In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.
Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.
At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
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.
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An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.
Instructors will find the latest edition pitched at a suitable level of difficulty and will appreciate its gradual increase in the level of sophistication as the student progresses through the book. Rather than inserting superficial applications at the expense of important mathematical concepts, the Beachy and Blair solid, well-organized treatment motivates the subject with concrete problems from areas that students have previously encountered, namely, the integers and polynomials over the real numbers.
Supplementary material for instructors and students available on the books Web site: www.math.niu.edu/~beachy/abstract_algebra/
In Chapter 1, the author discusses the essential ingredients of a mathematical system, and in the next four chapters covers the basic number systems, decompositions of integers, diophantine problems, and congruences. Chapters 6 through 9 examine groups, rings, domains, fields, polynomial rings, and quadratic domains.Chapters 10 through 13 cover modular systems, modules and vector spaces, linear transformations and matrices, and the elementary theory of matrices. The author, Professor of Mathematics at the University of Pittsburgh, includes many examples and, at the end of each chapter, a large number of problems of varying levels of difficulty.
It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived.
As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.
The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
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
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
The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.
"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.
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.
Solving Word Problems is one of the biggest hurdle that kids face in Algebra. A bit of imagination is required to understand and solve these type of problems along with the calculations.This book breaks simple word problems using graphics thus helping the kids to visualize and understand the word problems. It develops the imaginative thinking required to solve these problems from an early level. This will help the kids to solve difficult problems as they will learn to imagine, analyze and break the problem into small parts which gives a better understanding on how to solve these type of problems.
Do nice guys always finish last?
Does playing hard-to-get ever work?
What really makes for a good chat-up line?
When it comes to relationships, there’s no shortage of advice from self-help ‘experts’, pick-up artists, and glossy magazines. But modern-day myths of attraction often have no basis in fact or – worse – are rooted in little more than misogyny. In Attraction Explained, psychologist Viren Swami debunks these myths and draws on cutting-edge research to provide a ground-breaking and evidence-based account of relationship formation.
At the core of this book is a very simple idea: there are no ‘laws of attraction’, no foolproof methods or strategies for getting someone to date you. But this isn’t to say that there’s nothing to be gained from studying attraction. Based on science rather than self-help clichés, Attraction Explained looks at how factors such as geography, appearance, personality, and similarity affect who we fall for and why.
The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.
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
In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.
“This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications.”
– Electric Review
A comprehensive introduction, Linear Algebra: Ideas and Applications, Fourth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique.
The book introduces each new concept in the context of an explicit numerical example, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs.
Linear Algebra: Ideas and Applications, Fourth Edition also features:Two new and independent sections on the rapidly developing subject of wavelets A thoroughly updated section on electrical circuit theory Illuminating applications of linear algebra with self-study questions for additional study End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB® code
Linear Algebra: Ideas and Applications, Fourth Edition is an excellent undergraduate-level textbook for one or two semester courses for students majoring in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.
The chapters herein are arranged to provide insight into the breadth of studies unique to communication, acknowledging along the way the contributions of researchers from psychology, political science, and sociology. Heath and Bryant chart developments and linkages within and between ways of looking at communication. The volume establishes an orientation for the social scientific study of communication, discussing principles of research, and outlining the requirements for the development and evaluation of theories.
Appropriate for use in communication theory courses at the advanced undergraduate and graduate level, this text offers students insights to understanding the issues and possible answers to the question of what communication is in all forms and contexts.
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.
As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level.
The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.
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.
The University of Toronto Undergraduate Competition was founded to provide additional competition experience for undergraduates preparing for the Putnam competition, and is particularly useful for the freshman or sophomore undergraduate. Lecturers, instructors, and coaches for mathematics competitions will find this presentation useful. Many of the problems are of intermediate difficulty and relate to the first two years of the undergraduate curriculum. The problems presented may be particularly useful for regular class assignments. Moreover, this text contains problems that lie outside the regular syllabus and may interest students who are eager to learn beyond the classroom.
Throughout the book, Guerrero and Floyd highlight areas where research is either contradictory or inconclusive, hoping that in the years to come scholars will have a clearer understanding of these issues. The volume concludes with a discussion of practical implications that emerge from the scholarly literature on nonverbal communication in relationships – an essential component for understanding relationships in the real world.
Nonverbal Communication in Close Relationships makes an important contribution to the development of our understanding not only of relationship processes but also of the specific workings of nonverbal communication. It will serve as a springboard for asking new questions and advancing new theories about nonverbal communication. It is intended for scholars and advanced students in personal relationship study, social psychology, interpersonal communication, nonverbal communication, family studies, and family communication. It will also be a helpful resource for researchers, clinicians, and couples searching for a better understanding of the complicated roles that nonverbal cues play in relationships.
Practice makes perfect—and helps deepen your understanding of algebra by solving problems
1,001 Algebra I Practice Problems For Dummies, with free access to online practice problems, takes you beyond the instruction and guidance offered in Algebra I For Dummies, giving you 1,001 opportunities to practice solving problems from the major topics in algebra. You start with some basic operations, move on to algebraic properties, polynomials, and quadratic equations, and finish up with graphing. Every practice question includes not only a solution but a step-by-step explanation. From the book, go online and find:One year free subscription to all 1,001 practice problems On-the-go access any way you want it—from your computer, smart phone, or tablet Multiple choice questions on all you math course topics Personalized reports that track your progress and help show you where you need to study the most Customized practice sets for self-directed study Practice problems categorized as easy, medium, or hard
Whether you're studying algebra at the high school or college level, the practice problems in 1,001 Algebra I Practice Problems For Dummies give you a chance to practice and reinforce the skill s you learn in the classroom and help you refine your understanding of algebra.
Note to readers: 1,001 Algebra I Practice Problems For Dummies, which only includes problems to solve, is a great companion to Algebra I For Dummies, 2nd Edition which offers complete instruction on all topics in a typical Algebra I course.
The volume consists of three sections: introductory issues, types of relationships, and relationship processes. In the first section, there is an exploration of the functions and benefits of close relationships, the diversity of methodologies used to study them, and the changing social context in which close relationships are embedded. A second section examines the various types of close relationships, including family bonds and friendships. The third section focuses on key relationship processes, including attachment, intimacy, sexuality, and conflict.
This book is designed to be an essential resource for senior undergraduate and postgraduate students, researchers, and practitioners, and will be suitable as a resource in advanced courses dealing with the social psychology of close relationships.
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
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.
Topics include the normal structure of groups: subgroups; homomorphisms and quotients; series; direct products and the structure of finitely generated Abelian groups; and group action on groups. Additional subjects range from the arithmetical structure of groups to classical notions of transfer and splitting by means of group action arguments. More than 675 exercises, many accompanied by hints, illustrate and extend the material.
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.
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!
Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success.
Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebra I skills, because you'll need a strong foundation to build upon. From there, you'll work through practice problems to clarify concepts and improve understanding and retention.Revisit quadratic equations, inequalities, radicals, and basic graphs Master quadratic, exponential, and logarithmic functions Tackle conic sections, as well as linear and nonlinear systems Grasp the concepts of matrices, sequences, and imaginary numbers
Algebra II Workbook For Dummies, 2nd Edition includes sections on graphing and special sequences to familiarize you with the key concepts that will follow you to trigonometry and beyond. Don't waste any time getting started. Algebra II Workbook For Dummies, 2nd Edition is your complete guide to success.
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.
"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.
Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own.
Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.
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.
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 methods Relevant cultural vernacular and references Standard 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!
Basic Math & Pre-Algebra Workbook For Dummies is your ticket to finally getting a handle on math! Designed to help you strengthen your weak spots and pinpoint problem areas, this book provides hundreds of practice problems to help you get over the hump. Each section includes a brief review of key concepts and full explanations for every practice problem, so you'll always know exactly where you went wrong. The companion website gives you access to quizzes for each chapter, so you can test your understanding and identify your sticking points before moving on to the next topic. You'll brush up on the rules of basic operations, and then learn what to do when the numbers just won't behave—negative numbers, inequalities, algebraic expressions, scientific notation, and other tricky situations will become second nature as you refresh what you know and learn what you missed.
Each math class you take builds on the ones that came before; if you got lost somewhere around fractions, you'll have a difficult time keeping up in Algebra, Geometry, Trigonometry, and Calculus—so don't fall behind! This book provides plenty of practice and patient guidance to help you slay the math monster once and for all. Make sense of fractions, decimals, and percentages Learn how to handle inequalities, exponents, square roots, and absolute values Simplify expressions and solve simple algebraic equations Find your way around a triangle, circle, trapezoid, and more
Once you get comfortable with the rules and operations, math takes on a whole new dimension. Curiosity replaces anxiety, and problems start feeling like puzzles rather than hurdles. All it takes is practice. Basic Math & Pre-Algebra Workbook For Dummies is your ultimate math coach, with hundreds of guided practice practice problems to help you break through the math barrier.
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.