Sandifer is Professor of Mathematics at Western Connecticut State University.
Synopsis:
Synopsis:
Table of Contents
Translators' Introduction.- Cauchy's Introduction.- Preliminaries.- First Part: Algebraic Analysis.- On Real Functions.- On Quantities that are Infinitely Small or Infinitely Large, and on the Continuity of Functions.- On Symmetric Functions and Alternating Functions.- Determination of Integer Functions.- Determination of continuous functions of a single variable that satisfy certain conditions.- On convergent and divergent (real) series.- On imaginary expressions and their moduli.- On imaginary functions and variables.- On convergent and divergent imaginary series.- On real or imaginary roots of algebraic equations for which the first member is a rational and integer of one variable.- Decomposition of rational fractions.- On recursive series.- Notes on Algebraic Analysis.- Bibliography.- Index.
"Synopsis"
by Springer,"Synopsis"
by Springer, |
....
Show More. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. Explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics. Systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA. Covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space. Presents effective approaches to making GA an integral part of your programming. Includes numerous drills and programming exercises helpful for both students and practitioners. Companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book, and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter |
Reviews Description: Updated for the revised GRE, the Algebra Guide covers algebra in all its various forms (and disguises) on the GRE so that you can master fundamental techniques and nuanced strategies to solve for unknown variables of every type.
Each chapter builds comprehensive content understanding by providing rules, strategies and in-depth examples of how the revised GRE tests a given topic and how you can respond accurately and quickly. The Guide contains both "Check Your Skills" questions in the chapters that test your understanding as you go and "In-Action" problems of increasing difficulty, all with detailed answer explanations.
Purchase of this book includes one year of access to 6 of Manhattan GRE's online practice exams. |
Find a Saddle Brook Precalculus...Prealgebra
Discussion of the subject will start from the real number system. Addition, subtraction, multiplication and division will follow, using signed numbers including integers. Fractions, decimals, exponents, graphs,and first order variable expression/equation will be considered. |
Elementary Mathematics for Teachers is a textbook for a semester or two-quarter university course for pre-service teachers. It is also appropriate for courses for practicing teachers.
This book focuses exclusively on K-8 mathematics. It develops elementary mathematics at the level of "teacher knowledge". To that end, the text uses five Primary Mathematics Textbooks as a source of problems and to repeatedly illustrate several themes, including:
(a) How the nature of a mathematics topic suggests an order for developing it in the classroom.
(b) How topics are developed through "teaching sequences" which begin with easy problems and incrementally progress until the topic is mastered.
(c) How the mathematics builds on itself through the grades.
This approach is explained more fully in the following except, taken from the beginning of the textbook and addressed to the student.
Elementary Mathematics for Teachersis organized around numbers and arithmetic. The topics are covered roughly in the order they are developed in elementary school. The first three chapters cover most of the arithmetic of Grades K-3. Chapters 4 and 5 jump ahead to topics (prealgebra and prime numbers) usually covered in Grades 6 and 7; that jump allows us to review ideas about algebra and proofs which are needed for a "teacher's understanding" of the subsequent material. Chapters 6 and 7 return to the original timeline, developing fractions (as is done beginning in Grades 3 or 4) and the follow-up topics of ratios, proportions, percentages, and rates. The last two chapters complete the development of elementary arithmetic by discussing negative and real numbers.
The textbook is divided into short sections, each on a single topic, and each followed by a homework set focused on that topic. The homework sets were designed with the intention that all or most of the exercises will be assigned. Many of the homework exercises involve solving problems in actual elementary school textbooks (the 'Primary Mathematics' books described below). Others involve "studying the textbook" — carefully reading a section of the book and answering questions about the mathematics being presented, with attention to the prerequisites, the ordering, and the variety of problems on that topic. Both types of exercises will help you develop a teacher's understandingof elementary mathematics.
Supplementary Texts
This textbook is designed to be used in conjunction with the following five Primary Mathematicsbooks (all are U.S. Edition).
• Primary Mathematics 3A Textbook (ISBN 9789810185022)
• Primary Mathematics 4A Textbook (ISBN 9789810185060)
• Primary Mathematics 5A Textbook (ISBN 9789810185107)
• Primary Mathematics 5A Workbook (ISBN 9789810185121)
• Primary Mathematics 6A Textbook (ISBN 9789810185145)
These books were developed by the Curriculum Planning and Development Division of Singapore's Ministry of Education, and published by Federal Publications. While these books were initially created for Singapore elementary students, they have been adapted for use in the United States and other countries. We will refer to them as "Primary Math 3A", "Workbook 5A", and so on.
The Primary Mathematics series is printed as one course book per semester, each with an accompanying workbooks. The semesters are labeled 'A' and 'B' , so '5A' refers to the first semester of Grade 5. In each grade, the first semester focuses mainly on numbers and arithmetic, while the second semester focuses more on measurement and geometry.
To order the Elementary Mathematics for Teachers and the above five Primary Mathematics U.S. Edition books, click here.
Why the Primary Mathematics books?
The aim of this course is to develop an understanding of elementary mathematics at the level needed for teaching. The best way to do that is to study actual elementary school textbooks and to do many, many actual elementary school mathematics problems. The Primary Mathematics books were chosen for that purpose.
We will read and study these books with two goals in mind: understanding the mathematics and understanding the curriculum development. The Primary Mathematics books give an extraordinarily clear presentation of what elementary mathematics is and how it is organized and developed. They lay out the subject in depth, and they include a rich supply of exercises and word problems. The mathematics is always clean and correct, and topics are repeatedly covered from different approaches. Viewed from a broader perspective, these books provide much useful guidance about curriculum issues. They exhibit the principles of a well-designed curriculum better, it seems, than any textbook series currently available in English.
It is not surprising, then, that the Primary Mathematics books are also successful with
children! The Third International Mathematics and Science Study (TIMSS) rated Singapore's elementary students the best in the world in mathematics (it also found that the curriculum is highly coherent). These beautifully designed books are a major factor in student success.
As you read and do problems from these books, notice the following:
The absence of clutter and distraction. These books contain mathematics and nothing but mathematics. The presentation is very clean and clear, and is done using simple, concise explanations.
The coherent development. Each topic is introduced by a very simple example. It is then incrementally developed until, quite soon, difficult problems are being done. Topics are revisited for 'review' and the level of the mathematics is constantly ratcheted upward.
The short, precise definitions. The children pictured in the margins give the precise definitions and key ideas in very few words. These 'student helpers' often clearly convey an idea that might otherwise take an entire paragraph!
The "concrete Þ pictorial Þ abstract" approach. This approach results in a very clear introduction to a topic.
The books serve as teacher guides. The books make the mathematical content of each lesson clear to the teacher and help teachers plan lessons. They also provide examples and activities to be done in class and allow teachers flexibility in designing lessons.
That first point above should be stressed. The Primary Mathematics books are deliberately focused. They contain no distracting extras such as long introductions and summaries, biographical stories, explorations, or discussions of non-mathematical topics. Homework is relegated to workbooks, and group projects and explorations are put in separate teacher guides. The pictures effectively convey meaning; they are not there for stylistic reasons. The judicious use of white space makes the books easy and enjoyable to read. The resulting short textbooks keep young students focused on learning mathematics.
If you compare the Primary Mathematics books to other elementary textbooks, you will ap
Study and enjoy these books — and keep them! When you become a teacher, these books will be a valuable resource, helping with explanations, providing extra problems, and giving guidance in how to present mathematics.
Reading this Textbook
Students reading the Primary Mathematics books interact with the books at the places indicated by colored boxes. As explained in the preface of each book, the colored 'patches' are prompts for student participation and class discussions. They occur in relatively easy exercises, where they encourage active learning and allow students to check their understanding.
This textbook also includes "learning exercises" exercises embedded in the text, many with boxes ~ of various sizes prompting you to answer. Some of these exercises will be discussed in class, but usually you will encounter them while reading on your own. Do these exercises as you read! Most only take a minute or two. Pencil your answers next to the boxes (the boxes themselves are usually not large enough to hold answers). These exercises are designed to clarify the text and help make mathematical discussions more concrete. Some mathematical ideas are difficult to communicate in words, but quickly become clear by doing problems.
That same principle — that mathematics is best learned by solving problems — applies to the course as a whole. Read each section of the textbook, but leave plenty of time for doing the homework sets. They are the most important part of the course.
The Homework Sets
This course is built around homework problems from the Primary Mathematics books. As you do homework, bear in mind that the goal is not merely for you to do the problems, many of which are not hard. Instead, the goal is to think about problems from the perspective of a teacher. Teachers must be able to identify the key steps in solving a problem, so they can guide and prompt students. They must also be able to give clear, grade-appropriate presentations of solutions. Try to bring out these teaching aspects of problems in your homework solutions. In general,
Make your answers clear, concise, legible, and simple. They should look like an answer key to be handed out to an elementary school class.
This idea — clear, concise solutions — is one of the main themes of this course. You will
l earn many tricks and teaching devices which will help you craft such solutions, including models
Above is an extract from the preface of Elementary Mathematics for Teachers.
For teachers using Primary Mathematics Standards Edition textbooks and workbooks, here is a link to EMFT homework adaptation for the Standards Edition. This homework adaptation may be printed out and used at no cost by teachers using the EMFT textbook. They may not be sold or incorporated into any other document.
List of universities and colleges using Elementary Mathematics and Elementary Geometry for Teachers
The Elementary Mathematics for Teachers is written primarily for elementary teachers. A number of universities are already using this book as course material in classes for students taking mathematics education. This book is also suitable for individuals who would like to learn more about teaching elementary mathematics. |
Software for the Coloring of Graphs: a program for calculating chromatic
polynomials and counting proper colorings for finite graphs. Version 1.0,
1995; Version 2.1, August, 2001 (Downloadable from my web site: click
here to download).
"An Introduction to Computer Science" -- textbook and
laboratory book for CS 100, jointly with Paul Dobosh, 2003-2006, in progress.
Teaching/Professional Interests:
I divide my teaching equally between mathematics and
computer science. My scholarly interests also cross that gap--with
significant parts of my work involving ways in which the computer
can become a major factor in the teaching of mathematics (and
other disciplines). In particular, I am committed to the idea
that we can learn more easily and surely than at any time in the
past with the vastly richer base of mathematical examples that
the computer affords us. With this new and astonishingly powerful
tool we are freed to experiment and to observe new relationships
and structures. (See information on Software)
Mathematically, right now, I'm working on a set of
problems involving an infinite collection of periodic functions
which arise from the composing of standard periodic functions
in an unconventional way--a project that arose for me from just
the kind of computer experimentation I mentioned above. Students
who have had Math 301 could easily move into working in this area.
Our course, Math
251, Laboratory in Mathematical Experimentation, provides
a chance to expose people to this approach--the approach that
involves students in working through mathematical ideas in an
experimental environment. Rather than following the well-developed
track of definition...theorem...proof..., students are encouraged
to make conjectures on the basis of experimentation using the
computer. They can then use deductive arguments to confirm or
refute these conjectures. This course has made a definite difference
in the quality of our major in mathematics!
I have had a long-time interest in lattice theory and
partially ordered sets, and I have several times taught an advanced-level
course in lattice theory ( MA319
) and have taught a First- and Second-year Tutorial in that as
well.
In computer science, my activities are in the areas
of digital logic and computer graphics. Also, I am very interested
in designing and writing mathematical software, with a particular
emphasis on flexible user interface design. The graphics course
( CS331 )
would be a way of preparing students to work in graphics projects
and software design, and, of course, digital logic ( CS321
) would be a fruitful preparation for continuing in the area of
component design.
A summer music camp I attended in my youth was The Junior Conservatory
Camp. Its successor, The
Walden School, is still very much in operation and is thriving.
I am becoming involved in planning and promoting the Walden School
Alumni/Alumnae activities. |
Introduces students to the techniques of differential and integral calculus.
Emphasis is placed on practical applications of limits, derivatives and
integrals with business applications highlighted. This course also
provides experience with and information about the significance and specific
uses of the calculus in today's world. A graphics calculator is required.
Students are expected to have completed an equivalent of the course College
Algebra.
OBJECTIVES: This course serves general education, technology, business, and economics
students in achieving the following objectives.
1. To develop the concepts of the limit, derivative and
antiderivative of a function, and also of the definite
integral.
2. To consider applications, and particularly business
applications of the derivative and definite integral.
3. To provide information on the significance of Calculus in
today's world. |
Abstract Algebra - 3rd edition
Summary: Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their ...show moreinterplay lead to powerful results and insights in a number of different settings45 +$3.99 s/h
VeryGood
ocbookstx Richardson, TX
047143334966.00 +$3.99 s/h
VeryGood
bookemporium Bloomington, IN |
Short description
This eBook introduces the subjects of sequences and series, and introduces sequences in general, as well as arithmetic and geometric progressions, series within arithmetic and geometric progressions, the concepts of convergence and divergence as well as the binomial expansion. Suitable questions are asked throughout the discourse to test and develop the students comprehension of the subject.
Reviews
Review by:
Michele Zaffalon
on Oct. 11, 2013 :
I was disappointed to see that the ebook contains 6 chapters, of which only one is about sequences and series. The content is badly presented and shallow, there are few exercises, there are no solutions for self-studying. I can hardly believe that this is the level of math education for 16-18 year old.
I give one start because the rating system would not accept zero.
(reviewed the day of purchase) |
Linear Algebra With Application - 8th edition
Summary: Updated and revised to increase clarity and further improve student learning, the Eighth Edition of Gareth Williams' classic text is designed for the introductory course in linear algebra. It provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. It is organized into three parts that contain core and optional sections. There is then ample time for the instructor to select the material that...show more gives the course the desired flavor.Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of R(n) (make sure it is superscript n), matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on the material presented in Part1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, developing the rank/nullity theorem, and introducing spaces of matrices and functions.Part 3 completes the course with important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition.Throughout the text the author takes care to fully and clearly develop the mathematical concepts and provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more. New exercises can be found throughout that tie back to the modern examples in the text.Key Features of the Eighth Edition:-- Updated and revised throughout with new section material and exercises included in every chapter. -- Each section begins with a motivating introduction, which ties material to the previously learned topics. -- Carefully explained examples illustrate key concepts throughout the text. -- Includes such new topics such as QR Factorization and Singular Value Decomposition.-- Includes new app10 +$3.99 s/h
LikeNew
Bookbyte-OR Salem, OR
Almost new condition. SKU:978144967954551.0057.91 |
Big Idea Algebra 2 XLS
Students learn to solve many new types of problems in Algebra 1, and this bigidea highlights the types of problems students will be able to solve after they master the concepts and skills in this course.
Algebra: BIGIDEA2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals. Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties.
One idea we had and have implemented was putting the electronic data wall onto google docs (SPPS Apps). ... Last year there was a big push to teach more algebra. Teachers have noticed there is not a lot of algebra lessons so they are wondering what resources are available.
Developing Big Ideas in Algebra thru Technology and Hands on Activities ... This idea was also a Classroom Grant Award winner from last year. ... We have examples for use in Algebra 1 & 2, geometry, and Calculus that we have copied for you and with a little preparation, ...
Developing Big Ideas in Algebra thru Technology and Hands on Activities ... Attendees will experience classroom activities that will help all students work their way through integer operations to Algebra2 and perhaps beyond. ... This idea was also a Classroom Grant Award winner from last year.
2.2 Boolean Algebra2.3 Mapping into Logic Gates ... In this unit, we will extend the idea of a function to the whole of mathematics. 7.1 Functions as Relations Between Sets ... 9.2 How Big is an Infinite Set?
... with their college and career goals for 5 years as part of a non-profit program she developed called, TeenSpace. The idea to ... She is comfortable tutoring 6th grd math through Algebra2 ... She has tutored for over five years in organizations such as Kids on Campus, Big Brothers Big ...
Standard 2: Understands and applies concepts of algebra ... • Extracts the main idea of a problem ... • Knows a unit should be changed when the measurement becomes too big or too small • Uses the correct unit of measurement for a given situation (ITBS)
algebra by creating Smart Tools, demonstrating ... THE BIG SPLASH X X X With 1 sample, 1 extrapolation to the population, and Jasper encourages his young friend Chris as ... A CAPITAL IDEA ACI involves a sample within a sample, making the |
TI-30XS MultiView™
A. Teacher Software
Using the TI-30XS Multiview™ Emulator New
B. Using the TI-30XS MultiView™ Calculator
Using answers to previous calculations in the current entry
Working with fractions
Using Math Notation to calculate the area of a circle
Using Math Notation to calculate the side of a right triangle
Using the x10n key to enter numbers using Scientific Notation
Converting a number to a percentage
Assigning values to variables
Using Constant mode to repeat operations
Changing options in the Mode menu
Defining a set of list values using another list
Calculating 1-variable statistics
Using the Table to evaluate y values in an expression
TI-30XS MultiView™
Description
The new TI-30XS MultiView™ calculator allows students to broaden their exploration of math and science concepts by a host of powerful enhancements. The standard mathematical notation displays expressions in textbook format, like superscripted exponents, pi symbol and stacked fractions. The new Table feature enables students to explore "x-y" tables for a given function. Students can easily compare data in patterns using the Data/List Editor in the new List Formula feature. Combining these features with the MultiView Display to compare results and find patterns creates an essential tool for the classroom. |
Nuffield Advanced Mathematics option consists of six units of work, each on a different theme. Students had the opportunity, as part of their coursework, to develop an aspect of interest from one of the themes into a longer project. These topics were chosen to relate the learning in an A-level mathematics course and to deepen…
This MEP resource from CIMT is taken from text book 9B which covers the mathematics scheme of work for the second half of year 9.
Graphs, equations and inequalities covers: linear inequalities on a number line, solving linear inequalities, a recap of the equation of a straight line, graphs of quadratic functions, plotting quadraticsBook Two of Nuffield Advanced Mathematics built on the foundations started in Book One. Like the other books in the series it consisted mainly of activities through which students could develop their understanding of mathematical ideas and results, or could apply their knowledge and understanding to problems of various kinds.
Contents
Unit.
The pack has three sections:…
Book Three of Nuffield Advanced Mathematics contained the units that, with Books One and Two, made up the AS course. These units extended the students' knowledge of algebra, calculus, exponential functions and handling data. It also introduced vectors.
Contents
Unit 11: Equations and inequalities
Unit 12: Correlation andThese MEP materials from CIMT cover the mathematics scheme of work for the first half of year 8. The scheme of work outlines each of the units with notes and examples. Each of the units contains pages from the pupils' book. The scheme and books have been designed to cater for a range of levels.
Alongside the pupils'This MEP resource from CIMT is taken from text book 9B which covers the mathematics scheme of work for the second half of year 9.
Quadratic functions covers: a recap of drawing and transforming quadratic graphs, solving quadratics by factorisation and solving quadratics by completing the square.
The initial file forms part and area of a triangle.
The initial file forms part…
Book Four of Nuffield Advanced Mathematics included the first five units of the core A2 part of the advanced level course. The book showed how to find polynomials to fit given data, it gave a number of ways of solving equations by iteration, and it also introduced matrices and ideas of chaos. The first unit in the book was intended 9A which covers the mathematics scheme of work for the first half of year 9.
Base arithmetic covers: binary numbers, adding and subtracting binary numbers, multiplying binary numbers and other number bases.
The initial file forms part of the textbook. The activities sheet,…
This MEP resource from CIMT is taken from text book 8B which covers the mathematics scheme of work for the second half of year 8.
Units of measure covers: estimating using metric units of length, mass and capacity; converting between metric units, estimating using imperial units of length, mass and capacity; converting between…
This resource on Handling Data from Nuffield National Curriculum Mathematics was suitable for those students working towards an Intermediate GCSE. The units, at National Curriculum level six, begin by considering the history of information collecting from the Domesday book and early opinion polls and how they have evolved into the…
The two units in this Nuffield Advanced Mathematics option were independent of one another, and of unequal in length. 'Complex numbers' needed more time than 'Numerical methods'.
The unit on complex numbers developed the arithmetic and geometry of complex numbers and led up to a section on fractals. The…
The approach in this Nuffield Advanced Mathematics books was one of guided modelling supported by practical work. In each investigation, students were expected to:
• define the problem that you are going to investigate
• set up a mathematical model of the situation
• analyse the situation mathematically
•This book, published by NASEN, is a revision of Number Activities and Games, which was a best selling handbook formerly produced by the National Association for Remedial Education.
This text was classified primarily within Levels Two to Four of the National Curriculum New Attainment Target of 'Number', to provide teachers…
This MEP resource from CIMT is taken from text book 9B which covers the mathematics scheme of work for the second half of year 9.
Sequences includes: sequences with constant differences (linear, arithmetic sequences), generating a sequence from a formula, generating sequences from pictures, finding the formula for a linear sequence,…
This pack of worksheets, produced by the Spode Group, is designed to give students experience in problem solving during the early years of secondary school, and was written in response to publications encouraging the teaching mathematics through problem solving, investigations and discussion.
The pack contains twelve problems…
This MEP resource from CIMT is taken from text book 8B which covers the mathematics scheme of work for the second half of year 8.
Formulae covers: substitution into simple formulae, substituting positive and negative numbers into more complex formulae using BODMAS, solving simple linear equations, solving two-step linear equations,… |
Nonconvex Optimization is a multi-disciplinary research field that deals with the characterization and computation of local/global minima/maxima of nonlinear, nonconvex, nonsmooth, discrete and continuous functions. Nonconvex optimization problems are frequently encountered in modeling real world systems for a very broad range of applications including... more...
Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate... more...
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Calculus is one of the greatest achievements
of the human intellect.Sometimes
called the " mathematics of changes", it is the branch of mathematics
that deals with the precise way in which changes in one variable relate to
changes in another.In our daily
activities we encounter two types of variables: those that we can control directly and those that we cannot.Fortunately, those variables that we cannot
control directly often respond in some way to those we can.For example, the acceleration of a car
responds to the way in which we control the flow of gasoline to the engine; the
inflation rate of an economy responds to the way in which the national
government controls the money supply; and the level of antibiotics in a person's
bloodstream responds to the dosage and timing of a doctor's prescription.By understanding quantitatively how the
variables, which we cannot control directly, respond to those that we can, we
can hope to make predictions about the behavior of our environment and gain
some mastery over it.Calculus is one
of the fundamental mathematical tools used for this purpose.
Calculus was invented to answer questions
that could not be solved by using algebra or geometry.One branch of calculus, called
Differential calculus, begins with a question about the speed of moving
objects.For example, how fast does a
stone fall two seconds after it has been dropped from a cliff?The other branch of calculus, Integral
calculus, was invented to answer a very different kind of question:what is the area of a shape with curved
sides?Although these branches began by
solving different problems, their methods are the same, since they deal with
the rate of change.
Some anticipations of calculus can be seen in
Euclid and other classical writers, but most of the ideas appeared first in the
seventeenth century.Sir Isaac Newton
(1642 – 1727) and Gottfried W. Leibniz (1646 – 1716) independently discovered
the fundamental theorem of calculus.After its start in the seventeenth century, calculus went for over a
century without a proper axiomatic foundation.Newton wrote that calculus could be rigorously founded on the idea of
limits, but he never presented his ideas in detail.A limit, roughly speaking, is the value approached by a function
near a given point.During the
eighteenth century many mathematicians based their work on limits, but their
definition of limit was not clear.In
1784, Joseph Louis Lagrange (1736-1813) at the Berlin Academy proposed a prize
for a successful axiomatic foundation for calculus.He and others were interested in being as certain of the internal
consistency of calculus as they were about algebra and geometry.No one was able to successfully respond to
the challenge.It remained for Augustin
Louis Cauchy (1789-1857) to show, sometime around 1820, that the limits can be
defined rigorously by means of inequalities (Hughes-Hallett, 1998, 78).
Purpose of the study
Calculus is one of the subjects being taught
for higher mathematics in high schools and colleges.The purpose of this paper is to show how to use calculus in our
relationship with God. I will employ parallelism and contrast to teach the
values with the hope that through teaching calculus the teacher can bring
his/her students closer to God.
Application
¨God is the
greatest mathematician.According to
Avery J. Thompson, "Any credence given to the study of mathematics must
recognize that God is the original mathematician.And though, through the ages, humankind has experimented to be
able to draw conclusion in the areas of mathematics, God's laws are error-free
and constant.His everlasting
watch-care in the 'natural' cyclic phenomena of this earth daily proves His
mathematical supremacy.Galileo is
remembered for having acknowledged that 'mathematics is the language that God
used to create the universe'".
¨We are the
variables and God is the constant.God
doesn't change; He is the same God from the beginning.According to Malachi 3:6 (NIV) "I the
Lord do not change."As variables,
we depend on Him to give some predictability to life.Without some constancy, we would never be able to plan, or hope,
or know what to expect.God's laws,
both the moral law and the laws of nature, are as constant as He is.So we can expect that tomorrow the sun will
rise in the east, as it has done every day in the past.
¨A given value
(constant) helps in solving a given function.For example, it is estimated that x months from now, the population of a
certain community will be (function).At what rate will the population be changing
with respect to time 15 months (constant) from now?Solution:the rate of
change of the population with respect to time is the derivative of the
population function.That is, .The rate of change
of the population 15 months from now will be people per month.God, who we said is constant, is a "present help in time of trouble"(Psalm
46:1).Indeed, without God in one's
life, we will never find satisfactory solutions to problems.
¨In calculus, if
we violate the laws we will never find the right solution to the given problem
or function.When we violate the laws
of God our life become chaotic and we will never find peace or the right
solutions to our problems.
Limit and Limitless God
The
concept of limits is very important in calculus.Without limits calculus simply does not exist.Every single notion of calculus is a limit
in one sense or another.On the
contrary God has no limit.When we
apply the concept of limit, we examine what happens to the y-values of a function
f(x) as x gets closer and closer to
(but does not reach) some particular number, called a.If the y-values also get closer and closer
to a single number, L, then the number L is said to
be the limit of the function as x approaches a.Thus, we say that L is the limit of
f(x) as x approaches a.This is
written in mathematical shorthand as
where the symbol → stands for the word approaches.
If the y-values of the function do not get closer and closer to a single number
as x gets closer and closer to a, then the function has no limit
as x approaches a.Figure 1 shows the graph of a function that has a limit L
as x approaches a particular a.
Illustration:
X
1.0
1.5
1.9
1.95
1.99
1.995
1.999
2.0
2.001
2.005
2.01
2.05
2.1
2.5
3.0
f(x)
1.00
1.75
2.71
2.85
2.97
2.985
2.997
3.003
3.015
3.03
3.15
3.31
4.75
7.0
Left sideright
side
Table 1
y
y = f(x)=x2-
x+1
f(x)
3
f(x)
x2xx
Figure 1
"Limit" reminds us of the
experience of the Israelites, as they traveled through the wilderness.Most of the adult Israelites who came out
from Egypt did not enter the Promised Land except for Caleb and Joshua.The children of Israel "approached"
the Promised Land; generally speaking, all of them reached the border.But none of them would have made it were it
not for God's limitless love and grace.Even though they disobeyed Him so many times, God still kept His
covenant with the Israelites.
And
thus, the limitless love of God is demonstrated in many other ways:in the parable of the lost sheep, the
parable of the prodigal son, and even in the way God deals with His people today.Jeremiah 31: 3 (NIV) says:"I have loved you with an everlasting
love."2 Chronicles 16: 34 (NIV)
says:"His love endures forever."
Let's define continuity.The idea of continuity rules out breaks,
jumps, or holes by demanding that the behavior of the function near a point be
consistent with its behavior at the point.
Definition:The function f is said to be continuous from a
if and only if the following three conditions are satisfied:
i)
ii)
iii)
If
one or more of these three conditions fail to hold at a, the
function is said to be discontinuous at a.
Illustration:A wholesaler who sells a product by the kilogram (or fraction of
a kilogram) charges $2 per kilogram if 10 kg or less is ordered.If more than 10 kg is ordered, the
wholesaler charges $20 plus $1.40 for each kilogram in excess of 10 kg.Therefore, if x kilograms of the product ispurchased at a total cost of dollars, then andthat is,
Solution:i)
ii)
==
iii)
Therefore
C is continuous at 10.
We
can now use this definition to represent our faith in God.
i)If is our faith in God,
our faith in God exists
ii)
iii)
If any of the
above definitions does not exist, the function is said to be
discontinuous.One of the examples
showing that his faith in God was present was Moses when he led the Israelites
out in the desert.Moses and the people
were in the desert, but what was he going to do with them?They had to be fed and feed was what he did.
Moses needed to have around 1500 tons of food each day.To bring that much food each day, two
freight trains, each around a kilometer long would be needed.We all know they were out in the desert, so
they would need firewood to cook the food.This would take 4000 tons of wood and a few more freight trains, each a
kilometer long, just for one day.And
they were forty years in the desert.
They would
have to have water.If they only had to
have enough to drink and wash a few dishes, it would take around 11,000,000
gallons each day, and a freight train with tank cars, around 3 kilometers long,
just to bring water.
Then another
thing:they had to cross the Red
Sea.Now, if they went on a narrow
path, double file, the line would be around 1200 km long and would take 35
days and nights to get
through.So, there had to be space in
the Red Sea, around 5 km wide so that they could walk 500 abreast to get over
in one night.
But then,
there was another problem.Each time
they camped at the end of the day, they needed a big space, a total of around
2000 square kilometers long.
Do you think
Moses sat down to figure all this out before he left Egypt?Moses believed in God, and that God would
take care of everything for him.
The following
persons also demonstrated faith in God: Noah, when God asked him to build the
ark, when they hadn't experienced flood or rain before that time; Abraham, when
God asked him to leave his family and go to another place and also when God
asked him to offer his only son Isaac.
To maintain a
living and growing relation with God we need to have continuous communication
with Him through prayer, meditation, and reading of His Word.We must have faith or trust in Him.According to Psalms 32: 10, "The Lord's
unfailing love surrounds the man who trusts in Him".
Great is our
Lord and mighty in power; his understanding has no limit.Ps. 147:5(NIV)
Derivative and
Unchanging God
Derivative is
a mathematical tool that is used to study rate at which physical quantities
change.It is one of the two central
concepts of calculus, and it has a variety of applications, including curve
sketching, the optimization of functions, and the analysis of rates of change.
A typical problem to which calculus can be
applied is profit optimization.For
example: a manufacturer's monthly profit from the sale of radios was P(x)
= 400(15 – x)(x – 2) dollars when the radios were sold for x
dollars a piece.The graph of this
profit function, which is shown in Figure 2, suggests that there is an optimal
selling price x at which the manufacturer's profit will be
greatest.In geometric terms, the
optimal price is the x coordinate of the peak of the graph.
P(x)
Slope
is zero
Optimal price
x
Figure 2:
The
profit function P(x) = 400(15 – x)(x
– 2)
In this example, the peak can be
characterized in terms of lines that are tangent to the graph.In particular, the peak is the only point on
the graph at which the tangent line is horizontal, that is, at which the slope
is zero. To the left of the peak, the slope of the tangent is positive.To the right of the peak the slope is
negative.
Calculus is also one of the
techniques used to find the rate of change function.The rate of change of a linear function with respect to its
independent variables is equal to the steepness or slope of its straight-line
graph.Besides, this steepness or rate
of change is constant.
We can solve optimization problems
and compute rates of change if we have a procedure for finding the slope of the
tangent to a curve at a given point.
We begin with a function f, and on its graph we choose a point (x,
f(x)).Refer to Figure 3.We choose a small number h
≠ 0 and on the graph mark the point (x + h, f(x + h)).Now we draw the secant line that passes
through these two points.The situation
is pictured in Figure 4, first with h > 0 and then with h
< 0.
As h tends to zero
from the right (Figure 4), the secant line tends to the limiting position
indicated by the dashed line, and tends to the same limiting position as h
tends to zero from the left.The line
at this limiting position is what we call " the tangent to the graph at
the point (x, f(x)).
Since
the approximating secant lines have slopes
(*),
we can expect the tangent line,
the limiting position of these secants, to have slope
(**)
While (*) measures the steepness
of the line that passes through the points (x. f(x)) and (x +h, f(x
+h)), (**) measures the steepness of the graph at (x, f(x)) and is
called the "slope of the graph."
We can now define
differentiation.
A function f is
said to be differentiable at x if and only if
exists.
If this limit exists, it is
called the derivative of f at x, and is denoted by f'(x).
Notations:
y
Figure 3x
yy
ff
Limiting position
Secant
(x+h, f(x+h))
(x,
f(x))
Secant
xx
Figure 4
Note:the rate of
change of a function with respect to its independent variable is equal to the
steepness of its graph, which is measured by the slope of its tangent line at
the point in the question.Since the
slope of the tangent line is given by the derivative of the function, it
follows that the rate of change is equal to the derivative.
Illustrations:
1.It
is estimated that x months from now, the population of Mission College SDA
church will be At what rate will the
population be changing with respect to time 15 months from now?
Solution:
The rate of change of the population
with respect to time is the derivative of the population function.That is
Rate of change =
The
rate of change of the population 15 months from now will be people per month
2.
Distance(S)
Love(L)
Velocityv= dS/dt
GodG = dL/dt = 0
Table 2
Since
the derivative of the constant is zero and we know that God's love is constant
and it does not change, so the rate of change of God's love is zero.1 John 4:16(NIV) says:God is love. Hebrews 13: 8 says:"Jesus Christ (God) is the same
yesterday, today and forever."Hence God's love is the same yesterday, today and forever." There was enough, and more than
enough.In love there is no nice
calculation of less and more.God is like
that"(Barclay: p. 118)
Concavity and points of
Inflection:
The graph is concave up on an open
interval where the slope increases and concave down on an open interval where
the slope decreases.Points that join
arcs of opposite concavity are called points of inflection.The graph in Figure 5 has three of
them:(c1,f(c1)),
(c2, f(c2)), (c3, f(c3)).In our daily lives we also have ups and
downs and we have points of inflection, where we need to make decisions.According to Joshua 24: 15(NIV), "Choose
for yourselves this day whom you will serve."We cannot serve two masters; one master brings us up and the
other brings us down.
y
concave up
x
Figure 5
Integral and
the Orderly God
In many problems, the derivative of a
function is known and the goal is to find the function itself.For example, a sociologist who knows the
rate at which the population is growing may wish to use this information to
predict future population levels; a physicist who knows the speed of a moving
body may wish to calculate the future position of the body; an economist who
knows the rate of inflation may wish to estimate future prices.God knows the rate of progress in His people
and He knows when His work will be completed, so He can reliably predict His
second coming, predict the close of probation, etc.
The process of obtaining a function from its
derivative is called antidifferentiation or integration.
Let's define Antiderivative:
A
function F(x) for which
for
every x in the domain of f is said to be an antiderivative ( or
indefinite integral) of f.
The Antiderivatives of a Function:
If F and G are
antiderivatives of f, then there is a constant C such that
Integral Notation:It is customary to write
to express the fact that every
antiderivative (integral) of f(x) is of the form F(x) + C.For example, we can express the fact that
every antiderivative of is of the form by writing
The
symbol is called an integral sign and indicates that you are to find
the most general form of antiderivative or integral of the function following
it.
To apply integration we need to
follow specific rules, for example,
1.The power rule
of Integrals; , for n-1.
2.The Integral of ;
3.The Integral of ;
4.The Constant Multiple Rule for Integrals;
5.The Sum Rule
for Integrals;
There are more than 120 rules or properties
that can be used in Integration.There
is a specific rule that we apply for each kind of function.When God created this world, everything He
made had a specific role to play.For
example, the sun would give us light; air was for breathing; water was for
drinking and cleansing; trees, animals, and human beings were to live symbiotically;
gravity would keep everything from bouncing.And He put everything in order.God is a God of order.1
Corinthians 14:33 (NIV) says, " God is not a God of disorder but of peace."
Suppose that the known the rate at which a certain
quantity F is changing and we wish to find the amount by which
the quantity F will change between x = a and x
= b.We would first find F
by antidifferentiation and then
compute the difference.The
numerical result of such a computation is called definite integral of
the function f and is denoted by the symbol
.
Applications
of Integrals:
1.Calculate
the population of the town x months from now.
2.Total
cost of producing x units.
3.Total
consumption over the next t years.
4.Area
5.Volume
up to three dimension
Illustration:Area in Polar Coordinate
The hardest part in applying
the Area formula is determining the limits (boundary) of integration.This can be done as follows:
1.Sketch the
region R whose area is to be determined.
Genesis 2:7 (NIV) says:" God formed man of dust from the
ground."
2.Draw an
arbitrary "radial line" from the pole to the boundary curve
Genesis
1:27 (NIV) says: " God created man in His own image"
3.Ask, "Over
what interval of values must vary in order for the
radial line to sweep out the region R?"
4.Our answer in
Step 3 will determine the lower and upper limits of integration.
Psalms 8:5 (NIV) says:" Yet you have made him a little lower
than God."
Example:
Find the area
of the region in the first quadrant within the cardioid
r = 1 – cos
Solution:
The region and a typical radial line are
shown in Figure 5.For the radial line
to sweep out the region, must vary from 0 to .
To find the area of the region we
need to find the point where the radial line (point of reference).In order for us to find direction in our
life we need to have a point of reference, which is God.
y
x
The shaded region is swept out by the
radial line as varies from 0 to .
Figure 5
Conclusion
From
the above examples, we have shown some ways by which a mathematics teacher can
use concepts in calculus to help students understand more about God.Calculus, or any subject, should not be
taught in isolation but should be related to life and faith.True education should prepare a student not
only for this life but also for the life to come."True education means more than a preparation for the life
that now is. It has to do with the whole being, and with the whole period of
existence possible to the man. It is the harmonious development of the
physical, the mental, and the spiritual powers. It prepares the student for the
joy of the service in this world and for the higher joy of wider service in the
world to come." (White, Counsels on Education) It should introduce
the student to God and get him ready to enjoy His presence for eternity.
" Mathematics is a revelation of the
thought life of God.It shows Him to be
a God of system, order, and accuracy.He can be depended upon.His
logic is certain.By thinking in
mathematical terms, therefore, we are actually thinking God's thoughts after
Him." (SDA, p.6) |
My main area of interest is applied computational mathematics,
computer algebra, experimental mathematics, and pen-based computing. Other interests include discrete
mathematics, analysis of algorithms and automated theorem proving. In area of computer algebra,
I am mostly interested in integration, summation, simplification,
factorization, and computation of various special functions. |
books.google.co.uk - This... to Analytic Number Theory
Introduction to Analytic Number Theory, Volume 1
This in the next chapters include Dirichlet's theorem on primes in progressions, Gauss sums, quadratic residues, Dirichlet series, and Euler products with applications to the Riemann zeta function and Dirichlet L-functions. Also included is an introduction to partitions. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus.
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Analytic number theory II Introduction to Analytic Number Theory by tm. Apostol. Entry. You must be registered for the msc in Mathematics or. for another qualification towards which ... www3.open.ac.uk/ courses/ pdfs/ M829.pdf
About the author (1976)
Tom M. Apostol joined the California Institute of Technology faculty in 1950 and is now Professor of Mathematics, Emeritus. He is internationally known for his textbooks on Calculus, Analysis, and Analytic Number Theory, which have been translated into 5 languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international video festivals, and have been translated into Hebrew, Portuguese, French, and Spanish. His list of publications includes 98 research papers, 46 of them published since he retired in 1992. He has received several awards for his research and teaching. In 1978 he was a visiting professor at the University of Patras in Greece, and in 2000 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek. |
A Student's Guide to Vectors and Tens53.75
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About the Book
Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author. |
Algebra and Trigonometry - 2nd edition
Summary: Often, algebra & 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 algebra & trigonometry professors face. She uses a clear, voice that speaks directly to students- similar to how instructors commun...show moreicate to them in class. Students learning from this text will overcome common barriers to learning algebra & trigonometry and will build confidence in their ability to do mathematics2009 Hardcover Good Access Codes may not be valid on used books. Access Codes may not be valid on used books.
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Math 5/4 is a balanced, integrated mathematics program that includes incremental development of whole number concepts and computation; arithmetic algorithms, geometry and measurement; elapsed time; fractions, decimals and percents; powers and roots; estimation; patterns and sequences; congruency and similarity; and statistics and probability.
This is an excellent math program. It is easy for a home-school mom to use, and it gives a good foundation for upper level math. It is not a Christian publication so there are story problems that may mention things at a Christian might not agree with. They are few, but they can be a means of initiating a discussion to reinforce beliefs.
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Review 2 for Math 54, Third Edition, Student Text
Overall Rating:
4out of5
Date:October 1, 2007
Rachel Mcconnell
This is the first year we are doing homeschooling and I am pleased that Saxon Math curriculum is offered for homeschoolers. My daughter had this program at school so we are able to continue from where she started! |
Space and Counterspace
This classic examination of Projective Geometry offers a detailed exposition of the topic from a variety of perspectives and will be a great aid to Waldorf teachers and others seeking to penetrate the thinking behind this important topic. |
Mathematics plays a dual role of academic discipline on its own, and serves as the basic language for all the sciences. The Mathematics Department at East West University is designed to provide students with the mathematical skills that can be used in many careers, as well as in everyday life. Certain skills learned in the program will prepare students to apply mathematics to real-life situations, while other skills will provide a solid base for proof-writing and research. Upon completion of the program, a student will be well rounded enough to be able to choose either a career in industry or further studies in academia. The aim of the mathematics department is to prepare students to move into jobs for the future.
The discipline of mathematics offers a variety of programs in pure and applied mathematics to meet the needs of students in different academic and career areas. Program options include:
· Specialized Classes in Math that will prepare students who major in other disciplines to increase their effectiveness in their own particular fields.
· An Associate of Arts degree program in which a general liberal arts education can be combined with a solid background in Mathematics.
· A Bachelor of Arts degree program with a major in Mathematics, which prepares the student for a math-related career.
COLLEGE-PREPARATORY MATHEMATICS 4 CREDITS Prerequisite: Placement. The objective of this course is to increase competence in working with basic numbers so as to solidify students' foundational math skills. Topics include whole numbers, fractions, decimals, percents and signed numbers. Topics are integrated into the order of operations with an introduction to the blue-print for problem-solving. Students are assigned to this course based on placement tests. Credits do not count towards graduation.
MT123 FALL/WINTER/SPRING/SUMMER
ELEMENTARY ALGEBRA 4 CREDITS Prerequisite: MT121 or placement
This is the first in a sequence of algebra courses. Topics include transition to algebra, evaluating algebraic expressions, equations and inequalities, applications and word problems, the graph of a linear equation, slope of a line, properties of exponents, scientific notation, polynomials and operations with polynomials. Credits do not count towards graduation.
MT155 FALL/WINTER/SPRING/SUMMER
INTERMEDIATE ALGEBRA 4 CREDITS Prerequisite: MT123 or placement. Continuation of introductory algebra. Topics include factoring, solutions of quadratic equations by factoring, systems of linear equations and inequalities, rational expressions, simplification of radicals and exponents, the quadratic formula, graphing and applications to be used throughout the course.
BUSINESS CALCULUS 4 CREDITS Prerequisite: MT156 For students majoring in business. Introduction to calculus topics include: limits, continuity, functions, differentiation and integration of polynomial. Applications are developed and applied to business oriented.
MT201 FALL/SPRING
CALCULUS I 4 CREDITS Prerequisite: MT160 A first course in calculus sequence introduces the idea of limits, continuity, and derivatives. Further topics include techniques of differentiation, L'Hopital's Rule, higher order derivatives, and related rates.
MT202 FALL/WINTER
CALCULUS II 4 CREDITS Prerequisite: MT201 A continuation of MT201, this course covers applications of the derivative, the indefinite integral, and the definite integral and its applications. Newton's method, the mean-value theorem, and the fundamental theorem of calculus are among the other topics covered.
MT203 SPRING
CALCULUS III 4 CREDITS Prerequisite: MT202 A continuation of MT202, this course covers the advanced techniques of integration, the evaluation of the improper integrals, an introduction to differential equations, and infinite series. Specific topics include integrating with computer algebra systems, slope fields, Euler's method, and convergence tests for infinite series. Maclaurin and Taylor series are discussed as well.
MT221 FALL/WINTER/SPRING/SUMMER
FUNDAMENTALS OF STATISTICS 4 CREDITS Prerequisite: MT156 and CI213 Descriptive statistics, analysis and presentation of single variable data, including graphs, Pareto diagrams, histograms, measures of central tendency, measures of dispersion and measures of position, analysis of bivariate data, including linear correlation and linear regression, probability and probability distributions, including mean and variance of a discrete probability distribution and binomial distribution, normal distributions and applications of normal distributions.
ELEMENTARY DIFFERENTIAL EQUATIONS 4 CREDITS Prerequisite: MT203 An introductory look at classifying and solving basic types of differential equations. There is a focus on the first and second-order differential equations, both linear and non-linear, and their application to the physical sciences and engineering. Analytical and numerical techniques for solving will be discussed.
MT311 FALL
ABSTRACT ALGEBRA 4 CREDITS Prerequisite: MT203 Introduction to modern algebra. Topics include elements of axiomatic set theory, group theory, ring and field theory, permutation groups, subgroups, cosets and Lagrange's theorem.
MT322 SPRING
INFERENTIAL STATISTICS 4 CREDITS
Prerequisite: MT221
Inferential statistics with applications to business and behavioral science, hypothesis testing, including one-tailed and two-tailed tests in distributions for estimating (mean) with known (standard deviation), inferences involving one population, including Student's statistic for estimating with unknown , Chi-square distributions for estimating variances, inferences involving two populations, including estimating mean difference using two dependent samples and two independent samples respectively, applications of Chi-square statistics, including multinomial experiments and contingency tables. |
COMPLETE HOMESCHOOL KIT MATH 8/7
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COMPLETE HOMESCHOOL KIT MATH 8/7 Math 8/7 is the culmination of Saxon Homeschool Math for Middle Grades, reviewing arithmetic calculation, measurements, basic geometry, and other foundational concepts and skills. At the same time, Math 8/7 includes extensive pre-algebra exercises, preparing the students for upper-level mathematics. |
algebra 1, algebra 2 and calculus, algebra 2 and geometry algebra 1, algebra 2 and calculus |
Synopses & Reviews
Publisher Comments:
This book is intended to provide students with the appropriate mathematical tools and problem-solving experience to successfully compete in high-level problem solving competitions. In each section, the authors attempt to "fill in" the appropriate background and then provide the student with a variety of worked examples and exercises to help bridge the gap between what he or she may already know and what is required for high-level competitions. Answers or sketches of the solutions are given for all exercises. The book makes an attempt to introduce each area "gently" assuming little in the way of prior background - and teach the appropriate techniques, rather than simply providing a compilation of high-level problems.
Synopsis:
"Synopsis"
by Springer, |
Secondary School 'KS3 (Key Stage 3) - Maths - Transformations – Ages 11-14' eBook by Dr John Kelliher
Price:
$2.99 USD.
Approx. 870 words.
Language:
English.
Published on June 5, 2012.
Category:
Nonfiction.
This eBook introduces the subject of transformation as it relates to translations, reflections, rotations and enlargements either as individual operations or composite operations. In this eBook we illustrate each of these translations using right-angled triangles, but the principles developed extend to all 2D shapes as well as to 3D shapes using extensions |
for Elementary School Teachers
Future elementary and middle school teachers need a clear, coherent presentation of the mathematical concepts, procedures, and processes they will be ...Show synopsisFuture elementary and middle school teachers need a clear, coherent presentation of the mathematical concepts, procedures, and processes they will be called upon to teach. This text uniquely balances "what" they will teach (concepts and content) with "how" to teach (processes and communication). As a result, students using "Mathematics for Elementary School Teachers" leave the course knowing more than basic math skills; they develop a deep understanding of concepts that enables them to effectively teach others. This Fourth Edition features an increased focus on the 'big ideas' of mathematics, as well as the individual skills upon which those ideas are built |
A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra.
Related programs:
Student Database 5.25 - The Student Database software is a program that manages contacts. It was originally designed for counsellors and administrative personel in schools. It has extensive search and summary capabilities and it is built for ease of use. |
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Basic Notions of Algebra
Publisher:
Springer Verlag
Number of Pages:
258
Price:
109.00
ISBN:
3-540-25177-4
Let's begin with the conclusion: this is a truly wonderful book, one that anyone teaching abstract algebra should read and which should be pointed out to talented students, particularly those who want to know a little more about what and why abstract algebra is.
This book is volume 1 in the Algebra section of the Springer Encyclopaedia of Mathematical Sciences (and volume 11 in the overall series). The Encyclopaedia series started as a joint effort with the Soviet publisher VINITI, but has now evolved into a much more ambitious project, with new subseries covering many more areas. Some algebraic topics, such as Representation Theory, Number Theory, Algebraic Geometry, and Lie Groups and Algebras, have their own subseries, so the Algebra series does not cover those topics.
As the first volume in the Algebra series, Basic Notions of Algebra tries to give the "big picture": what the subject is about, what it is for, some hints of its history. Treatments of specific sub-areas are in other volumes of the Encyclopaedia series. The volumes in the original algebra series (to the extent I was able to determine) are:
Basic Notions of Algebra
Non-Commutative Rings, Identities
[Never published]
Infinite Groups and Linear Groups
Homological Algebra
Combinatorial and Asymptotic Methods of Algebra and Nonassociative Structures
Combinatorial Group Theory and Applications to Geometry
Representations of Finite-Dimensional Algebras
Finite Groups of Lie Type and Finite-Dimensional Division Algebras
As one can see, this is an ambitious series that attempts to provide an overview of many parts of contemporary algebra. Shafarevich's volume provides a fitting introduction to all this.
When trying to explain to people what algebra is, one can imagine two different strategies. The first is to attempt to define the subject, say as the study of "structures" or something along those lines. The second is simply to give a tour, pointing out the most important sights and their significance. Shafarevitch says a few words about algebra in general, arguing that it provides various structures that "coordinatize," in one way or another, various mathematical (and physical!) phenomena. He cites projective planes and quantum mechanics as two particularly rich examples of this.
On the whole, however, Shafarevich opts for the latter strategy. Starting with fields, he discusses many of the standard algebraic structures, explains their origins, the main theorems about each, and why they are interesting. In each case, he highlights connections with other parts of mathematics.
As a result, the book becomes a long argument by example. In effect, it displays how algebra can be deployed as "a way to understand mathematics," to use Sauders Mac Lane's famous description. So fields are defined in the usual way, but after giving the standard examples Shafarevitch mentions fields of rational functions, the function field of an algebraic curve, and fields of Laurent series. Groups are discussed first as symmetry groups, then as abstract groups, and the definition is followed by a description of the group of extensions of a module and of the Brauer group of a field. Crystallographic groups come up frequently and are treated in detail.
In the treatment of each kind of algebraic structure, Shafarevitch emphasizes the most important examples. When a simple short proof of a theorem is available, he gives it, but big theorems are simply cited without proof. Since many connections with other parts of mathematics are made, readers should expect to meet, here and there, notions that are new to them. That is usually not an obstacle: Shafarevich is very clear and easy to understand, and the dependence on other subjects is usually "local." So if one can't follow the explanation of how the notion of a Lie algebra is related to the invariant vector fields on a Lie group, one can just take it for granted and move on.
Most mathematicians learn something from this book. The examples are particularly well chosen, simple enough to understand and complicated enough to display the main features of the theory. Since Shafarevich is writing a kind of survey, he highlights what is important and ignores technical details.
It's all too easy, when teaching or learning algebra, to lose sight of the forest. I can't imagine a better way to reorient oneself than reading through this book. Shafarevich provides reliable and interesting guidance, and he often has something new or unexpected to show us.
Shafarevich's writing is spare and elegant. Only occasionally do we see a flash of wit or the author's personality. At one point, for example, he discusses the application of the theory of representations of Lie groups in quantum mechanics. After a very clear explanation of the connection, he ends by noting that "Similar ideas have been widely developed over the last twenty years, finding applications also outside the domain of strong interactions. But at this point the author's scant information on these matters breaks off."
Miles Reid's translation is, in general, quite good, showing little sign of "translation English." One of the few instances in which something goes wrong is when he uses "octavions" to refer to Cayley's "octonions." I hope I'm right that this isn't standard usage, because I find it very ugly.
The book concludes with a useful, if uncompromising, bibliography. Reid notes that he asked Shafarevich whether "references to classics of the subject might seem old-fashioned to modern students. Shafarevich's reply was that just because we know of other people's bad habits, it doesn't follow that we should encourage them, does it?"
This is a wonderful book, one that will enrich your understanding of algebra and deepen your knowledge of mathematics as a whole. Tolle, lege!
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College, and the editor of MAA Reviews. He has taught abstract algebra more times than he can count, and he hopes he will be able to pass on to his students some of what he has learned from this book. |
MA 099
Preparation for College Mathematics I
Course info & reviews
This is the first course of a two semester sequence intended for students with little or no algebra experience. This sequence is designed to prepare students for credit-bearing mathematics courses. It emphasizes a solid understanding of basic operations on rational numbers and the ability to manipulate variable expressions using basic ... |
Visual Optim is a math program for one dimension searching, linear programming, unconstrained nonlinear programming and constrained nonlinear programming. Visual Optim is a math program for one dimension searching, linear programming,...
PTC Mathcad Express is free-for-life engineering calculation software. You get unlimited use of the most popular capabilities in PTC Mathcad allowing you to solve, document, share and reuse vital calculations. PTC Mathcad Express is free-for-lifeVisual Complex is a graph software to create graph of complex function. 3D function graphs and 2D color maps can be created with this grapher. Visual Complex is a graph software to create graph of complex function. 3D function graphs and 2D color...
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Visual Math family edition. Visual Math product family 12 in 1 bundle special. Help family to teach or study mathematics. Visual Math family edition. Visual Math product family 12 in 1 bundle special. Help family to teach or study mathematics,...
Master Math Word Problems can help sharpen skills through practice. Solving word problems is an area where elementary students overwhelmingly display difficulties. Master Math Word Problems can help sharpen skills through practice. Third through...
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There are other sources on the web regarding mental calculation, but Professor Benjamin really makes it fun. There's a Great Courses Lecture series reflecting the content of this book. The power of the techniques in this book combined with the ability to graph well visually will undoubtedly lead to a keen mathematical mind that will set you apart from the rest. The techniques are shockingly simple; they just need to be committed to memory. I'm already teaching some of them to a four year old. She has nothing to unlearn, so she just absorbs it. She likes to gather up her dollies and 'Ride up to the Space Station, Jim...' I started teaching her brother trig at twelve and he starts at Harvard in the fall. (I'm already teaching her to draw the shapes of graphs.) I can only imagine where she will go. |
Pre-calculus is the gate-keeper course for transition to calculus, and is therefore as important as calculus itself for those intending or needing to study higher mathematics. Typically it includes a review of basic algebra topics; various types of functions--including trigonometric and polynomi... |
1. Using Maple to plot surfaces, using both cartesian and polar co-ordinate presentations. Interpret Maple output. Sketch some surfaces by hand.
2. Sketching level curves by hand.
3. Calculating first and second order partial derivatives from formulae, and from first principles.
4. Calculating the gradient function, and the derivative map.
5. Using the chain rule to calculate partial derivatives of composite functions, in both scalar and matrix forms.
6. Calculating the Taylor approximation of a function, up to the quadratic terms.
7. Identifying local extrema and critical points. Use the Hessian matrix to investigate the form of a surface at a critical point. Identify when the Hessian is positive definite, in two and three dimensions, using the subdeterminant criterion.
8. Using the Lagrange multiplier method to find local extrema of functions, under one constraint only.
9. Calculating easy double integrals. Change the order of integration in double integrals, for easy regions.
10. Calculating arc-length and surface areas for easy functions. Use Green's Theorem in the plane.
Assessment Information
Coursework (which may include a Project): 15%; Degree Examination: 85%. |
ALEX Lesson Plans
Title: Why so Cross?
Description:
This lesson will help students develop a deep understanding of what the solution to a system of linear equations means. They will investigate the graphs of systems as well as experiment with an online graphing calculator.
Standard(s): [MA2010] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8-EE8] [MA2010] AL1 (9-12) 20: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [A-REI6]
Subject: Mathematics (8 - 12) Title: Why so Cross? Description: This lesson will help students develop a deep understanding of what the solution to a system of linear equations means. They will investigate the graphs of systems as well as experiment with an online graphing calculator.
Title: Systems of Equations: What Method Do You Prefer?
Description:
The
Standard(s): [MA2010] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8-EE8 ALC (9-12) 2: Solve application-based problems by developing and solving systems of linear equations and inequalities. (Alabama)
Subject: Mathematics (8 - 12) Title: Systems of Equations: What Method Do You Prefer? Description: The |
Mathematics - General (484 results)
The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as wellinformed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large safety factor of deud wood in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing. The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials.
Arithmetic are fully developed, and sufficient examples are given to fix them on the mind. When a student is very apt and thoroughly understands the Pbimary Lessons, he may omit the EleMENTABY, and immediately take up this book, which is complete in itself. I have discarded puzzles of every kind, which only perplex the student without advancing him a step in science. A few simple principles of algebra are introduced, in order to elucidate more clearly, the different functions of interest, the series of equal ratios, and the square and cube root. Problems in mensuration are also given, the principles of which are derived from Geometry. Arithmetic is a pure mathematical science, and if its principles are systematically developed, the student will progress with easy and rapid steps, and when he has finished this b(5ok, he will discover that he has already so far ascended the hill of science that a retrospect will present to him many beauties which are greatly enhanced when seen in their harmonious relation to each other.
While this book presents a thoroughly practical kind of mathematics, as do also Books I and II, it is the purpose of the book to make the treatment sufficiently formal to enable the student to appreciate more fully the nature of pure mathematics. It is only by so doing that the door of the science can be opened sufficiently to enable him to determine whether he should pursue the subject further. In Book I the work in arithmetic was extended, the subject of intuitive geometry was introduced, and the algebraic formula was used when needed; in Book II the work in arithmetic was continued, particularly as it refers to the problems of everyday life, and such algebra as is essential in various practical lines was set forth; and now Book III offers a fitting close to an introductory course in mathematics by extending the work in practical algebra, by showing the nature and some of the practical uses of trigonometry, and by introducing the student to the first steps of demonstrative geometry.<br><br>The student who expects to enter college will find that the algebra given in this series satisfies the requirements in many cases and that even the highest requirements in both algebra and geometry can be met in a year or a year and a half more. The authors have had in mind the needs not only of this class of students but also of those students who do not expect to enter college and yet who wish for and are entitled to have a general survey of elementary algebra, an introduction to the meaning and the practical uses of trigonometry, and an idea of scientific demonstration as it appears in its most available form, the element of geometry.
In issuing this new volume of my Mathematical Puzzles, of which some have appeared in the periodical press and others are given here for the first time, I must acknowledge the encouragement that I have received from many unknown correspondents, at home and abroad, who have expressed a desire to have the problems in a collected form, with some of the solutions given at greater length than is possible in magazines and newspapers. Though I have included a few old puzzles that have interested the world for generations, where I felt that there was something new to be said about them, the problems are in the main original. It is true that some of these have become widely known through the press, and it is possible that the reader may be glad to know their source.<br><br>On the question of Mathematical Puzzles in general there is, perhaps, little more to be said than I have written elsewhere. The history of the subject entails nothing short of the actual story of the beginnings and development of exact thinking in man. The historian must start from the time when man first succeeded in counting his ten fingers and in dividing an apple into two approximately equal parts. Every puzzle that is worthy of consideration can be referred to mathematics and logic. Every man, woman, and child who tries to "reason out" the answer to the simplest puzzle is working, though not of necessity consciously, on mathematical lines. Even those puzzles that we have no way of attacking except by haphazard attempts can be brought under a method of what has been called "glorified trial" - a system of shortening our labours by avoiding or eliminating what our reason tells us is useless. It is, in fact, not easy to say sometimes where the "empirical" begins and where it ends.<br><br>When a man says, "I have never solved a puzzle in my life," it is difficult to know exactly what he means, for every intelligent individual is doing it every day. The unfortunate inmates of our lunatic asylums are sent there expressly because they cannot solve puzzles - because they have lost their powers of reason. If there were no puzzles to solve, there would be no questions to ask; and if there were no questions to be asked, what a world it would be! We should all be equally omniscient, and conversation would be useless and idle.<br><br>It is possible that some few exceedingly sober-minded mathematicians, who are impatient of any terminology in their favourite science but the academic, and who object to the elusive x and y appearing under any other names, will have wished that various problems had been presented in a less popular dress and introduced with a less flippant phraseology.
Bringing to life the joys and difficulties of mathematics this book is a must read for anyone with a love of puzzles, a head for figures or who is considering further study of mathematics. On the Study and Difficulties of Mathematics is a book written by accomplished mathematician Augustus De Morgan. Now republished by Forgotten Books, De Morgan discusses many different branches of the subject in some detail. He doesn't shy away from complexity but is always entertaining. One purpose of De Morgan's book is to serve as a guide for students of mathematics in selecting the most appropriate course of study as well as to identify the most challenging mental concepts a devoted learner will face. "No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed," states De Morgan in his introduction. The book is divided into chapters, each of which is devoted to a different mathematical concept. From the elementary rules of arithmetic, to the study of algebra, to geometrical reasoning, De Morgan touches on all of the concepts a math learner must master in order to find success in the field. While a brilliant mathematician in his own right, De Morgan's greatest skill may have been as a teacher. On the Study and Difficulties of Mathematics is a well written treatise that is concise in its explanations but broad in its scope while remaining interesting even for the layman. On the Study and Difficulties of Mathematics is an exceptional book. Serious students of mathematics would be wise to read De Morgan's work and will certainly be better mathematicians for it.
The orientalists who exploited Indian:-histC Ty a Ul literature about a century ago were not always perfect in their methods of investigation and consequently promulgated many errors. Gradually, however, sounder methods have obtained and we are now able to see the facts in more correct perspective. In particular the early chronology has been largely revised and the revision in some instances has important bearings on the history of mathematics and allied subjects. According to orthodox Hindu tradition the Surya Siddhanta, the most important Indian astronomical work, was composed over two million years ago! Bailly, towards the end of the eighteenth century, considered that Indian astronomy had been founded on accurate observations made thousands of years before the Christian era. Laplace, basing his arguments on figures given by Bailly considered that some 3, 000 years B.C. the Indian astronomers had recorded actual observations of the planets correct to one second; Playfair eloquently supported Bailly sviews ;Sir William Jones argued that correct observations must have been made at least as early as 1181 B.C.; and so on; but with the researches of Colebrooke, Whitney, Weber, Thibaut, and others more correct views were introduced and it was proved that the records used by Bailly were quite modem and that the actual period of the composition of the original Surya Siddhanta was not earliar than A.D.400. It may, indeed, be generally stated that the tendency of the early orientalists was towards antedating and this tendency is exhibited in discussions connected with two notable works, the Sulvasutras and the Bakhshali arithmetic, the dates of which are not even yet definitely fixed.
The Normal Mental Arithmetic: A Thorough and Complete Course by Analysis and Induction is a textbook written by Edward Brooks. This work provides readers with the opportunity to access a textbook that was used in Pennsylvania public schools in the mid-nineteenth century. The focus of Edward Brooks' textbook is to impart the mental skills required for success at arithmetic on public school students. In the introduction, the author criticizes the state of arithmetic teaching, stating that the methods current as of this text's publication were focused too much on formulas and not enough on developing mental skills. Thus, the focus of The Normal Mental Arithmetic is to teach students to use their ingenuity to solve mathematical problems. The book is structured as most textbooks are, with the text divided into lessons, each of which either presents a new topic or builds on a previously discussed topic. The majority of the work is a series of sample questions to be posed to students, with little in the way of explanation. Unlike many textbooks, the correct responses are not included anywhere in the book. The Normal Mental Arithmetic is not a candidate to be used in the classroom today. Modern teaching methods and textbooks have evolved far beyond those of the nineteenth century, and this book is good evidence of that development. The book is thus valuable to those interested in examining the history of educational methods and practices, and anybody else keenly interested in nineteenth century textbooks. The Normal Mental Arithmetic poses arithmetic problems that can still serve as good practice for the mathematic learner, however other facets of this text make it less suited for use in today's classroom. If you are a reader seeking to examine a nineteenth century textbook, Edward Brooks' work is a good example of one that was used in public schools throughout Pennsylvania.
William Timothy Call was a mathematician and an individual interested in using mathematics to improve daily life. In A New Method in Multiplication and Division, Call presents a method he personally devised to solve multiplication and division problems. In his introduction the author acknowledges that the method presented in this book is of no great significance, rather it is a curious way of attacking a problem that likely differs from what the reader has been taught. It is clear from the beginning that this is a book aimed at those with a keen interest in math. The book opens with Call's method for solving simple multiplication problems, before progressing to his method for problems of division. A New Method in Multiplication and Division is a brief work and one that will appeal to those for whom mathematics is a hobby. The subject matter is largely trivial, and while the methods detailed are effective, they are presented largely as a novelty. Those who are passionate about mathematics will likely enjoy the casual approach of the author and the general tone of the book. For readers passionate about mathematics and problem solving, William Timothy Call's A New Method in Multiplication and Division is recommended. This is not a textbook or a resource guide, but rather a lighthearted presentation of a simple but alternative mathematical approach, intended to entertain and inform the reader.
This work outlines for students of the third and fourth high-school years a more advanced and more thorough course in applied business mathematics than the ordinary first-year course in elementary commercial arithmetic. The attempt has been made to construct a practical course which will contain all the essential mathematical knowledge required in a business career, either as employee, manager, or employer.<br><br>The fact that the field has been covered in this text both more intensively and more comprehensively than it has yet been covered in other texts, and the added fact that the material gathered together has stood the test of six years experience in the teaching of large and varied classes of the fourth year in a city high school, seem sufficient warrant for its publication.<br><br>The work is adapted not only for use in the classroom but also as a reference manual for those actively engaged in business life. Thus it will be found a practical guide for, young employees who wish through private study to master the fundamental mathematics involved in "running a business." The tabulations, forms, illustrative examples, charts, logarithmic applications, and simple rules, are all applicable to the financial and other mathematical problems which business presents. Lack of knowledge of this side of a business, or inability to work out its mathematics, often results in haphazard guessing where accurate and careful calculations are required.
It is the business of schools to give children during the first six years of school life that kind of instruction in mathematics which will lead them to a quick recognition and a ready knowledge of number combinations and number operations, and then enable them to apply these number combinations and number operations to the solution of simple problems. The instruction for this period, if it is to serve its purpose, must be definite and specific.<br><br>At the end of the sixth year the pupil should have a thorough mastery of the number combinations in integers; of the four fundamental operations with integers, common fractions, and decimal fractions; of the common measurements; and of the use of all of these in the solution of problems. Since eternal review is the price of excellence in all mathematical work, especially in computations, this book contains a complete but not lengthy review of the work of the first six years. The reviews are arranged elastically, however, so that the time devoted to them can be determined by the needs of the class. Monotony, the one great drawback of reviews has been removed by connecting the matter reviewed by historical references of interest, by looking at it from a standpoint of business, by number contests, by using the matter to be reviewed as a background for new work.
This text differs widely from that marked out by custom and tradition. It treats the various branches of mathematics more with reference to their unities and less as isolated entities (sciences). It seeks to give pupils usable knowledge of the principles underlying mathematics and ready control of them. These texts are not an experiment; they were thoroughly tried out in mimeograph form on hundreds of high school pupils before being put into book form. The scope of Books I and II does not vary greatly from that covered in algebras and geometries of the usual type. However, Book I is different in that arithmetic, algebra, and geometry are treated side by side. The effect of this arrangement is increased interest and power of analysis on the part of the learner, and greater accuracy in results. Some pupils like arithmetic, others like algebra, still others like geometry; the change is helpful in keeping up interest. The study of geometry forces analysis at every step and stage; consequently written problems and problems to be stated have no terrors for those who are taught in this way. For several years mathematical associations have urged that all work should be based upon the equation. In accordance with this view we have made the demonstrations in this book largely algebraic, thus making the demonstration essentially a study in simultaneous equations. In this method of treatment, we have found it advantageous not to hurry the work. Pupils gain power, not in solving many problems, but in analyzing and tio?oxt 3 xaAwafcaxs.- ing the principles of a few.
The course of study in American high schools is in process of extensive change. The change commenced with the introduction of new subjects. At first science began to compete with the older subjects; then came manual training, commercial and agricultural subjects, the fine arts, and a whole series of new literary courses. In the beginning the traditional subjects saw no reason for mixing in this forward movement, and such phrases as "regular studies," "substantial subjects," and "serious courses" were frequently heard as evidences of the complacent satisfaction with which the well-established departments viewed the struggles for place of the newer subjects. Today, however, the teachers of mathematics and classics are less anxious than formerly to be classified apart. Even the more conservative now write books on why they do as they do and they speak with a certain vehemence which betokens anxiety. They also prepare many editions of their familiar type of textbook, saying of each that it is something which is both old and new. All these indications make it clear that the change in the high-school curriculum which began with the introduction of new subjects will not come to an end until many changes have been made in the traditional subjects also.<br><br>Over against the obstinate conservatism of some teachers is to be set the vigorous movement within all subjects to fit them effectively to the needs of students. The interest of today is in supervised study, in better modes of helping students to think, in economy of human energy and enthusiasm. This means inevitably a reworking of the subjects taught in the schools. It is the opportunity of this generation of teachers to work out the changes that are needed to make courses more productive for mental life and growth.<br><br>During this process of reform, mathematics has changed perhaps less than any other subject.
The Culmination of the Science of Logic. The striking analogy between the necessary forms of the process of reasoning and the simplest forms of geometry, exhibited by the author in that book, led him to the reflection that perhaps the processes of geometry would have been greatly simplified, and its operations therefore more easily performed, if the regular triangle and tetrahedron, instead of the square and cube, had been adopted as units of measure of surface and solidity. The determination of this question, as the author was well aware, required a better acquaintance with such operations and processes than he possessed, he being but a tyro, in the secondary sense of that word, in. mathematical science. A tyro may, however, ask questions; but to ask a question without at the same tittle giving, some reasons for the asking, would be to obtain Jf 6 it but slight and insufficient attention.
eBook
Rapid ArithmeticQuick and Special Methods in Arithmetical Calculation Together With a Collections of Puzzles and Curiosities of Numbers
by T. O'Conor Sloane
Rapid Arithmetic: Quick and Special Methods in Arithmetical Calculation, authored by doctor and lawyer T. O'Conor Sloane, is a guidebook to improving your mental math skills. The book is a mixture of valuable and applicable strategies for solving problems of arithmetic, and simple and amusing mental diversions. It is a work that treats the subject of mathematics as something that can be enjoyed. Rapid Arithmetic opens with a brief section on notation and signs before delving more fully into the subject matter. Separate chapters are presented covering addition, subtraction, multiplication and division, as well as fractions, the decimal point, exponents, and several other topics. Each chapter consists of an overview of the topic, as well as a variety of different strategies for tackling different mathematical problems. The author presents short practice activities throughout the work, intended to both reinforce the lesson and serve as fun diversion for the reader. T. O'Conor Sloane has a gift for making a challenging subject entertaining. Rapid Arithmetic is not a book only for the math enthusiast, but for anybody that sees the value in honing their arithmetical skills. It is a well-written and clearly presented treatise on the topic. Rapid Arithmetic: Quick and Special Methods in Arithmetical Calculation is the rare text about mathematics that can appeal even to one not interested in the subject. Sloane's methods can actually improve the daily life of the reader by allowing one to more quickly work out common math problems, and for this reason his work is highly recommended.
Counting a series of things and keeping tally of the tens on the fingers were processes used by primitive peoples. From the ten fingers arose ultimately the decimal system of numeration. Recording the results of counting was done by the Egyptians and other ancient nations by means of strokes and hooks; for one thing a single stroke | was made, for two things two strokes || were used, and so on up to ten which was represented by Π. Then eleven was written |Π, twelve ||Π, and so on up to twenty, or two tens, which was represented by ΠΠ. In this way the numeration proceeded up to a hundred, for which another symbol was employed.<br><br>Names for ||, |||, ||||, ΠΠ, etc., appear in the Egyptian hieroglyphics, but a special symbol for each name is not used. Probably the Hindoos first invented such symbols, and passed them on to the Arabs, through whom they were introduced into Europe.<br><br>2<br><br>Greek Notation<br><br>The Greeks used an awkward notation for recording the results of counting.
Thi 8 work was commenced sixteen years ago at the earnest solicitation of numerous teachers, who were dissatisfied with the textbooks then in use. That they were not alone in their opinion is evidenced by the number of new treatises, or revisions of old ones, printed since that time, and now used in the schools of this country. The crudeness of even the best Algebras of a quarter-century ago was mainly owing to the fact that, as a rule, mathematicians neglected the elementary branches for the more attractive fields of Higher and Applied Mathematics; hence blunders and inconsistencies were allowed which otherwise would not have been tolerated. The wonderful progress made in the Natural Sciences, and the extended use of Algebra in the treatment of Geometrical Magnitudes, have finally called the attention of educators to the necessity of improving the elementary treatises, and more rigidly limiting the meaning of the signs. That this agitation comes none too soon is evident to every thoughtful teacher, and can be readily seen by auy one who compares the various text-books used in our schools. Note the following inconsistencies: In some text-books now before me, 6 : 7 equals f;in others, 6 : 7 equals. In some, 6 -f 4 X 2 = 20;in others, 6 -- 4 X 2 = 14.Of course, the meaning and use of a sign depend upon agi eement, but it is of extreme importance that we do agree in such matters. In the same work, too, statements incompatible with each other are made; thus, a -i-bc and a -i-b Xc are said to have different values, and yet be and bXc are, in all woi ks, said to have one and the same meaning. Since a-h be and a -ib Xe differ only in She use of bXc for be, it is plainly necessary that one or the other of these two statements be changed. One of the objects in writing this book is to urge the adoption of the following law for Numerical Values; viz.,(l) Find the value of each term separately; thus, 6-f-4X 2 = 6 -f8= 14. (2)In finding the m, lue of a term, begin at the Right and use the signs in their oi der; thus, 6-f-4x 2 = 6-r-8= f.In other words, the jm tion of the term to the left of the division sign is the Dividend, and the part to the right is the divisor.
The arrangement is by subjects in order that a student may select those problems in which he is most interested, and that a teacher may readily arrange a course to meet the needs of his particular school. It is suggested that the work of the shop be correlated with that of the mathematical classroom. For example, when a student in a manual training high school is beginning to handle boards in the shop, he is commencing the study of algebra in his mathematical classroom. Let him be assigned some problems in the chapter on Board Measure, together with a review of work in fractions. From these problems he will acquire considerable information that will be useful in the shop, and from the formulas in board measure he will understand the meaning of letters as symbols of general number. If I and tstand for the length and thickness of the board that the student has just sawed off in the shop, they will have a definite meaning to him. The authors hope that the book will be found useful in any school where there are shops. It is adapted for use in the shop or the mathematical classroom, or in both. A student of this book should develop an appreciation of the value of mathematics in practical work, since all problems in the book are based on actual shop practice. He should learn to make a formula, solve it for any letter, and apply it intelligently. As he progresses the approximate nature of the results in real problems should become evident. He should learn that real problems very rarely come out even, that there is usually an allowance necessary for waste, and he should develop a certain judgment as to what that allowance is.
Teacher's Manual for First-Year Mathematics is a book written by George William Myers, a Professor of the Teaching of Mathematics and Astronomy at the University of Chicago. The book is intended as a teaching manual for teachers instructing their students using a textbook called First Year Mathematics. Myers' book is intended as a companion piece to the textbook First Year Mathematics, released by the same publishing company, The University of Chicago Press. The book makes effort to assist the teacher by providing them with a detailed how-to regarding teaching the specific problems presented in the textbook. Teacher's Manual is presented in chapters, each corresponding to a chapter in First Year Mathematics. Specific references are made to page numbers and problems presented in the textbook. In total, the book contains fourteen different chapters. Teacher's Manual for First-Tear Mathematics can only be used in conjunction with the appropriate textbook. Without access to First Year Mathematics, the book is of no use. It is however an excellent companion piece to the textbook, and those able to access the original textbook will surely find this text to be highly beneficial. While a well-written teacher's manual, George William Myers' book assumes the reader has access to the original textbook. If you are interested in making use of this manual, do ensure that you are also able to access First Year Mathematics.
A Textbook on Plumbing, Heating, and Ventilation was written by International Correspondence Schools in 1897. This is a 339 page book, containing 73443 words and 48 pictures. Search Inside is enabled for this title.
Mathematical Theory of the Stationary, Marine, and Locomotive Engines, has long been a desideratum; not only as an introduction to Tredgold slarge and important work on the same subject, but also for the use of a numerous class of students, who either have not time to read or the means of purchasing the large work just referred to. The author of this Introduction has taken great pains to supply this link in the chain of scientific research so much required, as well as to adapt it to the wants of practical men, by giving rules in words at length for their use; also for students who have not yet accustomed themselves to the application of mathematical formula?, by which their progress in studies of this kind will be greatly facilitated, until at length they arrive at full competence in both the theoretical and practical parts of these important subjects, and thus be prepared to understand with ease the various complexities of Tredgold slarge and complete work.
Elementary Mathematics. For this purpose it is certainly not necessary that the student should master the complex scheme of rigid argument from which these principles are ultimately deduced; for example, the Sixth Book of Euclid is in no way essential to an accurate practical knowledge of the properties of Similar Figures. A large number of worked examples have been inserted, and the book is well supplied with examples for practice. Both have been chosen with a view to elucidate principles, and to train the intelligence. The chapters on Algebra are intended to give the student a thorough grasp of the meaning and use of Algebraical Symbols, Formulae, and Equations, including equations of Variation. The theory of Indices has been explained with a view to its use in Logarithms. More complex algebraical operations, such as the manipulation of difficult fractions, have been omitted. In Geometry, both Plane and Solid, every effort has been made to appeal directly to the sense of shape and measurement, and to give suitable practice in the use of Mathematical Instruments for geometrical calculation. In Descriptive Geometry it is especially necessary to warn the student not to learn rules by rote, but to remember them in connection with the solid figures to which they are intended to apply.
While many distingmshed teachers unite in pronouncing my Elementary Arithmetic as the best work of the kind, well adapted to the purpose of teaching the science, as we Uas the art, of Arithmetic; others haye often expressed to me their belief that its usefulness would be greatly in creased by the addition of more examples of a practical kind; and in many cases I have been strongly urged to omit the answers. I am convinced that for certain grades of institutions it would be w;ell to have a greater variety of examples for practice, bu I do not so readily see the advantage of omitting the answers. I have always been inclined to believe the omission of the answers gave an opportunity for the pupil, and in seme cases for the teacher, to pass over many principles without thoroughly understanding them, since a result would frequently be obtained which might perhaps be quite erroneous; and having no answer with which to compare it, he dismisses the subject with the belief that he has conquered the difficulty, and that he imderstands clearly the principle especially designed to be brought outby the example.
This book is the result of twenty years of patient experiment in actual teaching. It is intended to be completed in the first year of the high school. It presents algebraic equations primarily as a device for the solution of problems stated in words, and gives a complete treatment of numerical equations such as are usually included in high-school algebra - one-letter and two-letter equations, integral and fractional, including one-letter quadratics and the linear-quadratic pair. So much of algebraic manipulation is included as is necessary for the treatment of these equations.<br><br>The arithmetic in the book is presented from a new point of view - that of approximate computation - and is utilized in the evaluation of formulas and in the solution of equations throughout the succeeding pages.<br><br>Geometrical facts are introduced as the basis of many algebraic and arithmetic problems, and wherever they are not intuitively accepted by the pupils they are accompanied by adequate logical demonstration. Proofs, and parts of proofs, are avoided when they seem to the pupils of an unnecessary and hair-splitting kind.<br><br>All problems are carefully graded, for it is by means of problems that each successive algebraic difficulty is introduced.<br><br>A great deal of pains has been taken to present new topics clearly and concretely, often dividing them into sub-topics each of which is separately illustrated and applied to practice. Definitions are generally prepared for by such advance work as will cause the student to feel the need of them; and where no need exists, they are omitted.
In this book, as in Junior High School Mathematics, Book I, the subject is presented in a natural psychological way. As in Book I, the treatment is also in accordance with the accepted views of a great majority of educators who have made exhaustive investigation of the ways and means available to get the most value out of mathematics in the organized junior and senior high school courses.<br><br>The work for the seventh year found in Book I has been connected by indissoluble bonds with the work of the eighth year found in this succeeding book, Book II, and the work found here will in turn be connected with the work to be found in Book III by equally close and strong connecting ties. The author, for the purpose of providing a continuous stream of consecutive work for a three-year course, has adopted the same basic method. It is best described, perhaps, by calling it without fear or favor the topical plan spiralized. Each topic is treated at sufficient length to create a lasting impression, and ever thereafter at intervals is brought up in reviews. The need of this eternal vigilance in review work, and the special demand of modern business and industry for greater facility in the handling of the four fundamental operations, is met by introducing this second book with the four fundamental operations with integers. As in Book I, these reviews are elastic, and can therefore be made to fit the needs of any particular class.
It is the authors hope and desire that this book, which is the outcome of years of study, work and observation, may be a help to the class of people to which he himself has the honor to belong, the working mechanics of the world. This is not intended solely as a reference book, but itmay also be studied advantageously by the ambitious young engineer and machinist; and, therefore, as far as believed practical within the scope of the work, the fundamental principles upon which the rules and formulas rest are given and explained. The use of abstruse theories and complicated formulas is avoided, as it is thought preferable to sacrifice scientific hairsplitting and be satisfied with rules and formulas which will give intelligent approximations within practical limits, rather than to go into intricate and complicated formulas which can hardly be handled except by mathematical and mechanical experts. In practical work everyone knows it is far more important to understand the correct principles and requirements of the job in hand than to be able to make elaborate scientific demonstrations of the subject; in short, it is only results which count in the commercial world, and every young mechanic must remember that few employers will pay for science only. What they want is practical science. Should, therefore, scientific men, (for whom the author has the greatest respect, as it is to the scientific investigators that the working mechanics are indebted for their progress in utilizing the forces of nature), find nothing of interest in the book, they will kindly remember that the author does not pretend it to be of scientific interest, and they will therefore, in criticizing both the book and the author, remember that the work was not written with the desire to show the reader how vulgarly or how scientifically he could handle the subject, but with the sole desire to promote and assist the ambitious young working mechanic in the worlds march of progress. P.Lobben. New York, October, 1899. |
It is assumed that the reader has a background in mathematics, including calculus.
Integrated navigation systems is the combination of an onboard navigation solution (position, velocity, and attitude) and independent navigation data (aids to navigation) to update or correct navigation solutions.
In this book, this combination is accomplished with Kalman filter algorithms.
This presentation is segmented into two parts.
In the first part, elements of basic mathematics, kinematics, equations describing navigation systems/sensors and their error models, aids to navigation, and Kalman filtering are developed.
Detailed derivations are presented and examples are given to aid in the understanding of these elements of integrated navigation systems.
For more information about the title Applied Mathematics in Integrated Navigation Systems (Aiaa EducationSecure Updates for Navigation Systems(October 10, 2011) — At the push of a button by the driver, control units download the car manufacturer's new software -- such as enhanced map material for the navigation system. To ensure that this data channel is ... > read more |
Why Autograph?
Why is Autograph different? Autograph is widely used by teachers and students on PCs and Macs, in the UK and many other countries of the world, and a version for IOS and Android tablets is well under way.
Autograph can help to visualise key concepts through dynamic objects,
and the user interface is straightforward and friendly.
Autograph has been localised in 21 languages (including Arabic).
There are a large number of resources online (videos, data, images, tutorials) and files can be saved straight to HTML for viewing on the web.
This session will cover graphing topics for the younger students. The interface gives users time to explore and investigate using a controllable 'slow plot' feature, and animations are particularly effective because of the ability to control the step in real time.
Topics covered will include the transformations of shapes and functions, fitting some mathematically interesting images, and some elementary data handling.
The tablet version is still under development, but this will be a rare opportunity for a sneak preview of this exciting new 'Cloud-based' version of Autograph.
AUTOGRAPH
for 16-19 year olds
11:00-13:00
As the material gets more advanced, the possibilities for using controllable dependent objects become more involved and more effective. This session will explore 2D topics from coordinate geometry to differential equations, and 3D topics from transformations of shapes to surfaces, lines and planes, and volumes of revolutuion.
There are also many opportunities to use Autograph in the teaching of probability and statistics topics from High School and 1st year College courses using real data. The study of discrete and continuous probability distributions is particularly effective in Autograph, including a clear treatment of Type 1 and Type 2 errors. |
Elementary Algebra W/PAC-Now
9780495389606
ISBN:
0495389609
Edition: 4 Pub Date: 2008 Publisher: Cengage Learning
Summary: This text blends instructional approaches that include vocabulary, practice, and well-defined pedagogy, along with an emphasis on reasoning, modeling, and communication skills. With an emphasis on the 'language of algebra', the author's foster students' ability to translate English into mathematical expressions and equations.
Tussy, Alan S. is the author of Elementary Algebra W/PAC-Now, published 2008 under ...ISBN 9780495389606 and 0495389609. One hundred thirty seven Elementary Algebra W/PAC-Now textbooks are available for sale on ValoreBooks.com, thirty two used from the cheapest price of $6.98, or buy new starting at $80.96 |
2008 | Series: Manga Guide To...
Think you can't have fun learning statistics? Think againProduct Description
About the Author
Shin Takahashi graduated from the Graduate School of Design at Kyushu University in Japan. He has worked as a lecturer and as a data analyst and is currently employed as a technical writer. Takahashi has published several books in the Japanese Manga Guide series, including Statistics-Factor Analysis Edition and Statistics-Regression Analysis Edition (both published by Ohmsha).I've been a fan of the Manga Guide series for some time but none have proven as useful and as necessary as the two math guides, The Manga Guide to Calculus and the Manga Guide to Statistics. To be fair, I come from a physics background so I have a bias towards the quantitative, but I'll never refer back to the Manga Guides to Physics, Electricity, or the Universe the way I have read and re-read these two.
This isn't a knock on those other titles, which are excellent. But somehow these subjects and this format are just a perfect fit for each other. I need a quick refresher on a particular technique, it's explained clearly and a small number of sample questions are given. For someone who knows the material and needs a refresher, these guides can't be beat. For students studying them for the first time, I would pair these slim guides with a thicker textbook or problem set for practice (the one thing these guides don't have) for an unbeatable combination.
4.0 out of 5 starsanother cartoon book guiding students in elementary statisticsNov. 18 2008
By Michael R. Chernick - Published on Amazon.com
Format:Paperback
I loved "The Cartoon Guide to Statistics" because it was humorous very simply told and yet accurately taught. Some of the material is so good that I now use it in my introductory biostatistics course.
The Manga Guide to Statistics does similar things but a little differently. This book is in cartoon strip form and the characters are familiar to many kids who these days wacth the Japanese cartoons on television and read the comic books. This includes my son Daniel who is a high school junior. Dan hates to read but loves math and science and this is the first statistics book that intrigued him enough to read it! I know is reading it and enjoying learning from it by the questions he asks. So like the other cartoon book on statistics this too is a gentle introduction for those with math skills and those with an aversion to mathematics. It shows how statistics is practical by illustrating the techniques on everyday real world data, such as the scores of bowling team players at a bowling alley. It covers the basic summary statistics, correlation, hypothesis testing and probability distributions. What I found interesting was that in addition to the ordinary Pearson product moment correlation they also provided intra-class correlation and Cramer's V (for categorical data). These methods are rarely covered in elementary texts.
One thing it has that is missing in "The Cartoon Guide to Statistics" is the teaching of how to use the computer to apply what they learn. In the final chapter they do this using Excel and teaching things step by step using screen shots of excel spreadsheets.
Throughout the book when a new statistic is introduced they go through the step by step details of the calculations. This is something that student do not necessarily need to learn in the age of computers and statistical computer packages. However, going through the tedium of the calculations has a way of reinforcing the concepts and it gives the student a better understanding of exactly what a variance and a standard deviation are.
I recommend this book for high school students to supplement what they learn in class or for independent self-learning. College student with weak math backgrounds who need an introduction to statistics may also find this book useful and interesting. It is working wonders for Dan who now wants to get the soon to be published Manga guides to physics, calculus, microbiology and databases! Unfortunately this one is the first to come out and the others won't appear until later in 2009.
14 of 14 people found the following review helpful
5.0 out of 5 starsBest statistics book ever. Buy now.March 28 2009
By Mike - Published on Amazon.com
Format:Paperback
I don't know where to start. This is the best statistics book. Ever.
I never thought I'd say this, but the authors have made a book on statistics FUN without dumbing it down (this effectively covers at least the entirety of a college level stat intro class).
As a student, this cleared up many problems I'd been having operationalizing fairly advanced formula within Excel. The chapter on inputting statistical formulae in Excel is amazing and worth the cost of the book in itself. The explanations of the formulas use concrete, real world examples. No gambling examples or other unnecesarily abstract or standard scenarios.
As a teacher, I bow down to Mr. Takahashi and the folks at Trend-pro. Their pedagogical expertise is unparalleled. I can only hope that one day I am 1/10th the teacher this man is. He made statistics, a fairly dry subject, not just palatable, but entertaining.
Arigato.
39 of 46 people found the following review helpful
2.0 out of 5 starsMuch Fun, Too Many ErrorsSept. 24 2009
By JT - Published on Amazon.com
Format:Paperback|Amazon Verified Purchase
Since I enjoyed the Manga Guide to Statistics, I guess the author achieved at least one objective of good teaching - keep the learner interested. The use of well thought out graphics and humorous examples are likely to encourage a learner to attend to the content. Still, maintaining interest and good teaching, while related, are not identical. One can maintain interest in ways that detract from learning as well as in ways that enhance learning. The tendency in this text to oversimplify (e.g., the discussion of what is and is not "measurable" at the beginning of the book, the underemphasis of the importance of random selection) are definite negatives. They will lead a learner with no background in the use of statistical procedures to mistaken conclusions about the meaning of measurements and the generalizability of findings. In at least one case, the oversimplification proceeds to the point of presenting information that is wrong (i.e., the examples of alternative hypotheses on pp. 172-173). To be fair, there are many "gentle" statistics texts that, as does the Manga Guide to Statistics, present the notion that the alternative hypothesis is simply "not the null hypothesis." Despite the popularity of this view, Neyman and Pearson (who developed statistical hypothesis testing theory 75 years ago) noted that the "not the null" formulation of the alternative hypothesis would lead to the acceptance of trivial effects as meaningful simply because they were "statistically significant." The "not the null" formulation of the alternative hypothesis creates other problems. For example, the null hypothesis on page 173, "The allowances of high school girls in Tokyo and Osaka are the same," has as its alternative, "The allowances of high school girls in Tokyo and Osaka are not the same." Stating the alternative hypothesis in this way does not permit an evaluation of the power of a statistical test (power refers to the probability that a test will detect a difference, change or relationship when it is present). As Neyman noted, since the test would have to detect an infinitesimal difference, the power would necessarily be infinitesimal as well. Instead, an alternative hypothesis should specify a minimum effect, e.g., "The allowances of high school girls in Tokyo and Osaka differ by an average amount of at least ¥500." By specifying a minimum effect to be detected, we can find the probability that a statistical hypothesis test would detect a difference of at least ¥500 (the test's power). Since I have to devote time to "unteaching" the "not the null" formulation of the alternative hypothesis, I am far from thrilled to see it here. Convincing learners that the easily understood "not the null" definition is wrong usually requires a lot of work and pain. After all, who likes being told that what they thought they understood, is what they still do not understand? This makes it more difficult for me to help my students understand the central importance of power to statistical testing. And, as Neyman pointed out, the power of a test is the main determinant of how useful it is. It may seem that I am asking too much of an introductory text. I do not think so. It is my experience that one must engage in some fairly sophisticated reasoning to understand the meaning of the results of a statistical analysis. The simple, obvious interpretation is almost always wrong (cf., Darrell Huff's How to lie with statistics). We do a learner no favors by simplifying a complex process to the point where we deceive the learner into thinking that they understand something that they do not. The trick (which I am still working on mastering) is to help learners learn how to enjoy the challenge of minimizing, but still living with, uncertainty (an important element of all statistical reasoning) and also to help them learn to be suspicious of "easy" answers. I recently got around to reading W. Edwards Deming's book, Out of the Crisis. In it, he made an observation about maintaining learner interest and quality teaching that is relevant to this book: "In my experience, I have seen a teacher hold a hundred and fifty students spellbound, teaching what is wrong." The Manga Guide to Statistics held my interest from the moment I started reading it. In fact, I read it in one sitting. I honestly enjoyed reading it, but it is wrong in too many places. I purchased the Manga Guide to Statistics thinking that I might use it in my introductory research methods courses. I shall not use it. I shall not recommend it. I shall not mention it.
Note: I apologize for the lengthy discussion of the alternative hypothesis. I am afraid that I am not clever enough to find another way to demonstrate the problem of oversimplification.
Neyman, J. & Pearson, E. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 231, 289-337. |
More About
This Textbook
Overview
Math for Welders is a combination text and workbook designed to help welding students learn and apply basic math skills. The basic concept behind each math operation is explained at the opening of the unit. Next, students are given clear instruction for performing the operation. Each unit includes a variety of weldingrelated practice problems to reinforce what the students have learned. The practice problems are identical to the types of problems the students will be required to solve in a welding shop. In addition to teaching basic math concepts, the problems give students a preview of the types of challenges they will face in a work environment. This helps the students develop solid troubleshooting skills that will serve them throughout their careers as welders.
Related Subjects
Meet the Author
After graduating from Wayne State University, Mr. Marion invested several years working for Chrysler Canada. He then transitioned to a teaching position at St. Clair College, focusing on math and technical drawing. Mr. Marion used his collective knowledge and experience to author Math for Welders as a career capstone |
Editorial Reviews
Review
This book is highly recommended for geometers of all ages and a wide range of expertise. It would be an excellent resource for a course taught with Dynamic Geomeetry Software. --Mary Coupland, Australian Mathematics Teacher
Book Description
The interesting theme of this book is that it is often the case that when some lines intersect, there are others that must also be part of the same intersection. Furthermore, there must be a reason why they intersect. Walser uses diagrams to display the intersections and there are three sections in the book. The first section is the introduction, where equations and their corresponding figures are presented. Section two is a series of 99 diagrams where the emphasis is on how they intersect. Each starts with three small figures, which build towards the larger, complete structure. The third and final section is a brief description of some well-known geometric proofs such as Jacobi's Theorem, Kiepert's Hyperbola and Ceva's Theorem.
I was fascinated with some of the 99 figures in the second section. They are designed to be understood as-is without having to resort to equations and textual descriptions. I found that to be the case, it was a rare instance when I had to look at the diagram for more than a few seconds before I understood it. This is an interesting way to teach the joy and wonder of mathematics. For in many cases if I had not seen the diagram, I would not have believed that so many different lines would have intersected the way they did. Especially when the intersection is a single point.
Published in Journal of Recreational Mathematics, reprinted with permission |
book of the Mathematics in Actionseries, Algebraic, Graphical, and Trigonometric Problem Solving , Fourth Edition, illustrates how mathematics arises naturally from everyday situations through updated and revised real-life activities and the accompanying practice exercises. Along with the activities and the exercises within the text, MathXL®and MyMathLab®have been enhanced to create a better overall learning experience for the reader. Technology integrated throughout the text helps readers interpret real-life data algebraically, numer... MOREically, symbolically, and graphically. The active style of this book
Cluster 2. Why Are the Trigonometric Functions Called Circular Functions?
Activity 6.6 Learn Trig or Crash!
Objectives:
1. Determine the coordinates of points on a unit circle using sine and cosine functions.
2. Sketch a graph of y = sin x and y = cos x.
3. Identify the properties of the graphs of the sine and cosine functions.
Activity 6.7 It Won't Hertz
Objectives:
1. Convert between degrees and radian measure.
2. Identify the period and frequency of a function defined by y = a sin (bx) or
y = a cos (bx) using the graph.
Activity 6.8 Get in Shape
Objectives:
1. Determine the amplitude of the graph of y = asin (bx) or y = a cos (bx).
2. Determine the period of the graph of y = a sin (bx) or y = a cos (bx) using a formula.
Activity 6.9 The Carousel
Objective:
1. Determine the displacement of the y = a sin (bx + c) and y = a cos (bx + c) using a formula.
Activity 6.10 Texas Temperature
Objectives:
1. Determine the equation of a sine function that best fits the given data.
2. Make predictions using a sine regression equation.
Cluster 2 What Have I Learned?
Cluster 2 How Can I Practice?
Chapter 6 Summary
Chapter 6 Gateway Review
Appendix A: Concept Review
Appendix B: Trigonometry
Appendix C: Getting Started with the TI-83/TI-84 Plus Family of Calculators
Glossary
The Consortium for Foundation Mathematics is a team of fourteen co-authors, primarily from the State University of New York and the City University of New York systems. Using the AMATYC Crossroads standards, the team developed an activity-based approach to mathematics in an effort to reach the large population of college students who, for whatever reason, have not yet succeeded in learning mathematics. |
Hotmath.com.
HOTMATH.COM(1) (Computer Output Microfilm) Creating microfilm or microfiche from the computer. A COM machine receives print-image output from the computer either online or via tape or disk and creates a film image of each page. . Hotmath, Inc. (18 Sunset DriveSunset Drive, locally known as Sunset Drive and Southwest 72nd Street, is an east-west street that runs south of downtown Miami, Florida in Miami-Dade County, Florida. , Kensington, CA 94707; c2006. Online resource. $49 per year for single households or $.75 per student for districts; volume discounts available. Additional information via e-mail schools@hotmath.com. JSAJSA - Japanese Standards Association.
Hotmath.com provides online homework assistance for math students in the middle grades through college. Step-by-step solutions are provided for odd-numbered homework problems from over 150 math textbooks. While a complete listing of textbooks is not provided, prospective users can verify the inclusion of specific titles through a free trial membership. Topical coverage includes Pre-Algebra, Algebra I and II, College Algebra, Trigonometrytrigonometry [Gr.,=measurement of triangles], a specialized area of geometry concerned with the properties of and relations among the parts of a triangle. Spherical trigonometry is concerned with the study of triangles on the surface of a sphere rather than in the , Geometry, Pre-Calculus and Calculus. A science section is currently in development. Users navigate to their textbook problems through subject browsing (e.g., Algebra). Students select problems, receive hints for completing formula steps and arrive at problem solutions. Relevant concept reviews are linked from each problem. Site design and navigation is spare and straightforward. Advertising for companies such as Texas Instruments See TI. (company) Texas Instruments - (TI) A US electronics company.
A TI engineer, Jack Kilby invented the integrated circuit in 1958. Three TI employees left the company in 1982 to start Compaq. and Smarthinking.com (a live online tutoringOnline tutoring refers to the process by which knowledge is imparted from a tutor, knowledge provider or expert to a student or knowledge recipient over the Internet. Online tutoring has been around almost as long as the Internet and takes the following form:
service) is displayed in the margins of several pages.
A "More Resources" section contains movie tutorials for Texas Instruments graphing calculators, review lessons, workbook activities and answers, and math activities and games. Some of these areas are still in development and need additional content. Hotmath.com is an emerging tutorial resource best considered on a case-by-case basis depending on student and district needs. Its provision of online content linked to classroom textbooks is worth further examination as a model for expanded student support and services. Ernie Cox, Libn., St. Timothy's SchoolSt. Timothy's School (HDGHS) is a four-year private all-girls boarding high school in Stevenson in Baltimore County, Maryland, United States. The school is located just north of Baltimore City in Baltimore County less than a mile north of I-695, the Baltimore Beltway. , Raleigh, NC
J--Recommended for junior high school students. The contents are of particular interest to young adolescents and their teachers.
S--Recommended for senior high school students. |
We will also make use of other resources as
listed on the course Resources web page.
Scientific Computing is something of a hybrid
subject, somewhere between
mathematics, computer science, and the other natural sciences.
The fundamental questions in this field deal with approximating
solutions to the equations underlying
mathematical models of physical processes. To construct robust
and accurate approximations
one needs to understand fully the mathematical theories and structures
that lead to exact solutions. However, once an efficient
and
accurate approximation scheme has been developed mathematically, it
must
be formalized in an algorithm so that a solution can be computed. Then
the output of the algorithm must be checked with the original physical
model to ensure that the mathematics is representative of reality.
In this course we will look at a wide variety of practical
situations
where numerical approximation of solutions is needed. Most of
these
will involve mathematical models of physical processes such as
the spread of disease, chemical reactions, and mechanics, as well as
models
in the social sciences.
Computer Work:
Implementation of algorithms will also be an important component of
the course. We will be using the computer software system Matlab as
our programming environment for algorithm design and analysis.
Matlab is the most commopnly used software package for numerical
computations in engineering and science. Matlab is located on all
of the computers in the MCS lab and elsewhere on campus. An
open-source "clone" of Matlab called FreeMat
is also available at
. There are versions of FreeMat available for Windows/Mac/Linux.
FreeMat is about 95% compatible with MatLab and should be
adequate for the projects in this course. Another open-source
alternative is Octave (
Matlab
is commercial software, and a full version is quite expensive. However,
there is a student version available for $99 (
One of the main advantages of the student edition is that it comes with
many very useful toolboxes beyond the base-level software (for example,
the Symbolic Toolbox that is a powerful package for symbolic algebra).
The student edition is a good deal, since academic pricing for
Matlab is $500 for the base package and $200 per toolbox.
Course Format: The course
will be structured as a seminar/discussion/lab course. Daily
readings
will be assigned and then discussed in the classroom. Additionally,
class time will be spent on brain-storming algorithm design and
testing. Outside research into applications of computaional
algorithms will be assigned from time to time, with reports given by
students during class. Approximately one day a week will be spent on
computer implementation of computational algorithms.
Assignments:
We will have periodic homework and programming assignments.
Assignments
will be given out in class and will also be on the course web
site.
There will be 3 projects (or problem sets) during the term. These
will involve a
more in-depth investigation into some course topic than would be
reasonable
for homework. The final project for the course will involve a
computational application, a written
report and an in-class presentation.
Final
Projects Presented: Presentations will take place the last
week of
classes and during the class's scheduled final period, which isFriday, May 18, 8am-10am.
Honor Policy:
Students are expected to abide by the college's Academic Honesty
Policy. Students are
encouraged to
discuss with one another topics from the course. However, the
work
done in the homework assignments, on lab projects, and on the final
project should be individual work unless otherwise
specified.
If you are having difficulty with an assignment you may ask fellow
students for assistance in understanding the assignment, but not for
assistance in doing the assignment. Feel free to ask me for
assistance at any time.
Disability
Services: Gustavus
Adolphus College is committed to ensuring the full participation of all
students in its programs. If you have a documented disability (or you
think you may have a disability of any nature) and, as a result, need
reasonable academic accommodation to participate in class, take tests
or benefit from the College's services, then you should speak with the
Disability Services Coordinator, for a confidential discussion of your
needs and appropriate plans. Course requirements cannot be waived, but
reasonable accommodations may be provided based on disability
documentation and course outcomes. Accommodations cannot be made
retroactively; therefore, to maximize your academic success at
Gustavus, please contact Disability Services as early as possible.
Disability Services is
located in the Advising and Counseling Center. |
N.E. Leonard and W.S. Levine
From the back cover of the 2nd edition:
Now your students can learn MATLAB 4.2, a remarkable time-saving tool
for anyone who studies or designs control systems. Through extensive
interactive examples and exercises that demonstrate MATLAB fundamentals
and its plotting capabilities, students quickly learn how to use the
software to perform calculations and generate graphs essential to
control system analysis and design.
The manual includes an introduction to SIMULINK software and Handle
Graphics. With SIMULINK, students can use block diagrams to simulate
linear and nonlinear systems and display the results.
Handle Graphics is MATLAB's tool for customizing graphics.
Using MATLAB follows the organization of Norman S. Nise's Control
System Engineering, Second Edition and is an ideal supplement to
the text. This manual can also be used alone as an independent guide
to MATLAB for student and professionals, or with other
control systems texts. |
{"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":21.04,"ASIN":"0387331956","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":296.98,"ASIN":"053495166X","isPreorder":0}],"shippingId":"0387331956::pmysQxKtALxMVUh5ossUAR5ECfzJCrjG1%2BfDegmsW1sUHYmHbK8Ux2GlCWFmQ2pdS5ZN%2F0ImkDQ%2Fd4rsusTgByo8cqPTqi6LXowpOz%2FJ%2Bvw%3D,053495166X::SteJZhWt462cev1Y22M6kLL6Q8tZ7NepQHz6OPYjLVna12a8ozoXtobN7bF1fxEXDrv7JrLG23UCdvCB3NFn7cj%2FxPg8mn6Xr0MszREFt book under review is a nice blend of three independent components of linear algebra: Theory, computation and applications. … The book is consisting of the author preface, six chapters, table of symbols, solutions to selected exercises, a bibliography containing 13 references and subject index. … The book is very useful for undergraduate students and nonspecialists." (Mohammad Sal Moslehian, Zentralblatt MATH, Vol. 1128 (6), 2008)
"This book is intended for a one or two semester course, with emphasis on linear algebra as an experimental science. … The text is written in a nice conversational style. Proofs are provided for most results … . The author also provides many computer exercises, projects, and report topics … . Instructors wanting to encourage precision in mathematical writing will find these assignments helpful. … This is a good text for those who want to introduce their students to applied discrete mathematics … ." (Henry Ricardo, The Mathematical Association of America, September, 2008)
From the Back Cover
Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. The student will develop a solid foundation in the following topics
*Gaussian elimination and other operations with matrices
*basic properties of matrix and determinant algebra
*standard Euclidean spaces, both real and complex
*geometrical aspects of vectors, such as norm, dot product, and angle
*eigenvalues, eigenvectors, and discrete dynamical systems
*general norm and inner-product concepts for abstract vector spaces
For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable.
Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory.
This is a very well written book. The author brings the 'topic to life' by showing how the linear algebra can be used in an applied setting. Also the graphics enable the reader to understand the material from a geometric perspective, as opposed to merely looking at terse algebraic equations.
Finally, the hints and answers section at the back of the book are very good for self study.
I have adopted this book as one of the texts for my introductory course on applied math. It's well written and has a diverse set of good examples drawn from everything from computer graphics to sports betting. It's fun to read, and in general, good.
It is significantly better than Olver and Shakiban's book of similar title and scope, and a heck of a lot cheaper. In a course like mine where I use several specialized books rather than one of the massive tomes that try (and fail) to cover all of applied math, low price is a factor for me.
Negatives include: too few theory problems, a fair number of typos, relegation of the LU factorization to a problem set. On the whole, though, it's not bad. |
Short Description for The Mathematical Olympiad Handbook Olympiad problems help able secondary pupils develop their mathematical muscles. Good Olympiad problems are unpredictable: this makes them worthwhile, but it also makes them seem hard and even unapproachable. This book contains some of the Mathematical Olympiads 1965-1996 in a form designed to help bright students overcome this barrier. Full description
Full description for The Mathematical Olympiad Handbook
Mathematical Olympiad competitions started in Hungary at the end of the nineteenth century, and are now held internationally. They bring together able secondary school pupils who attempt to solve problems which develop their mathematical skills. Olympiad problems are unpredictable and have no obvious starting point, and although they require only the skills learnt in ordinary school problems they can seem much harder. "The Mathematical Olympiad Handbook" introduces readers to these challenging problems and aims to convince them that Olympiads are not just for a select minority. The book contains problems from the first 32 British Mathematical Olympiad (BMO) papers 1965-96 and gives hints and outline solutions to each problem from 1975 onwards. An overview is given of the basic mathematical skills needed, and a list of books for further reading is provided. Working through the exercises provides a valuable source of extension and enrichment for all pupils and adults interested in mathematics. |
This course begins with a brief review of what students should already know about linear equations, with a focus on analyzing and explaining the process of solving equations. Students develop a strong foundation in working with linear equations in all forms, and they extend solution techniques to simple equations with exponents. Students then explore functions, including notation, domain and range, multiple representations, and modeling. Through the comparison of linear and exponential functions, students contrast the concepts of additive and multiplicative change. Students then apply what they have learned to linear models of data, analyzing scatterplots and using lines of best fit to apply regression techniques. The course closes with an exploration of rational exponents, quadratic and exponential expressions, and an introduction to non-linear functions, with a heavy emphasis on quadratics. |
Help:Math
MediaWiki uses a subset of AMS-LaTeX markup, a superset of LaTeX markup which is in turn a superset of TeX markup, for mathematical formulae. It generates either PNG images or simple HTML markup, depending on user preferences and the complexity of the expression. In the future, as more browsers become smarter, it will be able to generate enhanced HTML or even MathML in many cases. |
The purpose of this handbook is to help students of applied analysis to organize the necessary resources for the successful completion of independent study projects. The nature of these projects is somewhat novel for mathematics classes- the...
MATHLIB is a general purpose interactive mathematical workbench for research and design that fills the need for an analysis tool which is simple enough for an inexperienced user but sophisticated enough to realistically cope with the complex...
MATHLIB is a general purpose interactive mathematical workbench for research and design that fills the need for an analysis tool which is simple enough for an inexperienced user but sophisticated enough to realistically cope with the complex...
This book is meant as a user's introduction to the MATHLIB interactive analysis package. Our purpose here is to present the fundamental concepts and facilities that are used throughout the software package. Familiarity with the fundamentals will... |
Study Abroad Information for Current Linfield Students
January Term Abroad
MATH-298 Traversing the Eulerian Trail
Leonhard Euler was one of the most prolific mathematicians of all time. More important, however, was his impact on almost every field of mathematics. There are few areas of mathematics in which Euler's contributions have not played a significant role. In this course we shall retrace his steps, beginning in St. Petersburg and Berlin. It is in these two cities that Euler spent the majority of his life, alternating between positions at the St. Petersburg Academy and the Berlin Academy. We then end in Basel, Switzerland, the town of his birth, and where Euler attended the Universität Basel. The focus of the course is the mathematics of Euler. We investigate his work and influence in number theory, infinite series, logarithms, algebra, combinatorics, and graph theory. In addition, we consider how the concept of "proof" has changed from Euler's time to the present. This course counts toward the major and minor in Mathematics.
Prerequisite: MATH 170 with MATH 175 strongly recommended. Students will be required to enroll and participate in IDST 098 Orientation for International Study (1 credit) in Fall 2013. |
Introductory Algebra: Applied Approach - 9th edition
Summary: As in previous editions, the focus in INTRODUCTORY ALGEBRA remains on the Aufmann Interactive Method (AIM). Students are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. Student engagement is crucial to success. Presenting students with worked examples, and then providing them with the opportunity to immediately solve similar problems, helps them build their confide...show morence and eventually master the concepts. Simplicity is key in the organization of this edition, as in all other editions. All lessons, exercise sets, tests, and supplements are organized around a carefully constructed hierarchy of objectives. Each exercise mirrors a preceding objective, which helps to reinforce key concepts and promote skill building. This clear, objective-based approach allows students to organize their thoughts around the content, and supports instructors as they work to design syllabi, lesson plans, and other administrative documents. New features like Focus on Success, Apply the Concept, and Concept Check add an increased emphasis on study skills and conceptual understanding to strengthen the foundation of student success. The Ninth Edition also features a new design, enhancing the Aufmann Interactive Method and making the pages easier for both students and instructors to follow365434 |
...Oftentimes younger students do not get the attention & one-on-one instruction in the classroom that they need. And often parents are just unsure - I understand. There's the importance to understand, especially at a young age, the dance of numbers, & just feeling comfortable with how to think about & play with numbers
...The meat of Algebra 1 is its body of skills, which require lots of practice: solving for an unknown, writing the equation for a line, and so on. The list of essential concepts in Algebra 1 is shorter, yet no less essential, than those of Geometry and Algebra 2. In Algebra 2, students take the s... |
Description
Math Helper is a universal assistant app for solving mathematical problems for Algebra I, Algebra II, Calculus, and Math for secondary and university students, which allows you not only to see the answer or result of a problem but also obtain a detailed solution.
Derivatives, limits, geometric shapes, the task of statistics, matrices, systems of equations and vectors – this and more in Math Helper!
FEATURES ✧ 8 topics and 41 sub-sections ✧ Localization for Russian, English, Italian, French, German, and Portuguese ✧ Intel ® Learning Series Alliance quality mark. ✧ About 10,000 customers worldwide have supported the further development of Math Helper by their purchase ✧ The application is equipped with a convenient multi-function calculator and extensive theoretical guide
SUPPORT ✪ Thank you all for helping us to reach 300,000 downloads of Math Helper Lite ✪ You could also support us with good feedback at Google Play or by way of the links shown below ✪ Our Facebook page: ✪ Ideas and problems discussed here ✪ Or you can reach us directly by email
WHAT IS NEXT We have plans to implement ● Better derivative calculator ● Step-by-step integrator ● Limits and series expansion ● Numbers and polynoms division and multiplication ● Implement a new design and add 50+ new problems ● New applications, like Formulae reference for university and symbolic calculators
Math Helper is a universal algebra calculator similar to mathway for anyone who has to deal with higher mathematics. You can be a student of a university or graduate, but if you suddenly need emergency assistance in mathematics – this tool can be right at your fingertips! |
This text is written to promote student success while maintaining the integrity of the course. Sullivan draws on his teaching experience and background in statistics and mathematics to achieve this balance. The four basic principles characterize the approach of this text; generating and maintaining student interest, promoting student success and confidence, providing extensive and effective opportunity for student practice and allowing for flexibly of teaching styles. |
Precalculus is a course that prepares students for Calculus by expanding on topics such as Advanced Algebra, Trigonometry, and Analysis. Since it is a preparatory course, it is important to grasp the concepts that are taught because they will be fundamental when applied to Calculus. Elementary ... |
..."tools" module which has functions of a scientific calculator and a powerful module of formal calculation, allowing...the derivative calculation, the integral calculation, the factorization, the symbolic calculation, the fractional...
...Sicyon is all-in-one scientific calculator for every student and professor, researcher and developer....The core of Sicyon is an expression (VBScript/JScript) calculator with features as: estimate a function using variables,...function; solve 1-6 equations, minimums, maximums and definite integral of 2D/3D function; fit a function over data...
...do calculus: differentiate an expression, or find its integral and ask how this was found.
You can...designed for usability. The main window is a calculator with an amazing 38 digits of precision. You...You can hide the title bar. Keep the calculator open all the time, on top of other... |
Product Description
The LFBC Math program is a solid one, beginning with the knowledge that God created everything, and, because of this, order has resulted. It teaches that students can expect exactness, preciseness, and completeness in arithmetic/mathematics, just as they can expect it in God's creation. We start with the basic facts. Strong emphasis is given to learning the multiplication tables early. Later we proceed to the more complicated and abstract concepts in the upper grades.
Set includes:
Studyguide: All materials for the student's academics, including text and activity questions
Studyguide Answers: Contains answers for the studyguide
Weekly Quizzes
Weekly Quiz Answers
Quarter Tests: Students take a test at the end of each 9-week periodi
Quarter Test Answers
All Scripture used in the curriculum is taken from the King James Version.
Product Reviews
Landmark's Freedom Baptist Math M135, Grade 7
3
5
1
1
On the positive side, this course begins with simple arithmetic and mathematical concepts, and each week builds upon the previous work. Also, in general, the descriptions given of new concepts or mathematical functions are sufficient for a 7th grader to grasp (though not always). In addition, each week's work not only introduces several new operations or concepts, but also features review problems from previous weeks. On the negative side, each week contains four lessons of between 40 and 75 problems each, plus a weekly "review" test. There are no natural pauses, or built-in "cushions," so if the student takes an extra day to master a difficult area, he has fallen behind. Once behind, the size of the daily lessons makes catching up daunting if not intimidating, and can seem to the student as if he's being punished for simnply taking longer to understand. Same problem if the student needs to take a day off, for example, to go to the dentist. Since almost every lesson contains something new, they can't simply be assigned as homework on such days. If your child struggles with math, or suffers from "math-phobia," this is not the course for you.
November 6, 2006 |
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics |
ractical Problems in Math for Automotive Technicians
Comprehensive and easy-to use, this updated edition covers every type of practical math problem that automotive technicians will face on the job. The subject matter is organized in a knowledge-building format that progresses from the basics of whole number operations into percentages, linear measurements, ratios, and the use of more complex formulas. Complete coverage of fundamentals, as well as more advanced computations make this book suitable for both beginning and advanced technicians. With a special section on graphs, scales, test meters, estimation, and invoices used in the workplace, this book is tailor-made for any automotive course of study |
FLY Through -- Algebra
Get step-by-step help solving your beginning algebra homework. FLY Through Algebra is the faster, easier way to learn how to solve your beginning algebra problems. Get help with Single Variable Equations, Inequalities, Factoring, and even graphic linear equations.
If this is your first time to the site, let us welcome you to what we hope will become your new daily source of FLY Through -- Algebra Algebra reviews, previews, and news from around the net. |
Mathematical Skills with Geometry, 8/e by Baratto/Bergmanis part of the latest offerings in the successful Hutchison Series in Mathematics. The eigth edition continues the hallmark approach of encouraging the learning of mathematics by focusing its coverage on mastering math through practice.This worktext seeks to provide carefully detailed explanations and accessible pedagogy to introduce basic mathematical skills and put the content in context. The authors use a three-pronged approach (I. Communication, II. Pattern Recognition, and III.... MORE Problem Solving) to present the material and stimulate critical thinking skills. Items such as Math Anxietyboxes, Check Yourselfexercises, and Activitiesrepresent this approach and the underlying philosophy of mastering math through practice. The exercise sets have been expanded, organized, and clearly labeled. Vocational and professional-technical exercises have been added throughout. Repeated exposure to this consistent structure should help advance the student's skills in relating to mathematics. The book is designed for a one-semester basic math course and is appropriate for lecture, learning center, laboratory, or self-paced courses. It is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone. |
Mathematics for
Elementary School Teachers II is the second of a two-part series designed to
meet the educational needs of prospective K-8 teachers and those professionals
who need mathematics for certification from an accredited college, professional
development or continuing education. Emphasis is placed on strategies for
problem solving and the teaching of fundamental skills. Topics include
operations of real numbers and algebraic thinking, probability, data
analysis/statistics, geometry, and concepts of measurement.
GENERAL INFORMATION
The class is offered
directly online through Pearson Education at:
It was formerly known as Course Compass and is not found on Blackboard;
however, the course can be accessed through the LCSC Distance Learning portal.
Follow the on-screen
instructions to register and enroll, or click For Students for step-by-step instructions.
Instructor Course
ID code:
yeoman88904
Student access code: you can purchase just
the MyMathLab packet or the text/packet combo from the LCSC bookstore or you can purchase access online using a credit card.The access packet includes a virtual text.
A valid LCMAIL address that you
check daily.Considerable information is
sent by email.
Create a login name and password.
CLASS WORK BEGINS
AUGUST 26, 2012
Assignments and exams
all have available and due dates that are strictly adhered to.Therefore, it is important that
students are ready to begin class work on the starting date. |
Introductory Algebra - 4th edition
Summary: Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief.Introductory Algebra, Fourth Editionwas written to provide students with a solid foundation in algebra and to help stuents make the transition to intermediate algebra. The new edition offers new resources like theStudent Organizerand now includesStudent Resourcesin the back of the book to help students on their que...show morest91.001726384
$100 |
An application for math plot.Can be used arithmetic operations, trigonometric functions (angles measured in radians), decimal, natural logarithms, the logarithm to an arbitrary ground, whole and fractional parts of numbers |
Buy An Introduction to the Theory of Groups by Paul Alexandroff and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!
To an algebraist the theory of group characters presents one of those fascinating situations, where the structure of an abstract system is elucidated by a unique set of numbers inherent in the system. But the subject also has a practical aspect, since group characters have gained importance in several branches of science, in which considerations of symmetry play a decisive part. This is an introductory text, suitable for final-year undergraduates or postgraduate students. The only prerequisites are a standard knowledge of linear algebra and a modest acquaintance with group theory. Especial care has been taken to explain how group characters are computed. The character tables of most of the familiar accessible groups are either constructed in the text or included amongst the exercise, all...
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A user-friendly introduction to metric and topological groupsTopological Groups: An Introduction provides a self-contained presentation with an emphasis on important families of topological groups. The book uniquely provides a modern and balanced presentation by using metric groups to present a substantive introduction to topics such as duality, while also shedding light on more general results for topological groups.Filling the need for a broad and accessible introduction to the subject, the book begins with coverage of groups, metric spaces, and topological spaces before introducing topological groups. Since linear spaces, algebras, norms, and determinants are necessary tools for studying topological groups, their basic properties are developed in subsequent chapters. For concreteness,...
LessBuy Symmetry: An Introduction to Group Theory and Its Applications by Roy McWeeny and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!...
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This comprehenisve gro up practice text prepares students to work with either treatment or task oriented groups, this comprehensive rev ised edition offers the most up-to-date research available and continues to stress the importance of developing skills in group- work. St udents receive a thorough grounding in areas that vary from treatment to organizational and community settings. Numerous case studies, practice examples, and guiding principles add to the ease and readability of this popular text. Content is tied to CSWE's core competencies and practice behaviors that are necessary for generalist and specialized social work practice with groups.
Introduction to Security has been the leading text on private security for over thirty years. Celebrated for its balanced and professional approach, this new edition givesfuture security professionalsa working professionals, and is also used as a core security textbook in universities throughout the$45.60
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Group Work Leadership: An Introduction for Helpers presents an evidence-based approach to the theory and practice of group work. Renowned counselor, psychologist, and group work fellow Dr. Robert K. Conyne advances this unique and evolving service in a three-part, comprehensive overview of the skills necessary for trainees of counseling and other helping professionals to succeed in group settings. Section I covers the breadth and foundations of group work; best practice and ethical considerations; dynamics and processes in group work; and how groups tend to develop over time. Section II explores group work leadership styles, methods, techniques, and strategies, as well as both traditional and innovative group work theories. Section III examines the role of reflection in group practice, Introduction to Complex Reflection Groups and Their Braid Groups - Brou?, Michel THIS IS A BRAND NEW UNOPENED ITEM. Description This103.07
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Buy Introduction to Group Analytic Psychotherapy: Studies in the Social Integration of Individuals and Groups by S. H. Foulkes and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!Practical and concise, this book offers specific techniques to make small group interactions more effective and efficient. Groups in Process continues to balance traditional and progressive approaches to teaching small group communication, drawing together the best of current researchIntroduction to Fluoropolymers demystifies fluoropolymers for a wide audience of designers, engineers, sales staff and managers. This important group of high-performance polymers has applications across a wide range of market sectors, including automotive, aerospace, medical devices, high performance apparel, oil & gas, renewable energy / solar photovoltaics, electronics / semiconductor, pharmaceuticals, and chemical processing. Dr. Ebnesajjad covers the history and applications of a wide variety of materials, including expanded polytetrafluoroet hylene, polyvinyl fluoride, vinylidene fluoride polymers and fluoroelastomers, just to name a few. Properties and applications are illustrated by real-world examples as diverse as waterproof clothing, vascular grafts and coatings for aircraft...
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Buy Individuals, Groups and Organizations Beneath the Surface: An Introduction by Lionel F. Stapley and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!This supplement by Lori Ann Fowler of Tarrant County College contains both in- and out-of-class group activities (utilizing resources such as MicroCase Online Data exercises from Wadsworth's Online Sociology Resource Center) that students can tear out and turn in to the instructor once complete. Also included are ideas for video clips to anchor group discussions, maps, case studies, group quizzes, ethical debates, group questions, group project topics, and ideas for outside readings for students to base group discussions on. Both a workbook for students and a repository of ideas, instructors can use this guide to get ideas for any Introductory Sociology class.Buy Group Theory in Quantum Mechanics: An Introduction to Its Present Usage by Volker Heine |
1 Introduction 12 The size of the community and of mathematical research activity 23 New areas of application, and their increasing significance 44 New tools: computers and information technology 55 New forms of mathematical activity 6
Mathematical activity has changed a lot in the last 50 years. Some of thesechanges, like the use of computers, are very visible and are being implemented inmathematical education quite extensively. There are other, more subtle trends thatmay not be so obvious. We discuss some of these trends and how they could, orshould, influence the future of mathematical education.
1 Introduction
Mathematical activity (research, applications, education, exposition) has changed a lotin the last 50 years. Some of these changes, like the use of computers, are very visibleand are being implemented in mathematical education quite extensively. There are other,more subtle trends that may not be so obvious. Should these influence the way weteach mathematics? The answer may, of course, be different at the primary, secondary,undergraduate and graduate level.Here are some of the general trends in mathematics, which we should take into account.1
1.
The size of the community and of mathematical research activity
is increasingexponentially; it doubles every 25 years or so. This fact has a number of consequences:the impossibility of keeping up with new results; the need of more efficient cooperationbetween researchers; the difficulty of identifying "core" mathematics (to be mastered atvarious levels); the need for better dissemination of new ideas. How can mathematicaleducation prepare future researchers and appliers of mathematics, future decision makersand the informed public for these changes?
2.
New areas of application, and their increasing significance.
Information technology,sciences, the economy, and almost all areas of human activity make more and more useof mathematics, and, perhaps more significantly, they use all branches of mathematics,not just traditional applied mathematics. How can we train our students to recognizeproblems where mathematics can help in the solution?
3.
New tools: computers and information technology.
This is perhaps the most visiblenew feature, and accordingly a lot has been done to introduce computers in education.But the influence of computers on our everyday life and research is also changing fast:besides the design of algorithms, experimentation, and possibilities in illustration andvisualization, we use email, discussion groups, on-line encyclopedias and other internetresources. Can education utilize these possibilities, keep up with the changes, and alsoteach students to use them in productive ways?
4.
New forms of mathematical activity.
In part as an answer to the issues raisedabove, many new forms of mathematical activity are gaining significance: algorithms andprogramming, modeling, conjecturing, expository writing and lecturing. Which of thesenon-traditional mathematical activities could and should be taught to students?I will say some more about these trends, and discuss the question of their influenceon mathematical education. I will make use of some observations from my earlier articles[6, 7].
2 The size of the community and of mathematical re-search activity
The number of mathematical publications (along with publications in other sciences) hasincreased exponentially in the last 50 years. Mathematics has outgrown the small andclose-knit community of nerds that it used to be; with increasing size, the profession isbecoming more diverse, more structured and more complex.Mathematicians sometimes pretend that mathematical research is as it used to be:that we find all the information that might be relevant by browsing through the newperiodicals in the library, and that if we publish a paper in an established journal, thenit will reach all the people whose research might utilize our results. But of course 3
/
4of the relevant periodicals are not on the library table, and even if one had access to allthese journals, and had the time to read all of them, one would only be familiar with theresults of a small corner of mathematics.A larger structure is never just a scaled-up version of the smaller. In larger and morecomplex animals an increasingly large fraction of the body is devoted to "overhead": thetransportation of material and the coordination of the function of various parts. In largerand more complex societies an increasingly large fraction of the resources is devoted to2
non-productive activities like transportation information processing, education or recre-ation. We have to realize and accept that a larger and larger part of our mathematicalactivity will be devoted to communication.This is easy to observe: the number of professional visits, conferences, workshops,research institutes is increasing fast, e-mail is used more and more. The percentage of papers with multiple authors has jumped. But probably we will reach the point soonwhere mutual personal contact does not provide sufficient information flow.There is another consequence of the increase in mass: the inevitable formation of smaller communities, one might say subcultures. One response to this problem is thecreation of an activity that deals with the secondary processing of research results. Forlack of a better word, I'll call this expository writing, although I'd like to consider it moreas a form of mathematical research than as a form of writing: finding the ramificationsof a result, its connections with results in other fields, explaining, perhaps translating itfor people coming from a different subculture.Are there corresponding changes in mathematical curricula and, more generally, inthe way we teach mathematics? The first, and most pressing, problem is the sheer size of material that would be nice (or absolutely necessary) to teach. In addition, as we will see,we should put more emphasis on (which also means giving more teaching time to) somenon-traditional mathematical activities like algorithm design, modeling, experimentationand exposition. I also have to emphasize the necessity of preserving problem solving as amajor feature of teaching mathematics.How to find time to learning concepts, theorems, proofs, especially with the rapidexpansion of material, and at a time when class time devoted to mathematics is beingreduced in many countries? Which of the new areas should make its way to education (onthe secondary or college level), and which of the traditional material should be left out?This is not a one-time crisis: mathematical research is not showing any signs of slowingdown.One possible answer to this question is to leave the teaching of any recently developedarea of mathematics to later in the education, to Masters and PhD programs. The troublewith this approach is that many educated people will never meet the mathematics of thelast 200 years, which will contribute to the unfortunate but persistent misconception thatmathematics is a closed subject. Many of the new areas of mathematics are importantfor understanding developments in technology and science, and by not teaching them wegive up illuminating the increasing role of mathematics in modern life.The other possible answer is to remove from the curriculum traditional material that isdeemed less important. This approach has the negative effect of eroding well-establishedmethods for teaching mathematical thinking. For example, elementary geometry has beenpurged from the curriculum in many countries. While this kind of geometry is indeedperipheral in modern mathematical
research
, it is of course still important in
applications
,and, perhaps even more important, its study is very instrumental in the development of spatial conception, and, perhaps even more significantly, in understanding the real natureof mathematical proofs, the "Aha" event when an incomprehensible connection becomesclear through looking at it the right way.I have no easy answer to this question. Probably one must concentrate on mathe-matical competencies like problem solving, abstraction, generalization and specialization,logical reasoning and use of mathematical formalism, along with the non-traditional skillsmentioned above (see e.g. [10]). One could select a mixture of classical and more modern3 |
This unit looks at complex numbers. You will learn how they are defined, examine their geometric representation and then move on to looking at the methods for finding the nth roots of complex numbers and the solutions to simple polynominal equations.
The subject Statistics will provide you with basic theoretical knowledge in the sphere of statistical methods and procedures used by performing analyses on concrete data of economic or biotechnological character. Teaching of this subject is supported by standard software tools (especially Microsoft Excel 2003®). |
0073016055
9780073016054
Basic Mathematical Skills with Geometry with MathZone:Maintaining its hallmark features of carefully detailed explanations and accessible pedagogy, this edition also addresses the AMATYC and NCTM Standards. In addition to the changes incorporated into the text, a new integrated video series and multimedia tutorial program are also available. Designed for a one-semester basic math course, this successful worktext is appropriate for lecture, learning center, laboratory, or self-paced courses.
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Rent Basic Mathematical Skills with Geometry with MathZone 6th edition today, or search our site for Donald textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by McGraw-Hill Education. |
Steve Demme, creator of Math U-See, combines hands-on methodology with incremental instruction and continual review in this manipulative-based program. It excels in its hands-on presentation of math concepts that enables students to understand how math works. It is one of the rare multi-sensory math programs that continue to use manipulatives up through Algebra 1.
Manipulative Blocks, Fraction Overlays, and Algebra and Decimal Inserts are used at different levels to teach concepts, primarily using the "rectangle building" principle. This basic idea, consistently used throughout the program—even through algebra—is one of the best ways to demonstrate math concepts.
One of the things I think makes Math-U-See so popular is that many parents and teachers find that author Steve Demme's presentations of math concepts helps them to finally comprehend much that they were taught in math but never understood. Parents and teachers with a new or renewed enthusiasm for math then do a much better job teaching their own children. Math-U-See uses a "skill-mastery" approach, requiring students to demonstrate mastery of each topic before moving on. The program also builds in systematic review for previously learned concepts.
There are eight books for elementary grades titled Primer, Alpha, Beta, Gamma, Delta, Epsilon, Zeta, and Pre-Algebra. The Greek letter designations were chosen particularly to emphasize the order of learning rather than grade level designation. Students should move on to the next level once they've mastered the content of a book. These first eight books are followed by Algebra 1, Geometry, Algebra 2, PreCalculus with Trigonometry, and Calculus. Placement tests for the different levels are available free at the Math-U-See website.
Student books are perfect-bound, and the pages are perforated and punched so they can easily be removed, written upon, and placed in binders. (Test books have been redesigned in this same fashion.) Student books now have much more practice work than they did in earlier editions, and they include many word problems. Honors exercises have been incorporated into the student books for Pre-Algebra through PreCalculus. These optional, additional problems stretch students to higher levels of understanding and application of math concepts covered within the lessons.
Test booklets for each course have tests to be used at the end of each lesson plus four unit tests and a final exam. Neither student worktext pages nor tests are reproducible; you need to purchase books for each student. Student workbooks and test booklets are the only consumable items in each course.
Instruction manuals are printed in hardcover books with full-color covers so they might be used a number of times. Calculus, the only exception, has a softcover, comb-bound book, although that will likely change to hardcover with the next printing. Complete answer keys with solutions are now included for all problems at all levels, an especially helpful feature at upper levels.
All books are printed in black and white with no illustrations other than mathematical ones....
The program covers all basic math concepts and all of those in the elementary-level Common Core Standards, but it does not try to correlate the teaching of concepts at the same grade level or in the same order as the Core Standards. Everything gets covered eventually, but in a more sensible order than the standards, in my opinion.
For each level you need both the student kit and the instruction pack. The student kit for each level includes a student workbook and a test booklet for most levels.
For Primer through Algebra 1, you will also need to purchase the set of Manipulative Blocks, but these are very reasonably priced. Math-U-See's manipulatives are primarily plastic blocks somewhat similar to Base Ten Blocks and Cuisenaire Rods, color-coded to correspond to each number...Fraction Overlays are added at Epsilon level and Algebra/Decimal Inserts are added at the Zeta level. That means, the same sets of manipulatives are each used over at least a few years.
The instruction pack for each level includes an instruction manual plus one or more DVDs that "teach the teacher." Note that DVDs have subtitles for the hearing impaired. Parents must watch the DVDs to understand the basic concepts that are the foundation of the program. On the DVDs, Demme works through each level, lesson-by-lesson, demonstrating and instructing. Demme's presentation is enthusiastic and engaging as he clearly explains why and what he is doing. He throws in lots of math tricks, the kind that make you scratch your head and ask yourself why they never taught us that in school....
There are plenty of practice problems in the latest editions of Math-U-See, but students who need more practice have free access to a computation drill program on the Math-U-See website....
As you move into the high school level books, students are able to work more independently. The instruction manual for each level is written to the student. Students need to watch the DVD presentation then read through the instruction manual before tackling the workbook. Workbooks include extra instruction for unusual problems, especially for some of the honors problems, but they do not serve as complete coursebooks on their own.
The honors exercises provide more challenging practice, more critical thinking, practical applications, more complex word problems, test prep practice, and preparation for the math required in advanced science courses. The addition of the honors exercises largely alleviates concerns I expressed in my review in the first edition of Top Picks about the program's ability to challenge advanced students. Students can also move through the texts more rapidly if they master the lessons quickly....
The DVD instructional component might make a huge difference...since Demme does a great job of explaining and illustrating concepts. However, I very much appreciate the fact that the newest editions' instruction manuals for these and other high school level courses now include a teaching component so that students do not have to rely entirely on the DVDs.
Note: Math U See announced updated editions available March 2013 with a number of improvements. Among them are:
- an extra "Application and Enrichment" activity page added to the student workbook for levels Primer through Zeta
- more thorough coverage of concepts encountered on standardized tests
- more work with word problems
- updated instruction manuals with improved or expanded explanations and answers for new problems
Pricing
Math-U-See is sold only through Math-U-See representatives. Check the Math-U-See website for the distributor in your area and for a free demo |
Synopses & Reviews
Publisher Comments:
Just the critical concepts you need to score high in pre-algebra
This practical, friendly guide focuses on critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to standard formulas and simple variable equations. Pre-Algebra Essentials For Dummies is perfect for cramming, homework help, or as a reference for parents helping kids study for exams.
Get down to the basics — get a handle on the basics of math, from adding, subtracting, multiplying, and dividing to exponents, square roots, and absolute value
Conquer with confidence — follow easy-to-grasp instructions for working with fractions, decimals, and percents in equations and word problems
Take the "problem" out of word problems — learn how to turn words into numbers and use "x" in algebraic equations to solve word problems
Formulate a plan — get the lowdown on the essential formulas you need to solve for perimeter, area, surface area, and volume
Open the book and find:
How to find the greatest common factor and least common multiple
Tips for adding, subtracting, dividing, and multiplying fractions
How to change decimals to fractions (and vice versa)
Algebraic expressions and equations
Essential formulas
How to work with graphs and charts
Learn to:
Work with and convert fractions, decimals, and percents
Solve for variables in algebraic expressions
Get the right answer when solving basic math problems
Synopsis:Synopsis:
"Synopsis"
by Wiley,"Synopsis"
by Ingram, |
As part of the Standard Deviants teaching video series, this video is designed to help the viewer learn the basics of pre-algebra. Written by university professors, the information presented outlines what a student taking college mathematics needs to understand. The high speed of the lessons may turn off some viewers, but those willing to stop and rewind will find the information useful and easy to understand. Standard Deviants: Pre-Algebra Part 1 is the first installment in the pre-algebra series and covers sections on integer exponents, exponetial terms, rules of exponents, square roots and absolute value. For those wishing to continue their learning, Standard Deviants: Pre-Algebra Part 2 expands upon the lessons in this video. ~ Ed Atkinson, Rovi |
Calculus
Offers training in vectors and matrices, vector analysis, and partial differential equations. This book introduces vectors at the outset and serves ...Show synopsisOffers training in vectors and matrices, vector analysis, and partial differential equations. This book introduces vectors at the outset and serves at many points to indicate geometrical and physical significance of mathematical relations. It covers numerical methods at various points, because of the insights they give about theory.Hide synopsis
Description:Fair. 0201799375 Student Edition. Missing up to 10 pages. Heavy...Fair. 0201799375 Advanced Calculus
I study this book entirely in a calculus review (first edition). The points are:
1- The exposition is clear and didatic even in points difficults and delicates
2- The sections are short and with exercises in growing level of dificulty with much adequates hints
3- It's necessary to resolve all |
Created as an extension of the Chapter Opener applications and general calculus concepts, Calculus Labs are a series of 20 technology lab projects that utilize computer algebra systems. Each lab includes an introduction with background information, observations, a statement of the purpose of the lab, and references for further investigation of the topic of the lab. A variety of open-ended questions that require students to analyze, explore, and compare are an integral part of each lab. Software specific data files, graphs and equations are available for each lab series. The labs are referenced in the text where it seems most appropriate to assign them, however, they are flexible enough to be assigned at the instructor's discretion.
Chapter Application/Location
Lab
Chapter P - Eruptions of Old Faithful
Lab 1 Modeling Old Faithful's Eruptions
Chapter 1- Swimming Speed: Taking It to the
Limit
Lab 2 The Limit of Swimming Speed
Chapter 2 - Gravity: Finding It Experimentally
Lab 3 Falling Objects
Chapter 2 - Review Exercises
Lab 4 Boyle's Law
Chapter 3 - Packaging: The Optimal Form
Lab 5 Packaging
Chapter 4 - The Wankel Rotary Engine and Area
Lab 6 Wankel Rotary Engine
Chapter 5 - Plastics and Cooling
Lab 7 Newton's Law of Cooling
Chapter 6 - Constructing an Arch Dam
Lab 8 Constructing an Arch Dam
Chapter 6 - Section 7
Lab 9 Stretching a Spring
Chapter 7 - Making a Mercator Map
Lab 10 Calculus of a Mercator Map
Chapter 8 - The Koch Snowflake: Infinite Perimeter?
Lab 11 Koch Snowflake
Chapter 8 - Section 8
Lab 12 Analyzing a Bouncing Tennis Ball
Chapter 9 - Exploring New Planets
Lab 13 Comets
Chapter 10 - Suspension Bridges
Lab 14 Suspension Bridges
Chapter 11 - Race Car Cornering
Lab 15 Race Car Cornering
Chapter 11 - Review Exercises
Lab 16 Putting a Shot
Chapter 12 - Satellite Receiving Dish
Lab 17 Satellite Dishes, Flashlights, and Solar
Energy Collectors
Chapter 13 - Hyperthermia Treatments for Tumors
Lab 18 Hyperthermia Treatments for Tumors
Chapter 14 - Mathematical Sculpture
Lab 19 Mathematical Sculptures
Chapter 15 -
Lab 20 Interacting Populations
Some resources
on this page are in PDF format and require Adobe® Acrobat® Reader. You can download the free reader
below!
The labs are provided in PDF format. Each lab can be printed individually. To view the lab files you will need Adobe Acrobat. Select the computer algebra system you are using. |
Algebra : Beginning and Intermediate - 2nd edition
Summary: Intended for combined introductory and intermediate algebra courses, this text retains the hallmark features that have made the Aufmann texts market leaders: an interactive approach in an objective-based framework: a clear writing style, and an emphasis on problem-solving strategies. The acclaimed Aufmann Interactive Method, allows students to try a skill as it is introduced with matched-pair examples, offering students immediate feedback, reinforcing the concept, ident...show moreifying problem areas, and, overall, promoting student success.
New! Interactive Exercises appear at the beginning of an objective's exercise set (when appropriate), and provide students with guided practice on some of the objective's underlying principles.
New! Think About It Exercises are conceptual in nature and appear near the end of an objective's exercise set. They ask the students to think about the objective's concepts, make generalizations, and apply them to more abstract problems. The focus is on mental mathematics, not calculation or computation, and help students synthesize concepts.
New! Important Points have been highlighted to capture students' attention. With these signposts, students are able to recognize what is most important and to study more efficiently.
New! Coverage of evaluating functions, graphing functions, and the vertical line test has been added to Section 3.2.
New! An explanation that the x-coordinate of an x-intercept is a zero of a function can now be found in Section 3.3.
New! Chapter 10 now begins with graphing absolute value functions as an introduction to translations of graphs.
New! Improved Introductions to exponential and logarithmic functions in Chapter 11 will lead to greater student understanding of and interest in these topics.
4.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method 4.2 Solving Systems of Linear Equations by the Addition Method 4.3 Solving Systems of Equations by Using Determinants and by Using Matrices 4.4 Application Problems 4.5 Solving Systems of Linear InequalitiesGood
TXTBookSales1 Evansville, IN
Instructor annotated edition Every book shipped with tracking number. May contain informative highlighting, markings, or cool sticker on the front. Overall pretty good shape. May not include Supplemen...show morets, CDs or Access Codes. -Good-63 +$3.99 s/h
Good
One Stop Text Books Store Sherman Oaks, CA
2007-01-22 Hardcover |
This workbook provides students with an opportunity to practice the areas tested on the exam. The worksheets are designed to accompany the CAHSEE Math Curriculum as well as allowing students to apply... More > their knowledge and expand their understanding of number sense, statistics, data analysis, and probability, measurement and geometry, algebra and functions, mathematical reasoning, and algebra I. For curriculum information, contact us at info@ssformath.com< Less
This study guide provides parents, teachers and students with multiple opportunities to practice and master the math content areas on the CAHSEE. The lessons use plain language to define academic... More > concepts and simplify seemingly complicated ideas within the California state standards. The topics covered within the workbook mirror the test itself: number sense, statistics, data analysis and probability, measurement and geometry, algebra and functions, mathematical reasoning and algebra I. All questions are formatted to match the CAHSEE and there are three complete practice tests included. This is the ideal solution for tutorial, home study or independent study students.< Less
This workbook has the entire practice set for the Pre Algebra curriculum, followed by the answer keys. This is a valuable learning aid for teachers and parents who want to supplement classroom... More > instruction. All these books are available from Simplified Solutions for Math on LULU. Contact Simplified at ss4math@gmail.com for more information and a complete set of PowerPoint presentations for each lesson, free with purchase of curriculum. Completely self-contained, ideal for home schooling as well as traditional classrooms.< Less
Simplified Solutions for Math provides a series of curriculum and workbooks to meet the needs of teachers and parents who want to either supplement classroom instruction or provide complete... More > instruction. All the curriculum products come complete with lesson plans, PowerPoint presentations, and worksheets. This "Product Overview" allows you to see the materials being offered and the form in which it is being delivered. All our books are available from on LULU. Contact Simplified at ss4math@gmail.com for more information and a complete set of PowerPoint presentations for each lesson, free with purchase of curriculum. Our products are completely self-contained, ideal for home schooling as well as traditional classrooms.< Less |
Graduate textbooks often have a rather daunting heft. So it's pleasant for a text intended for first-year graduate students to be concise, and brief enough that at the end of a course nearly the entire text will have been covered. This book manages that feat, entirely without sacrificing any materia more...
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility... more...
This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters,. new material on axiom of Choice, p-groups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics. - ;Developed to meet the needs... more...
Praise for the first edition "This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and... more...
This book Abstract Algebra has been written primarily from student's point of view. So that they can easily understand various mathematical concepts, techniques and tools needed for their course. Efforts have been made to explain such points in depth, so that students can follow the subject easily. A large number of solved and unsolved problems... more... |
MAPLE is a powerful computer algebra system that can perform many mathematical calculations.It can also be used as a programming language.This lab is intended to introduce both of these capabilities.The MAPLE program is available to UCCS students in the computer lab in EAS 136.
Logging into the System
On the log-in screen, you will see a prompt for your username and password.Type in your username first.This will be the first letter of your first name followed by the first seven letters (or less) of your last name.For example, if your name is John Williams, then your username will be JWilliam.
If you have not previously logged in, you will need the initial password.This is usually the first eight digits of your student ID number.After you log in you will be asked to change this password, make sure you remember it!
**Note
If for some reason either your username or your password does not work, first check that the DOMAIN is set to UFP.If it still doesn't work, ask someone for help.
Starting out with MAPLE
Double click the MAPLE icon on the desktop.This will open a MAPLE worksheet, and you should see a prompt in the upper left corner that looks like this:
>
Maple as a Calculator
The prompt is where everything begins and ends in MAPLE.Now we will look at a few of the functions MAPLE can perform.First, notice that MAPLE can function as an expensive calculator.Try typing the following:
> 2+2;
If you did this correctly, you should get the answer displayed underneath in blue.(Notice that all commands in MAPLE are displayed in red, while solutions are displayed in blue.Text will be in black.)
**Note
You have to end commands in maple with a colon or a semicolon.If you end a line with a colon, the command will be executed, but the solution will not be displayed.If you end a line with a semicolon (as above), the solution will be displayed in blue in the middle of the screen.
We can continue with multiplication.The asterisk symbol (*) is used to indicate multiplication.You cannot leave it out.Try typing the following lines:
> 2*2;
> (2)(2);
Notice that the line without the asterisk gives the wrong solution.
Subtraction should be written as follows:
> 5-3;
Now on to division.Try typing the following line:
> 5/3;
Notice that MAPLE simply reproduces the fraction.In order to come up with a decimal solution, try typing 5.0 instead of 5 in the equation.This tells MAPLE that you want a decimal answer.Then you will get the following solution:
> 5.0/3;
MAPLE also has a function that will automatically evaluate the expression entered.It is called evalf().Try typing
> evalf(5/3);
This command evaluates the expression and gives you the answer in what the computer calls a "floating point" number.That just means that it will give you the answer in decimal form.
Now try a few of your own calculations!
Assigning Variables in MAPLE
It is often convenient to take a long expression and give it a name.That way, you don't have to repeatedly type in the long expression.Assignment in MAPLE is done with the operator ':='.For example, the following line assigns the letter 'a' the approximate value of Pi.
> a:=3.14159;
Now every time the letter 'a' is used in an expression, it will actually refer to the value for Pi!Try typing the following:
> a;
> 2*a;
**Note
If you try to use just the '=' instead of ':=', the assignment will not be made
Help in MAPLE
In the example above, the value for Pi was assigned to a variable to save it.Does the value for Pi have to be entered everytime it is used? Maybe MAPLE has a better choice.There are two ways to find help in MAPLE.The first is to use the scroll down menu at the top of the screen.This menu is very similar to the help used in other programs.Simply use the mouse to click on 'Help', and then select the option of your choice.The second way to find help in MAPLE is to use the command line.The command for help is a question mark '?' followed by a search string.Try typing the following line and then pressing 'Enter'.
> ?Pi
MAPLE brought up a window with not just Pi listed, but also some of the other constants it uses.There is no need to type the value for Pi everytime it is used.Instead, substitute the constant, 'Pi'.
**Note
It is not necessary to type in the entire word when searching for help.For example, to find help on functions, you can simply type '?fun'.MAPLE will bring up a menu of close matches and you can choose the one that best suits your needs.
Exponents in MAPLE
If you wish to find, for example, 13 to the fifth power, then you can easily do it in MAPLE.The caret '^' (or 'hat') is used in exponentiation.Try typing
> 13^5;
Remember that you can also use the exponent operator to compute the roots of numbers.If you want to find the cube root of 876, simple type
> evalf(876^(1/3));
Exercises on Exponents:
Find solutions for the following:
1.)9.8 to the fifth power
2.)2 to the eighth power
3.)The square root of 225, 488.0
Built in MAPLE functions
MAPLE has the same built in functions that you see in scientific calculators.A few examples are, sin(x), cos(x), tan(x), log(x), sqrt(x), and exp(x).Try typing the following:
> log(10.0);
This answer tells you that log(x) does not mean the base 10 logarithm, but the natural logarithm.If you don't know what that is, don't fret.The natural logarithm is simply a logarithm with base e (approximately 2.718).
The trigonometric functions should be entered in the same way, for example, sin(2*Pi) should be as below,
> sin(2*Pi);
Now try typing sin2*Pi, omitting the parentheses.What is the result?
MAPLE also recognizes the inverse trigonometric functions.For instance, the inverse tangent is 'arctan'.Recalling that the inverse tangent of 1 is Pi/4, we can enter it as below to see that the arctan function works as expected.
> 4*arctan(1.0);
Now, let's look at e.Try computing e to the tenth power.
> e^10.0;
Well, it didn't evaluate that, so now try to use the evalf function to obtain a solution.
> evalf(e^10.0);
Oops, that didn't work either.In MAPLE, e^x is not a valid command.MAPLE is treating the letter 'e' as an undefined variable, just like it would 'x'.To find e^x, use the function, exp(x).
> exp(10.0);
Exercises on Built in Maple functions:
Find solutions for the following:
1.)The cosine of Pi/4
2.)e to the 13
3.)The square root of 488
Defining Functions in MAPLE
MAPLE far exceeds a basic calculator when it comes to handling functions.Our first task for this section is to learn how to define a function in MAPLE.Let's take for example, f(x)=x^2+2x+4.To enter this into MAPLE, try typing,
> f:=(x)->x^2+2*x+4;
Now f is defined as a function of x.Typing
> f(x);
demonstrates that MAPLE remembers our function.Not only that, but say you want to find f(x+4).All you have to do now is type
> f(x+4);
and MAPLE does the rest.If you want to find the function value at 7, say f(7), type
> f(7);
and MAPLE computes the function value for you.What a time saver!!!
Exercises on Defining functions in MAPLE:
1.)Define h(x)=9*x^2+28*x+8
2.)Find the function value at 24
3.)Find the function value if it is shifted x+2
Solving Polynomial Equations in MAPLE
Now that you can define functions in MAPLE, let's begin learning how to solve polynomial equations.Type the following line to define a polynomial t(x).
> t:=x->x^3-4*x^2-11*x+30;
Now that the polynomial t(x) is defined, there are a number of things that can be done to manipulate and to solve it.First, the polynomial can be factored, try typing the following:
> factor(t(x));
That command factored the function into its easiest rational form.In the case above, the solutions are now apparent, 2,5, and -3.The solution for the function can also be found by using the function solve().The next line demonstrates the solve() command.
> solve(t(x));
The above function was relatively simple, let's try one that does not have an obvious solution.Define a polynomial v(x) as below and factor it.
> v:=x->x^4-4*x^3+x+2;
> factor(v(x));
This function could not be factored into an easy solution, so try to solve it using solve().(Try typing it first without the evalf())
> evalf(solve(v(x)));
We can see that solving the equation yields four solutions, 1, 3.9, and -0.45+0.55I and -0.45-0.55I.The I is what is called an imaginary number.An imaginary unit is defined as I=sqrt(-1) or I^2=-1.For example, the equation x^2=-25 has two roots, 5I and -5I.If you put these back into the equation, you will see that they really do form the solution.
The solution for even the complicated polynomial can be found using the factor() and solve() functions in MAPLE.
Exercises on Solving Polynomials in MAPLE:
1.)Define h(x)=x^4-11x^3-3x^2+171
a.)Factor the polynomial
b.)Give the solutions of the polynomial
2.)Define j(x)=10x^3 + 15*x-270
a.)Factor the polynomial (if possible)
b.)Give the roots of the polynomial (in simplest form)
Basic Plots in MAPLE
The command for graphing in MAPLE is simply 'plot()'.Inside the parentheses, you will enter first the function, then the range of x values, separated by commas.Let's start off with a linear function, p(x)=2x+8.
> plot(2*x+2,x=-10..10);
Well that was easy.We'll try something a little more difficult this time.Try plotting sin(x).
> plot(sin(x),x=-2*Pi..2*Pi);
MAPLE plots have a lot of functionality.If you use your mouse to right click on the plot you just made, you will get a menu of options.Try changing the style of the graph and the axes and see what happens.
You can plot two functions together using the display command in MAPLE.Let's try to plotb(x)=cos(x) along with c(x)=cos(2x).
> p1:=plot(cos(x),x=-2*Pi..2*Pi):
> p2:=plot(cos(2*x),x=-2*Pi..2*Pi):
> display(p1,p2);
**Note
To display multiple plots within one graph, it is also possible to list them within a single command.For the above example, the command 'plot([cos(x),cos(2*x)],x=-2*Pi..2*Pi)' will yield the same result.
Now we're going to try a function that requires us to change the range of the y-values so that we can see the function clearly.Let's try plotting the following functions. (To do this we will need to use MAPLE's library of plots.The first line of code below will import that library.)
> with(plots):
> p3:=plot(sqrt(x),x=-10..10):
> p4:=plot(exp(x),x=-10..10):
> display(p3,p4);
As you can see, MAPLE uses the range of y from 0 to about 25000!But we can't even see the squareroot function.We need to redefine our y-values so that we can see more of the plot.Let's try y from 0 to 10 and see what heppens.
> p5:=plot(sqrt(x),x=-10..10,y=0..10):
> p6:=plot(exp(x),x=-10..10,y=0..10):
> display(p5,p6);
Now we can clearly see what happens in a smaller portion of the graph.You can change the domain and the range of your graph to "zoom" in or out on any portion of your graph. |
Essentials of Mathematics for Elementary Teachers - 6th edition
Summary: Appropriate Topical Sequence: Moves from the concrete to the pictorial to the abstract, reflecting the way math is generally taught in elementary schools. Problem Solving Emphasis: Features the largest collection of problems (over 2200), worked examples, and problem-solving strategies in any text of its kind. Applications: Statistics and probability receive a thorough treatment at an appropriate level. Geometry Coverage: The treatment of two and three dimensional...show more shapes is based on the van Hiele model. Measurement is treated extensively in both the metric and customary systems. Integrated Technology: Technology is integrated throughout the text in a meaningful way. The technology includes activities from the expanded eManipulative activities, spreadsheet activities, Geometer's Sketchpad activities, and calculator activities using a graphics calculator and Math Explorer. ...show lessBOOKS_AT_HALF PITTSTON, PA
0471455865 FASTER SERVICE FROM US!!! MAY HAVE COVER WEAR, CREASES, HIGHLIGHTING, UNDERLINING, WRITING OR BENT. FASTER SERVICE FROM US!!!6TH EDITION STAPLE ON PAGE. Intact & readable. PLEASE NOTE~ we rated this book USED~ACCEPTABLE due to likely defects such as highlighting, writing/markings, folds, creases, ETC. We ship from Dallas wi...show morethin 1 day & we |
,...
Show More, licensed trades, maintenance, and other trades. You'll learn how to apply concepts of algebra, geometry, and trigonometry and their formulas related to occupational areas of study. Plus, you'll find out how to perform basic arithmetic operations and solve word problems as they're applied to specific trades.Maps to a course commonly required by vocational schools, community and technical college, or for certification in the skilled tradesCovers the basic concepts of arithmetic, algebra, geometry, and trigonometry Helps professionals keep pace with job demandsWhether you're a student currently enrolled in a program or a professional who is already in the work force, Technical Math For Dummies gives you everything you need to improve your math skills and get ahead of the pack |
Algebra and Trigonometry, Second Edition
Book Description: This book presents the traditional content of Precalculus in a manner that answers the age-old question of "When will I ever use this?" Highlighting truly relevant applications, this book presents the material in an easy to teach from/easy to learn from approach. KEY TOPICS Chapter topics include equations, inequalities, and mathematical models; functions and graphs; polynomial and rational functions; exponential and logarithmic functions; trigonometric functions; analytic trigonometry; systems of equations and inequalities; conic sections and analytic geometry; and sequences, induction, and probability. For individuals studying Precalculus |
Math Content Standard A: Content of Math
Key Element 4. Functions and Relations
A student who meets the content standard should represent,
analyze, and use mathematical patterns, relations, and
functions, using methods such as tables, equations, and
graphs
Algebra for All
Algebra is a gatekeeper that allows students to go on
to the work force and to a higher education. Students
who do not have the algebraic concepts are denied opportunities
that affect their futures. The way we teach algebra needs
to be a rich, technology assisted applicable course that
challenges and enriches a student's ability to solve problems.
Algebra should be taught as a means of representation
and be integrated with statistics, geometry, and discrete
mathematics. As a means of representation, algebra provides
a language that uses verbal, tabular, graphical, and symbolic
forms to model and answer questions about quantitative
patterns and relationships. These patterns and relationships
often arise in contexts involving data, shape, or change.
Thus, algebra in this broader conception is intimately
tied to other mathematical strands. |
Summary: A text for a precalculus course for students who have completed a course in intermediate algebra or high school algebra II, concentrating on topics essential for success in calculus, with an emphasis on depth of understanding rather that breadth of coverage. Linear, exponential, power, and periodic functions are introduced first, then polynomial and rational functions, with each function represented symbolically, numerically, graphically, and verbally. Contains many ...show moreworked examples and problems using real world data. Can be used with any technology for graphing functions.
From the Calculus Consortium based at Harvard University, this comprehensible book prepares readers for the study of calculus, presenting families of functions as models for change. These materials stress conceptual understanding and multiple ways of representing mathematical ideas. ...show less2003 |
Do Not Leave Your Language Alone.
Khan Academy
Algebra
Topics covered from very basic algebra all the way through algebra II. This is the best algebra playlist to start at if you've never seen algebra before. Once you get your feet wet, you may want to try some of the videos in the "Algebra I Worked Examples" playlist.
Algebra I Worked Examples
180 Worked Algebra I examples (problems written by the Monterey Institute of Technology and Education). You should look at the "Algebra" playlist if you've never seen algebra before or if you want instruction on topics in Algebra II. Use this playlist to see a ton of example problems in every topic in the California Algebra I Standards. If you can do all of these problems on your own, you should probably test out of Algebra I (seriously).
Arithmetic
The most basic of the math playlists. Start here if you have very little background in math fundamentals (or just want to make sure you do). After watching this playlist, you should be ready for the pre-algebra playlist.
Art History
Spontaneous conversations about works of art where the speakers are not afraid to disagree with each other or art history orthodoxy. Videos are made by Dr. Beth Harris and Dr. Steven Zucker along with other contributors.
CAHSEE Example Problems
Sal working through the 53 problems from the practice test available at for the CAHSEE (California High School Exit Examination). Clearly useful if you're looking to take that exam. Probably still useful if you want to make sure you have a solid understanding of basic high school math.
Calculus
Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists)
California Standards Test: Algebra I
Sal works through the problems from the CA Standards released questions: . Good videos to review Algebra I (The "Algebra I Worked Examples" playlist is more comprehensive and should probably be watched first).
California Standards Test: Algebra II
Sal works through 80 questions taken from the California Standards Test for Algebra II. Good place to review the major topics in Algebra II even if you're not in California. Many of these topics are taught in more depth in the "Algebra" playlist.
California Standards Test: Geometry
Sal does the 80 problems from the released questions from the California Standards Test for Geometry. Test at . Basic understanding of Algebra I necessary.
Linear Algebra
SAT Preparation
I am going to work through every problem in the College Board "Official SAT Study Guide." You should take the practice tests on your own, grade them and then use these videos to understand the problems you didn't get or review. Have fun!
ck12.org Algebra 1 Examples
Select problems from ck12.org's Algebra 1 FlexBook (Open Source Textbook). This is a good playlist to review if you want to make sure you have a good understanding of all of the major topics in Algebra I.
I just want to say I'm new to blogging and site-building and certainly savored your web-site. Probably I'm want to bookmark your site . You actually have remarkable stories. Thanks a lot for revealing your webpage |
Although few mathematicians would quarrel with the
proposition that the algebraic notation taught
in high school is a language
(and indeed the primary language of mathematics),
yet little attention has been paid to the possible
implications of such a view of algebra.
This paper adopts this point of view to illuminate
the inconsistencies and deficiencies of conventional
notation and to explore the implications of analogies
between the teaching of natural languages
and the teaching of algebra.
Based on this analysis it presents a simple
and consistent algebraic notation, illustrates its power
in the exposition of some familiar topics in algebra,
and proposes a basis for an introductory course in algebra.
Moreover, it shows how a computer can, if desired,
be used in the teaching process, since the language
proposed is directly usable on a computer terminal.
A.2 Arithmetic Notation
We will first discuss the notation of arithmetic,
i.e., that part of algebraic notation which does not involve
the use of variables. For example, the expression 3-4
and (3+4)-(5+6) are arithmetic expressions,
but the expressions 3-X and (X+4)-(Y+6) are not.
We will now explore the anomalies of arithmetic notation
and the modifications needed to remove them.
Functions and symbols for functions.
The importance of introducing the concept of "function"
rather early in the mathematical curriculum is now widely recognized.
Nevertheless, those functions which the student encounters first
are usually referred to not as "functions" but as "operators".
For example, absolute value (|-3|)
and arithmetic negation (-3) are usually referred to as operators.
In fact, most of the functions which are so fundamental
and so widely used that they have been assigned some graphic symbol
are commonly called operators
(particularly those functions such as plus and times
which apply to two arguments),
whereas the less common functions which are usually referred to by
writing out their names (e.g. Sin, Cos, Factorial) are called functions.
This practice of referring to the most common
and most elementary functions as operators is surely an unnecessary
obstacle to the understanding of functions
when that term is first applied to the more complex functions encountered.
For this reason the term "function" will be used here
for all functions regardless of the choice of symbols used to represent them.
The functions of elementary algebra are of two types,
taking either one argument or two.
Thus addition is a function of two arguments (denoted by X+Y)
and negation is a function of one argument (denoted by -Y).
It would seem both easy and reasonable to adopt one form
for each type of function as suggested by the foregoing examples,
that is, the symbol for a function of two arguments occurs
between its arguments, and the symbol for a function of one argument
occurs before its argument.
Conventional notation displays considerable anarchy on this point:
1.
Certain functions are denoted by any one of several symbols
which are supposed to be synonymous but which are, however,
used in subtly different ways.
For example, in conventional algebra X×Y and XY
both denote the product of X and Y .However,
one would write either 3×Y or 3X or X×3 or 3×4 ,but
would not likely accept X3 as
an expression for X×3 ,nor 3 4
as an expression for 3×4 .
Similarly, X÷Y and X/Y are supposed to be synonymous,
but in the sentence "Reduce 8/6 to lowest terms",
the symbol / does not stand for division.
2.
The power function has no symbol, and is denoted by position only,
as in XN .The
same notation is often used to denote the Nth element
of a family or array X .
3.
The remainder function (that is, the integer remainder of
dividing X into Y) is used very early in arithmetic
(e.g., in factoring) but is commonly not recognized as a function on par
with addition, division, etc., nor assigned a symbol.
Because the remainder function has no symbol and is commonly
evaluated by the method of long division,
there is a tendency to confuse it with division.
This confusion is compounded by the fact that the term
"quotient" itself is ambiguous,
sometimes meaning the quotient and sometimes the integer part
of the quotient.
4.
The symbol for a function of one argument sometimes occurs
before the argument (as in -4) but may also occur
after it (as in !4 for factorial 4)
or on both sides (as in |X| for absolute value of X).
Table A.1 shows a set of symbols which can be used
in a simple consistent manner to denote the functions
mentioned thus far,
as well as a few other very useful basic functions
such as maximum, minimum, integer part, reciprocal, and exponential.
The table shows two uses for each symbol, one to denote
a monadic function (i.e. a function of one argument),
and one to denote a dyadic function
(i.e. a function of two arguments).
This is simply a systematic exploitation of the example set
by the familiar use of the minus sign,
either as a dyadic function (i.e., subtraction as in 4-3)
or as a monadic function (i.e., negation as in -3).
No function symbol is permitted to be elided;
for example, X×Y may not be written as XY .
Monadic form f b
f
Dyadic form a f b
Definition or example
+3 ↔ 0+3
-3 ↔ 0-3
×3 ↔ (3>0)-(3<0)
÷3 ↔ 1÷3
⌈ 3.14 ↔ 4
⌈¯3.14 ↔ ¯3
⌊ 3.14 ↔ 3
⌊¯3.14 ↔ ¯4
*3 ↔ (2.71828...)*3
⍟*5 ↔ 5 ↔*⍟5
|¯3.14 ↔ 3.14
Name
Plus
Negative
Signum
Reciprocal
Ceiling
Floor
Exponential
Natural
logarithm
Magnitude
+
-
×
÷
⌈
⌊
*
⍟
|
Name
Plus
Minus
Times
Divide
Maximum
Minimum
Power
Logarithm
Remainder
Definition or example
2+3.2 ↔ 5.2
2-3.2 ↔ ¯1.2
2×3.2 ↔ 6.4
2÷3.2 ↔ 0.625
3⌈7↔ 7
3⌊7↔ 3
2*3↔ 8
10⍟3 ↔ Log 3 base 10
10⍟3 ↔ (⍟3)÷⍟10
3|8 ↔ 2
Table A.1
A little experimentation with the notation of Table A.1 will show
that it can be used to express clearly a number of matters
which are awkward of impossible to express in conventional notation.
For example, X÷Y is the quotient of X divided
by Y ;either ⌊(X÷Y) or ((X-(Y|X))÷Y
yield the integer part of the quotient of X
divided by Y ;
and X⌈(-X) is equivalent to |X .
In conventional notation the
symbols < , ≤ , = , ≥ , > ,
and ≠ are used to state relations among quantities;
for example, the expression 3<4 asserts
that 3 is less than 4 .
It is more useful to employ them as symbols for dyadic functions defined
to yield the value 1 if the indicated relation actually holds,
and the value zero if it does not.
Thus 3≤4 yields the value 1 ,
and 5+(3≤4) yields the value 6 .
Arrays.
The ability to refer to collections or arrays of items
is an important element in any natural language
and is equally important in mathematics.
The notation of vector algebra embodies the use of arrays
(vectors, matrices, 3-dimensional arrays; etc.)
but in a manner which is difficult to learn
and limited primarily to the treatment of linear functions.
Arrays are not normally included in elementary algebra,
probably because they are thought to be difficult
to learn and not relevant to elementary topics.
A vector (that is, a 1-dimensional array) can be represented
by a list of its elements (e.g., 1 3 5 7)
and all functions can be assumed to be applied element-by-element.
For example:
In addition to applying a function to each element of an array,
it is also necessary to be able to apply some specified function
to the collection itself.
For example, "Take the sum of all elements",
or "Take the product of all elements", or
"Take the maximum of all elements".
This can be denoted as follows:
+/2 5 3 2
12
×/2 5 3 2
60
⌈/2 5 3 2
5
The rules for using such vectors are simple and obvious
from the foregoing examples.
Vectors are relevant to elementary mathematics in a variety of ways.
For example:
1.
They can be used
(as in the foregoing examples) to display the patterns produced
by various functions when applied to certain patterns of arguments.
They can be used
to represent rational numbers. Thus if 3 4 represents the fraction three-fourths,
then 3 4×5 6 yields 15 24 , the product
of the fractions represented
by 3 4 and 5 6 .Moreover, ÷/3 4 and ÷/5 6 and ÷/15 24 yield
the actual numbers represented.
4.
A polynomial can be represented by its vector
of coefficients and vector of exponents.
For example, the polynomial with coefficients 3 1 2 4 and exponents 0 1 2 3 can
be evaluated for the argument 5 by the following expression:
+/3 1 2 4 × 5 * 0 1 2 3
558
Constants.
Conventional notation provides means for writing any positive constant
(e.g., 17 or 3.14) but there is no distinct notation
for negative constants, since the symbol - occurring in a number
like -35 is indistinguishable from the symbol for the negation function.
Thus negative thirty-five is written as an expression,
which is much as if we neglected to have symbols for five and zero
because expressions for them could be written in a variety of ways
such as 8-3 and 8-8 .
It seems advisable to follow Beberman
[1]
in using a raised minus sign to denote negative numbers.
For example:
3 - 5 4 3 2 1
¯2 ¯1 0 1 2
Conventional notation also provides no convenient way to represent numbers
which are easily expressed in expressions of the
form 2.14×108or 3.265×10¯9 .A
useful practice widely used in computer languages is
to replace the symbols ×10 by the symbol E (for exponent)
as follows: 2.14E8 and 3.265E¯9 .
Order of execution.
The order of execution in an algebraic expression is commonly specified by parentheses.
The rules for parentheses are very simple,
but the rules which apply in the absense of parentheses are complex and chaotic.
They are based primarily on a hierarchy of functions
(e.g., the power function is executed before multiplication,
which is executed before addition) which has apparently arisen
because of its convenience in writing polynomials.
Viewed as a matter of language,
the only purpose of such rules is the potential economy
in the use of parentheses and the consequent gain
in readability of complex expressions.
Economy and simplicity can be achieved by the following rule:
parentheses are obeyed as usual
and otherwise expressions are evaluated from right to left
with all functions being treated equally.
The advantages of this rule and the complex and ambiguity
of conventional rules are discussed in Berry
[2],
page 27 and in Iverson
[3],
Appendix A.
Even polynomials can be conveniently written without parentheses
if use is made of vectors.
For example, the polynomial in X with
coefficients 3 1 2 4 can be written
without parentheses
as +/3 1 2 4 × X * 0 1 2 3 .Moreover,
Horner's expression for the efficient evaluation of this same
polynomial can also be written without parentheses as follows:
3+X×1+X×2+X×4
Analogies with natural language.
The arithmetic expression 3×4 can be viewed as an order
to do something, that is,
multiply the arguments 3 and 4 .Similarly,
a more complex expression can be viewed as an order to perform
a number of operations in a specified order.
In this sense, an arithmetic expression is an imperative sentence,
and a function corresponds to an imperative verb in natural language.
Indeed, the word "function" derives from the Latin verb
"fungi" meaning "to perform".
This view of a function does not conflict with the usual
mathematical definition as a specified correspondence
between the elements of domain and range,
but rather supplements this static view with a dynamic view
of a function as that which produces the corresponding value
for any specified element of the domain.
If functions correspond to imperative verbs,
then their arguments (the things upon which they act)
correspond to nouns.
In fact, the word "argument" has (or at least had)
the meaning topic, theme, or subject.
Moreover, the positive integers, being the most concrete of arithmetical objects,
may be said to correspond to proper nouns.
What are the roles of negative numbers, rational numbers,
irrational numbers, and complex numbers?
The subtraction function, introduced as an inverse to addition,
yields positive integers in some cases but not in others,
and negative numbers are introduced
to refer to the results in these cases.
In other words, a negative number refers to a process
or the result of a process, and is therefore analogous to an abstract noun.
For example, the abstract noun "justice"
refers not to some concrete object
(examples of which one may point to) but to a process or result of a process.
Similarly, rational and complex numbers refer to the results of processes;
division, and finding the zeros of polynomials, respectively.
A.3 Algebraic Notation
Names.
An expression such as 3×X can be evaluated only
if the variable X has been assigned an actual value.
In one sense, therefore, a variable corresponds to a pronoun
whose referent must be made clear before any sentence including it
can be fully understood.
In English the referent may be made clear by an explicit statement,
but is more often made clear by indirection
(e.g., "See the door. Close it."),
or by context.
In conventional algebra, the value assigned to a variable name
is usually made clear informally by some statement such as
"Let X have the value 6 "
or "Let X=6 ".
Since the equal symbol (that is, '=') is also used in other ways,
it is better to avoid its use for this purpose
and to use a distinct symbol as follows:
X←6
Y←3×4
X+Y
18
(X-3)×(X-5)
3
Assigning names to expressions.
In the foregoing example, the expression (X-3)×(X-5) was written
as an instruction to evaluate the expression
for a particular value already assigned to X .
One also writes the same expression for the quite different notation
"Consider the expression (X-3)×(X-5) for any value
which might later be assigned to the argument X ."
This is a distinct notion which should be represented by distinct notation.
The idea is to be able to refer to the expression
and this can be done by assigning a name to it.
The following notation serves:
∇ Z ← G X
Z←(X-3)×(X-5)∇
The ∇'s indicate that the symbols between them
define a function;
the first line shows that the name of the function is G .The
names X and Z are dummy names standing
for the argument and result, and the second line shows how they are related.
Following this definition, the name G may be used as a function.
For example:
G 6
3
G 1 2 3 4 5 6 7
8 3 0 ¯1 0 3 8
Iterative functions can be defined with equal ease
as shown in Chapter 12.
Form of names.
If the variables occurring in algebraic sentences
are viewed simply as names, it seems reasonable to employ names
with some mnemonic significance as illustrated by the following sequence:
LENGTH←6
WIDTH←5
AREA←LENGTH×WIDTH
HEIGHT←4
VOLUME←AREA×HEIGHT
This is not done in conventional notation,
apparently because it is ruled out by the convention that
the multiplication sign may be elided; that is, AREA
cannot be used as a name because it would be interpreted
as A×R×E×A .
This same convention leads to other anomalies as well,
some of which were discussed in the section on arithmetic notation.
The proposal made there (i.e., that the multiplication sign
cannot be elided) will permit variable names of any length.
A.4 Analogies with the Teaching of Natural Language
If one views the teaching of algebra as the teaching of a language,
it appears remarkable how little attention is given
to the reading and writing of algebraic sentences,
and how much attention is given to identities, that is,
to the analysis of sentences with a view to determining
other equivalent sentences;
e.g., "Simplify the expression (X-4) × (X+4) ."
It is possible that this emphasis accounts
for much of the difficulty in teaching algebra,
and that the teaching and learning processes in natural languages
may suggest a more effective approach.
In the learning of a native language one can distinguish
the following major phases:
1.
An informal phase, in which the child learns to communicate in a combination
of gestures, single words, etc., but with no attempt to form grammatical sentences.
2.
A formal phase, in which the child learns to communicate in formal sentences.
This phase is essential because it is difficult or impossible to communicate
complex matters with precision
without imposing some formal structure on the language.
3.
An analytics phase, in which one learns to analyze sentences
with a view to determining equivalent
(and perhaps "simpler" or "more effective") sentences.
The extreme case of such analysis is Aristotelian Logic,
which attempts a formal analysis of certain classes of sentences.
More practical everyday cases occur
every time one carefully reads a composition
and suggests alternative sentences which convey the same meaning
in a briefer or simpler form.
The same phases can be distinguished in the teaching of algebraic notation:
1.
An informal phase
in which one issues an instruction to add 2 and 3
in any way which will be understood. For example:
2 + 3 Add 2 and 3
2 2
3 +3
--- ---
Add two and three
Add // and ///
The form of the expression is unimportant,
provided that the instruction is understood.
2.
A formal phase
in which one emphasizes proper sentence structure and would not
accept expressions such as
2
6 × 3 or 6 × (add two and three)
---
in lieu of 6×(2+3) .Again, adherence
to certain structural rules is necessary to permit the
precise communication of complex matters.
3.
An
analytic phrase in which one learns to analyze sentences
with a view to establishing certain relations (usually identity)
among them.
Thus one learns not only that 3+4 is equal to 4+3
but that the sentences X+Y and Y+X are equivalent,
that is, yield the same result whatever the meanings are assigned
to the pronouns X and Y .
In learning a native language, a child spends many years
in the informal and formal phrases (both in and out of school)
before facing the analytic phrase.
By this time she has easy familiarity with the purpose of a language
and the meanings of sentences which might be analyzed and transformed.
The situation is quite different in most conventional courses in algebra
— very little time is spent in the formal phase
(reading, writing and "understanding" formal algebraic sentences)
before attacking identities such as commutativity, associativity,
distributivity, etc.).
Indeed, students often do not realize that they might quickly
check their work in "simplification" by substituting
certain values for the variables occurring in the original
and derived expressions and comparing the evaluated results
to see if the expressions have the same "meaning",
at least for the chosen values of the variables.
It is interesting to speculate on what would happen
if a native language were taught in an analogous way,
that is, if children were forced to analyze sentences at a stage
in their development when their grasp of the purpose and meaning
of sentences were as shaky as the algebra student's
grasp of the purpose and meaning of algebraic sentences.
Perhaps they would fail to learn the converse,
just as many students fail to learn the much simpler task of reading.
Another interesting aspect of learning the non-analytic aspects
of a native language is that much (if not most) of the motivation
comes not from an interest in language,
but from the intrinsic interest of the material
(in children's stories, everyday dialogue, etc.)
for which it is used.
it is doubtful that the same is true in algebra —
ruling out statements of an analytic nature (identities, etc.),
how many "interesting" algebraic sentences
does a student encounter?
The use of arrays can open up the possibility
of much more interesting algebraic sentences.
This can apply both to sentences to be read
(that is, evaluated) and written by students.
For example, the statements:
produce interesting patterns
and therefore have more intrinsic interest than similar expressions
involving only single quantities.
For example, the last expression can be construed as yielding
a set of possible areas for a rectangle
having a fixed perimeter of 12 .
More interesting possibilities are opened up
by certain simple extensions of the use of arrays.
One example of such extensions will be treated here.
This extension allows one to apply any dyadic function
to two vectors A and B so as to obtain
not simply the element-by-element product produced by the
expression A×B but a table of all products
produced by pairing each element of A
with each element of B .For example:
The following analysis suggests the development
of an algebra curriculum with the following characteristics:
1.
The notation used is unambiguous, with simple and consistent rules of syntax,
and with provision for the simple and direct use of arrays.
Moreover, the notation is not taught as a separate matter,
but is introduced as needed in conjunction with the concepts represented.
2.
Heavy use is made of arrays to display mathematical properties
of functions in terms of patterns observed in vectors and matrices (tables),
and the make possible the reading, writing, and evaluation
of a host of interesting algebraic sentences before approaching
the analysis of sentences and the concomitant development of identities.
Such an approach has been adopted in the present text,
where it has been carried through as far as the treatment
of polynomials and of linear functions and linear equations.
The extension to further work in polynomials,
to slopes and derivatives, and to the circular and hyperbolic functions
is carried forward in Chapters 4-8 of Iverson
[3].
It must be emphasized that the proposed notation,
though simple, is not limited in application to elementary algebra.
A glance at the bibliography of Rault and Demars
[4]
will give some idea of the wide range of applicability.
The role of the computer.
Because the proposed notation is simple and systematic
it can be executed by automatic computers
and has been made available on a number of time-shared
computer terminal systems.
The most widely used of these
is described in Falkoff and Iverson
[5].
It is important to note that the notation is executed directly,
and the user need learn nothing about the computer itself.
In fact, each of the examples in this appendix are shown
exactly as they would be typed on a computer terminal keyboard.
The computer can obviously be useful in cases
where a good deal of tedious computation is required,
but it can be useful in other ways as well.
For example, it can be used by a student to explore
the behaviour of functions and discover their properties.
To do this a student will simply enter expressions
which apply the functions to various arguments.
If the terminal is equipped with a display device,
then such exploration can even be done collectively
by an entire class.
This and other ways of using the computer
are discussed by Berry et al
[6]
and in Appendix C.
Rault., J. C., and G. Demars, "Is APL Epidemic? Or a study of its growth
through an extended bibliography",
Fourth International APL User's Conference,
Board of Education of the City of Atlanta, Georgia, 1972. |
This course explores the connections between math and art in two and three dimensions. The class includes an exploration of Escher's work, tiling the plane, fractals, and the golden ratio. It also covers topics such as graphing equations and geometric constructions. |
the O- & N(A)-Level Mathematics syllabuses, including the aims, content, outcomes and the approaches to teaching and learning. This document comprises 5 chapters as described below. Chapter 1 provides an overview of the curriculum review, the goals and aims of the
The OLevel Additional Mathematics syllabus assumes knowledge of OLevel Mathematics. The general aims of the mathematics syllabuses are to enable students to: • acquire the necessary mathematical concepts and skills for continuous learning in
Cambridge OLevel Mathematics is recognised by universities and employers throughout the world as proof of mathematical knowledge and understanding. Successful Cambridge OLevel Mathematics candidates gain lifelong skills, including:
o College LevelMath Test (not all will be routed to this test)-- There are 20 questions on the College-Level Mathematics. The College-Level Mathematics test assesses from intermediate algebra through precalculus.
oMATH 1540 Advanced Calculus 2 o One 2000 levelMATH course as an upper level elective; Completes an honors thesis under the direction of a member of the mathematics faculty or completes a second 2000 level course in lieu of the honors thesis; and
Level 1 ALEKS Math Placement Assessment – Next Steps Your advisor has placed you into a Math course using the table on page 2. If you would like to know more about how you performed on you placement assessment, go to KSUALEKS.kent.edu, enter your
lower levelMath accounted for 1 in 10 individuals who successfully emerged from developmental Math. Upper level developmental Math-placed students were over represented among the individuals who passed the highest level developmental Math course.
Pure Math 101 Pure Math I MOVED up to London in October 1956 and entered the Royal College of Science. ... chemistry, and physics, and "O" level in a modern language (I chose Russian). The whole year was seen as something of an experiment: would |
Bookmarks
CBSE Syllabus for Class VIII 2010 And 2011 – Mathematics
CBSE is the recognized board which divides the syllabus in such a way that it does not make learning boring and it also minimizes the burden of students. CBSE syllabus for class VIII 2010 and 2011 for mathematics subject is divided in following categories:
· Number system
· Algebra
· Ration and Proportion
· Geometry
· Data handling
· Introduction to graphs
Here are some of the sub-categories which you need to study in detail:
Number System
(i) Rational Numbers:
· Properties of rational numbers.
· Consolidation of operations on rational numbers.
· Representation of rational numbers on the number line
· Word problem
(ii) Powers
· Integers as exponents.
· Laws of exponents with integral powers
(iii) Squares, Square roots, Cubes, Cube roots
· Square and Square roots
· Square roots using factor method and division method for numbers
· Cubes and cubes roots
· Estimating square roots and cube roots
(iv) Playing with numbers
· Number puzzles and games
· Deducing the divisibility test rules of 2, 3, 5, 9, 10 for a two or three-digit number
· Writing and understanding a 2 and 3 digit number in generalized form |
Smart implementation of the Common Core State Standards requires both an overall understanding of the standards and a grasp of their implications for planning, teaching, and learning. This quick-start guide provides a succinct, all-in-one look at
The structure, terminology, and emphases of the Common Core mathematics standards at the high school level, including the areas that represent the most significant changes to business as usual.
The meaning of the individual content standards, addressed by domain and cluster, within all six conceptual categories—Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability.
How the content standards, practice standards, and designated modeling standards connect across domains, categories, grade bands, and traditional course boundaries to help students develop both deep conceptual understanding and functional, real-world application skills.
Here, mathematics teachers and teacher leaders will find information they need to begin adapting their courses and practices to ensure all students master the new and challenging material the standards present and graduate ready for college or career—updated with the new codes and referrals released in September 2012.
The grade-level and subject-specific quick-start guides in the Understanding the Common Core Standards series, edited by John Kendall, are designed to help school leaders and school staffs turn Common Core standards into coherent, content-rich curriculum and effective, classroom-level lessons.
AMITRA SCHWOLS serves as a consultant at Mid-continent Research for Education and Learning (McREL). As an analyst at McREL, she has reviewed, revised, and developed standards documents for many districts, state agencies, and organizations. She has also reviewed instructional materials, created lesson plans, and conducted research on a wide variety of education topics. Ms. Schwols's work with the Common Core State Standards includes development of gap analysis, crosswalk, and transition documents, as well as facilitating groups of teacher leaders on their implementation.
KATHLEEN DEMPSEY is a principal consultant with McREL. In this role, Ms. Dempsey works to provide services, strategies, and materials to support improvement in mathematics education, curriculum development, formative assessment, and integration of instructional technology. Additionally, Ms. Dempsey currently serves as a primary investigator for two mathematics studies funded by the Institute of Education Sciences.
JOHN KENDALL (Series Editor) is Senior Director in Research at McREL in Denver. Having joined McREL in 1988, Mr. Kendall conducts research and development activities related to academic standards. He directs a technical assistance unit that provides standards-related services to schools, districts, states, and national and international organizations. He is author of Understanding Common Core State Standards, senior author of Content Knowledge: A Compendium of Standards and Benchmarks for K–12 Education, and the author or coauthor of numerous reports and guides related to standards-based systems. |
How YouMayUse This Resource Guide This guide is divided into chapters that match the chapters in the third editions of Technical Mathematics and Technical Mathematics with ...
Physics Fundamentals Worksheet Name 1. Joseph Olander, when confronted by the Board of Trustees at Evergreen State College about the fact that his transcripts showed that ...
A Wonderful Trig. Review Worksheet on Law of Sine and Law of Cosine Show all work on your own paper. Draw a diagram for each problem... Label the diagram completely. on Law of Sines and Cosines0001.pdf
1-1: Tables and Graphs What is statistics? What is data? What is a variable? What is population? What is a sample? What is a survey? What ... of Year Worksheet.pdf
Use the area formulas you learned in the chapter to solve the following problems #15 -22. 15. ) Determine the area of the triangle shown in Problem #9.
Applications of Math 10 Homework Outline Record the date when each homework section is assigned. Record a (check mark) for when the homework is complete. documents/10 apps Hmwk Outline.pdf
APPLICATIONS OF MATH 11 HOMEWORK OUTLINE Record the date when each section is assigned Record a check mark ( ) when the homework is complete you must SHOW YOUR ... documents/11 apps Hmwk Outline.pdf
7 PREREQUISITE SKILLS WORKSHEET FOR PHYSICS Prerequisite Skills Activity Objectives for Grade/Course State Standards Use sine, cosine, and tangent to solve for unknown side of ... |
Calculators are allowed within each mathematics classroom as a tool to facilitate calculations within complex problems. However, if the intent of the problem is a simple calculation such as a typical number sense problem found on an AIMS test review, calculators are not allowed.
To support this policy:
* Calculators ARE NOT ALLOWED within the Algebra 1/2 classes.
* A basic scientific calculator may be used within the Geometry classes.
All Geometry classes use the "AIMing for Success" program to incorporate daily practice on AIMS performance objectives within their regular activities.
All juniors and seniors have the option to enroll in individualized AIMS tutoring sessions held after school.
Help
All mathematics teachers encourage students to seek additional on any concepts causing confusion or if an assignments requires an individual more than 30 minutes to complete. Regular office hours are held both before anf after school.
Categories
Students can expect to receive daily homework assignments (including Fridays) designed to practice curriculum objectives. Assignments will generally be started during the class period, but students should expect to be responsible for up to 30 minutes of daily work outside of the class period. |
online course offered by the Saylor Foundation.'This introductory mathematics course is for you if you have a...
see more
This is a free online course offered by the Saylor Foundation.'In this course, you will study basic algebraic operations and...
see more
This is a free online course offered by the Saylor Foundation.'In this course, you will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes the solutions to algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing of linear equations. You will apply these skills to solve real world problems (word problems). Each unit will have its own application problems, depending on the concepts you have been exposed to. This course is also intended to provide you with a strong foundation for intermediate algebra and beyond.This course will begin with a review of some math concepts formed in pre-algebra, such as order of operations and simplifying simple algebraic expressions to get your feet wet. You will then build on these concepts by learning more about functions, graphing of functions, evaluation of functions, and factorization. You will spend time on the rules of exponents and their applications in distribution of multiplication over addition/subtraction.' |
Trade in A Concise Introduction to Pure Mathematics for an Amazon.co.uk gift card of up to £6.80, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more
Book DescriptionProduct Description
Review
"Liebeck's book, A Concise Introduction to Pure Mathematics, is one of the best I have seena gentle but fascinating introduction into the culture of mathematicsmathematics will [no longer] be viewed as some abstract black box" - From the Foreword by Robert Guralnick, University of Southern California, Los Angeles
This book is ideal for A-level students who are considering doing a numerate degree, particularly maths. It contains lots of useful methods and tricks, with full proofs of every theorem. It isn't highly technical, nor does it go into much depth, but it is an excellent primer and will make you realise some of the amazing things that can be proved quite simply with the right concepts.
The gap between high school and university mathematics is quite noticeable. I found this book to be an excellent book to prep a smooth landing to university mathematics. (The best one out of a long list of other similar books I had a look at)
Starts of really easy and clear but still goes beyond the "surface" when required. The chapters are structured very short, which I thought was a good thing.
It has a lot of worked examples. However, the book does not have solutions to the end-of-chapter exercises, which I thought was a long minus since I was reading the book on my own as a self study..
I bought this book after having it recommended to me from 3 independent sources and it was well recommended. I've just finished A2 maths, about to start Further Maths and looking to study Maths at University. It offers a great introduction to parts of mathematics I was unaware of in great style and detail. This book covers a vast number of topics and covers a suprising volume in just a few pages on each.
If you have any feeling that you want to study maths further, buy this book and it will show you why. |
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