Everything you need to pass the exam and get the college credit you deserve.
CLEP* is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities. For over 15 years, REA has helped students pass the CLEP* exam and earn college credit while reducing their tuition costs.
Our CLEP* test preps are perfect for adults returning to college (or attending for the first time), military service members, high-school graduates looking to earn college credit, or home-schooled students with knowledge that can translate into college credit.
There are many different ways to prepare for the CLEP*. What's best for you depends on how much time you have to study and how comfortable you are with the subject matter. Our test prep for CLEP* College Algebra and the free online tools that come with it, will allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.
Here's how it works:
Diagnostic exam at the REA Study Center focuses your study
Our online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you can personalize your prep and review where you need it the most.
Most complete subject review for CLEP* College Algebra
Our targeted review covers all the material you'll be expected to know for the exam and includes a glossary of must-know terms.
Two full-length practice exams
The online REA Study Center gives you two full-length practice tests and the most powerful scoring analysis and diagnostic tools available today. Instant score reports help you zero in on the CLEP* College Algebra topics that give you trouble now and show you how to arrive at the correct answer-so you'll be prepared on test day.
Alpha Teach Yourself Algebra I in 24 Hours provides readers with a structured, self-paced, straight-forward tutorial on algebra. It's the perfect textbook companion for students struggling with algebra, a solid primer for those looking to get a head start on an upcoming class, and a welcome refresher for parents tasked with helping out with homework. The book provides 24 one-hour lessons, with each chapter designed to build on the previous one.
? Covers classifying number sets, expressions, polynomials, factoring, radicals, exponents and logarithms, and much more
? Each chapter ends with a quiz so readers can identify where they may need more help
Factor fearlessly, conquer the quadratic formula, and solve linear equations
There's no doubt that algebra can be easy to some while extremely challenging to others. If you're vexed by variables, Algebra I For Dummies, 2nd Edition provides the plain-English, easy-to-follow guidance you need to get the right solution every time!
Now with 25% new and revised content, this easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems with confidence. You'll understand how to factor fearlessly, conquer the quadratic formula, and solve linear equations.Includes revised and updated examples and practice problemsProvides explanations and practical examples that mirror today's teaching methodsOther titles by Sterling: Algebra II For Dummies and Algebra Workbook For Dummies
Whether you're currently enrolled in a high school or college algebra course or are just looking to brush-up your skills, Algebra I For Dummies, 2nd Edition gives you friendly and comprehensible guidance on this often difficult-to-grasp subject.
Tips for simplifying tricky basic math and pre-algebra operations
Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.Explanations and practical examples that mirror today's teaching methodsRelevant cultural vernacular and referencesStandard For Dummiesmaterials that match the current standard and design
Basic Math & Pre-Algebra For Dummies takes the intimidation out of tricky operations and helps you get ready for algebra!
Written by two pioneers of the concept of math anxiety and how to overcome it, Arithmetic and Algebra Again has helped tens of thousands of people conquer their irrational fear of math.
This revised and expanded second edition of the perennial bestseller:Features the latest techniques for breaking through common anxieties about numbers Takes a real-world approach that lets mathphobes learn the math they need as they need it Covers all key math areas--from whole numbers and fractions to basic algebra Features a section on practical math for banking, mortgages, interest, and statistics and probability Includes a new section on the graphing calculator, a chapter on the metric system, a section on word problems, and all updated exercises
Trying to tackle algebra but nothing's adding up? No problem! Factor in Algebra Demystified, Second Edition and multiply your chances of learning this important branch of mathematics.
Written in a step-by-step format, this practical guide covers fractions, variables, decimals, negative numbers, exponents, roots, and factoring. Techniques for solving linear and quadratic equations and applications are discussed in detail. Clear examples, concise explanations, and worked problems with complete solutions make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.
It's a no-brainer! You'll learn how to:Translate English sentences into mathematical symbols Write the negative of numbers and variables Factor expressions Use the distributive property to expand expressions Solve applied problems
Simple enough for a beginner, but challenging enough for an advanced student, Algebra Demystified, Second Edition helps you master this essential math subject. It's also the perfect resource for preparing you for higher level math classes and college placement tests.
Linear Sentences in One Variable
Segments, Lines, and Inequalities
Linear Sentences in Two Variables
Linear Equations in Three Variables
Relations and Functions
Radicals and Complex Numbers
Quadratics in One Variable
Exponential and Logarithmic Functions
Sequences and Series
This popular study guide shows students easy ways to solve what they struggle with most in algebra: word problems. How to Solve Word Problems in Algebra, Second Edition, is ideal for anyone who wants to master these skills. Completely updated, with contemporary language and examples, features solution methods that are easy to learn and remember, plus a self-test.
Practice makes perfect—and helps deepen yourunderstanding of algebra by solving problems
1,001 Algebra I Practice Problems For Dummies, with freeaccess to online practice problems, takes you beyond theinstruction and guidance offered in Algebra I For Dummies,giving you 1,001 opportunities to practice solving problems fromthe major topics in algebra. You start with some basic operations,move on to algebraic properties, polynomials, and quadraticequations, and finish up with graphing. Every practice questionincludes not only a solution but a step-by-step explanation. Fromthe book, go online and find:One year free subscription to all 1,001 practice problemsOn-the-go access any way you want it—from your computer,smart phone, or tabletMultiple choice questions on all you math course topicsPersonalized reports that track your progress and help show youwhere you need to study the mostCustomized practice sets for self-directed studyPractice problems categorized as easy, medium, or hard
Whether you're studying algebra at the high school or collegelevel, the practice problems in 1,001 Algebra I PracticeProblems For Dummies give you a chance to practice andreinforce the skill s you learn in the classroom and help yourefine your understanding of algebra.
Note to readers: 1,001 Algebra I Practice Problems ForDummies, which only includes problems to solve, is a greatcompanion to Algebra I For Dummies, 2nd Edition which offerscomplete instruction on all topics in a typical Algebra Icourse.
Fortunately, there's Schaum's. This all-in-one-package includes more than 1,900 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 30 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.
More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand.
This Schaum's Outline gives you1,940 fully solved problems Hundreds of additional practice problems with answers Coverage of all course concepts
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!
Schaum's Outlines--Problem Solved.
Ready to learn math fundamentals but can't seem to get your brain to function? No problem! Add Pre-Algebra Demystified, Second Edition, to the equation and you'll solve your dilemma in no time.
Written in a step-by-step format, this practical guide begins by covering whole numbers, integers, fractions, decimals, and percents. You'll move on to expressions, equations, measurement, and graphing. Operations with monomials and polynomials are also discussed. Detailed examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.
It's a no-brainer! You'll learn:Addition, subtraction, multiplication, and division of whole numbers, integers, fractions, decimals, and algebraic expressions Techniques for solving equations and problems Measures of length, weight, capacity, and time Methods for plotting points and graphing lines
Simple enough for a beginner, but challenging enough for an advanced student, Pre-Algebra Demystified, Second Edition, helps you master this essential mathematics subject. It's also the perfect way to review the topic if all you need is a quick refresh.
Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive it off the lot? Can you really afford an XBox 360 and a new iPhone? Learn how to put algebra to work for you, and nail your class exams along the way.
Your time is way too valuable to waste struggling with new concepts. Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, Head First Algebra uses a visually rich format specifically designed to take advantage of the way your brain really works.
Practice Makes Perfect: Algebra II presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations, as well as an introducing you to probability and trigonometry. Inside you will find the help you need for boosting your skills, preparing for an exam or re-introducing yourself to the subject. More than 500 exercises and answers covering all aspects of algebra will get you on your way to mastering algebra!
"The main object of this book is to dispel the fear of mathematics," declares author W. W. Sawyer, adding that "Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject." Now retired, Sawyer won international renown for his innovative teaching methods, which he used at colleges in England and Scotland as well as Africa, New Zealand, and North America. His insights into the pleasures and practicalities of mathematics will appeal to readers of all backgrounds.
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.
By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.
Algebra II builds on your Algebra I skills to prepare you fortrigonometry, calculus, and a of myriad STEM topics. Workingthrough practice problems helps students better ingest and retainlesson content, creating a solid foundation to build on for futuresuccess.
Algebra II Workbook For Dummies, 2nd Edition helps youlearn Algebra II by doing Algebra II. Author and math professorMary Jane Sterling walks you through the entire course, showing youhow to approach and solve the problems you encounter in class.You'll begin by refreshing your Algebra I skills, because you'llneed a strong foundation to build upon. From there, you'll workthrough practice problems to clarify concepts and improveunderstanding and retention.Revisit quadratic equations, inequalities, radicals, and basicgraphsMaster quadratic, exponential, and logarithmic functionsTackle conic sections, as well as linear and nonlinearsystemsGrasp the concepts of matrices, sequences, and imaginarynumbers
Algebra II Workbook For Dummies, 2nd Edition includessections on graphing and special sequences to familiarize you withthe key concepts that will follow you to trigonometry and beyond.Don't waste any time getting started. Algebra II Workbook ForDummies, 2nd Edition is your complete guide to success.
-- A natural transition from basic math to algebra, with a review of relevant concepts and operations.
-- An introduction to linear equations and functions, including graphing and inequalities.
-- Explanations of how to solve absolute-value equations and radical equations.
-- Instructions on how to perform operations on polynomials, and factoring.
-- An exploration of how to work with quadratic equations and quadratic functions; and rational expressions, equations, and functions.
-- Special sidebars pointing out the reasoning behind the techniques, which is an essential part of Common Core instruction.
-- Separate workbook section of extra Algebra practice problems-like getting two books in one!
The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.
No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
Whether you're brushing up on pre-Algebra concepts or on your way toward mastering algebraic fractions, factoring, and functions, CliffsQuickReview Algebra I can help. This guide introduces each topic, defines key terms, and carefully walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such asEquations, ratios, and proportionInequalities, graphing, and absolute valueCoordinate GeometryRoots and radicalsQuadratic equations
CliffsQuickReview Algebra I acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review—you decide what works best with your needs. Here are just a few ways you can search for topics:Use the free Pocket Guide full of essential informationGet a glimpse of what you'll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapterUse the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to knowTest your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource CenterUse the glossary to find key terms fast.
With titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades.
". . .recommended for the teacher and researcher as well as forgraduate students. In fact, [it] has a place on everymathematician's bookshelf." -American Mathematical Monthly
Linear Algebra and Its Applications, Second Edition presents linearalgebra as the theory and practice of linear spaces and linear mapswith a unique focus on the analytical aspects as well as thenumerous applications of the subject. In addition to thoroughcoverage of linear equations, matrices, vector spaces, game theory,and numerical analysis, the Second Edition featuresstudent-friendly additions that enhance the book's accessibility,including expanded topical coverage in the early chapters,additional exercises, and solutions to selected problems.
Beginning chapters are devoted to the abstract structure of finitedimensional vector spaces, and subsequent chapters addressconvexity and the duality theorem as well as describe the basics ofnormed linear spaces and linear maps between normed spaces.
Further updates and revisions have been included to reflect themost up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjointmatrix
The Householder algorithm for turning self-adjoint matricesinto tridiagonal formThe compactness of the unit ball as a criterion of finitedimensionality of a normed linear spaceAdditionally, eight new appendices have been added and cover topicssuch as: the Fast Fourier Transform; the spectral radius theorem;the Lorentz group; the compactness criterion for finitedimensionality; the characterization of commentators; proof ofLiapunov's stability criterion; the construction of the JordanCanonical form of matrices; and Carl Pearcy's elegant proof ofHalmos' conjecture about the numerical range of matrices.
Clear, concise, and superbly organized, Linear Algebra and ItsApplications, Second Edition serves as an excellent text foradvanced undergraduate- and graduate-level courses in linearalgebra. Its comprehensive treatment of the subject also makes itan ideal reference or self-study for industry professionals.
And if this e-book leaves you wanting even more! more! more! there's The Math Dude's Quick and Dirty Guide to Algebra, with even more math number games, explanations, and—dare we say it—fun.
- Teaches general principles that can be applied to a wide variety of problems.
- Avoids the mindless and excessive routine computations that characterize conventional textbooks.
- Treats algebra as a logically coherent discipline, not as a disjointed collection of techniques.
- Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.
- Omits digressions, excessive formalities, and repetitive exercises.
- Covers all the algebra needed to take a calculus course.
- Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it.
1. A Few Basics
5. Linear & Quadratic Equations
6. Inequalities & Absolute Values
7. Coordinates in a Plane
8. Functions & Graphs
9. Straight Lines
12. Types of Functions
14. Dividing Polynomials
15. Systems of Linear Equations
16. Geometric Progressions & Series
17. Arithmetic Progressions
18. Permutation & Combinations
19. The Binomial Theorem
20. Mathematical Induction
Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger’s clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory.
This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach.
Topics covered include:• Rings• Integral domains• The fundamental theorem of arithmetic• Fields• Groups• Lagrange’s theorem• Isomorphism theorems for groups• Fundamental theorem of finite abelian groups• The simplicity of A n for n 5• Sylow theorems• The Jordan-Hölder theorem• Ring isomorphism theorems• Euclidean domains• Principal ideal domains• The fundamental theorem of algebra• Vector spaces• Algebras• Field extensions: algebraic and transcendental• The fundamental theorem of Galois theory• The insolvability of the quintic
U Can: Basic Math & Pre-Algebra For Dummies is thefun, friendly guide to making sense of math. It walks you throughthe "how" and "why" to help you master the crucial operations thatunderpin every math class you'll ever take. With no-nonsenselessons, step-by-step instructions, practical examples, and plentyof practice, you'll learn how to manipulate non-whole numbers,tackle pesky fractions, deal with weights and measures, simplifyalgebraic expressions, and so much more. The "learn it – doit" style helps you move at your own pace, with lesson-sizedexplanations, examples, and practice. You also get access to 1,001more practice problems online, where you can create customizedquizzes and study the topics where you need the most help.
Math can be hard — and the basics in U Can: Basic Math& Pre-Algebra For Dummies lay the foundation for classesdown the line. Consider this resource as your guide to mathmastery, with step-by-step help for learning to:Put numbers in their placeMake sense of fractions, decimals, and percentsGet a grasp of basic geometrySimplify basic algebraic equations
Believe it or not, math can be fun! And the better youunderstand it now, the more likely you are to do well in school,earn a degree, and get a good job. U Can: Basic Math &Pre-Algebra For Dummies gives you the skills, understanding,and confidence you need to conquer math once and for all.
"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." MATHEMATICAL REVIEWS
This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text.
“The text is geared to the needs of the beginning graduate student, covering with complete, well-written proofs the usual major branches of groups, rings, fields, and modules...[n]one of the material one expects in a book like this is missing, and the level of detail is appropriate for its intended audience.” (Alberto Delgado, MathSciNet)
“This text promotes the conceptual understanding of algebra as a whole, and that with great methodological mastery. Although the presentation is predominantly abstract...it nevertheless features a careful selection of important examples, together with a remarkably detailed and strategically skillful elaboration of the more sophisticated, abstract theories.” (Werner Kleinert, Zentralblatt)
For the new edition, the author has completely rewritten the text, reorganized many of the sections, and even cut or shortened material which is no longer essential. He has added a chapter on Ext and Tor, as well as a bit of topology.
Key features of Number Theory: Structures, Examples, and Problems:
* A rigorous exposition starts with the natural numbers and the basics.
* Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties.
* Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered.
* Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems.
* Glossary, bibliography, and comprehensive index round out the text.
Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels.
The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book.
Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.
The quickest route to learning a subject is through a solid grounding in the basics. So what you won’t find in Easy Algebra Step-by-Step is a lot of endless drills. Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused exercises that are linked to core skills--enabling learners to grasp when and how to apply those techniques.This book features: Large step-by-step charts breaking down each step within a process and showing clear connections between topics and annotations to clarify difficulties Stay-in-step panels show how to cope with variations to the core steps Step-it-up exercises link practice to the core steps already presented Missteps and stumbles highlight common errors to avoid
You can master algebra as long as you take it Step-by-Step!
It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.
Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.
The book covers key foundation topics:
o Taylor series methods
o Runge--Kutta methods
o Linear multistep methods
and a range of modern themes:
o Adaptive stepsize selection
o Long term dynamics
o Modified equations
o Geometric integration
o Stochastic differential equations
The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
* Gradual progression in problem difficulty builds and strengthens mathematical skills and techniques
* Basic topics include trigonometric formulas and identities, their applications in the geometry of the triangle, trigonometric equations and inequalities, and substitutions involving trigonometric functions
* Problem-solving tactics and strategies, along with practical test-taking techniques, provide in-depth enrichment and preparation for possible participation in various mathematical competitions
* Comprehensive introduction (first chapter) to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry expose advanced students to college level material
103 Trigonometry Problems is a cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training.
Other books by the authors include 102 Combinatorial Problems: From the Training of the USA IMO Team (0-8176-4317-6, 2003) and A Path to Combinatorics for Undergraduates: Counting Strategies (0-8176-4288-9, 2004).
Elements of Topology provides a basic introduction to point-set topology and algebraic topology. It is intended for advanced undergraduate and beginning graduate students with working knowledge of analysis and algebra. Topics discussed include the theory of convergence, function spaces, topological transformation groups, fundamental groups, and covering spaces.
The author makes the subject accessible by providing more than 250 worked examples and counterexamples with applications. The text also includes numerous end-of-section exercises to put the material into context.
The text begins with an informal introduction to the algebra of classes, exploring union, intersection, and complementation; the commutative, associative, and distributive laws; difference and symmetric difference; and Venn diagrams. Professor Goodstein proceeds to a detailed examination of three different axiomatizations, and an outline of a fourth system of axioms appears in the examples. The final chapter, on lattices, examines Boolean algebra in the setting of the theory of partial order. Numerous examples appear at the end of each chapter, with full solutions at the end.
This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.Presentation of many new results in one place for the first time.First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals. Fredholm determinants and Painlevé equations.The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities.Fredholm determinants and inverse scattering theory.Probability densities of random determinants.
Key topics and features of Basic Algebra:
*Linear algebra and group theory build on each other continually
*Chapters on modern algebra treat groups, rings, fields, modules, and Galois groups, with emphasis on methods of computation throughout
*Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry
*Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems
*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; includes blocks of problems that introduce additional topics and applications for further study
*Applications to science and engineering (e.g., the fast Fourier transform, the theory of error-correcting codes, the use of the Jordan canonical form in solving linear systems of ordinary differential equations, and constructions of interest in mathematical physics) appear in sequences of problems
Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs.
If your child is struggling with math, then this book is for you; the short book covers the topic and also contains 30 practice problems to work with.
This subject comes from the book “Sixth Grade Math (For Home School or Extra Practice)”; it more thoroughly covers more fifth grade topics to help your child get a better understanding of fourth grade math. If you purchased that book, or plan to purchase that book, do not purchase this, as the problems are the same.
Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.