The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    The calculus is not a hard subject and I prove this through an easy to read and obvious approach spanning only 100 pages. I have written this book with the following type of student in mind; the non-traditional student returning to college after a long break, a notoriously weak student in math who just needs to get past calculus to obtain a degree, and the garage tinkerer who wishes to understand a little more about the technical subjects. This book is meant to address the many fundamental thought-blocks that keep the average 'mathaphobe' (or just an interested person who doesn't have the time to enroll in a course) from excelling in mathematics in a clear and concise manner. It is my sincerest hope that this book helps you with your needs.Show more Show less

    From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

    Practical Algebra is an easy andfun-to-use workout program that quickly puts you in command of allthe basic concepts and tools of algebra. With the aid of practical, real-life examples and applications, you'll learn: * The basic approach and application of algebra to problemsolving * The number system (in a much broader way than you have known itfrom arithmetic) * Monomials and polynomials; factoring algebraic expressions; howto handle algebraic fractions; exponents, roots, and radicals;linear and fractional equations * Functions and graphs; quadratic equations; inequalities; ratio, proportion, and variation; how to solve word problems, andmore Authors Peter Selby and Steve Slavin emphasize practical algebrathroughout by providing you with techniques for solving problems ina wide range of disciplines--from engineering, biology, chemistry, and the physical sciences, to psychology and even sociology andbusiness administration. Step by step, Practical Algebra shows youhow to solve algebraic problems in each of these areas, then allowsyou to tackle similar problems on your own, at your own pace.Self-tests are provided at the end of each chapter so you canmeasure your mastery.

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

    It contains many puzzles and their solutions and aims to attract many readers in an age where computer science, logic, and mathematics are becoming increasingly important and popular.

    The text offers a flexible organization, enabling instructors to adapt the book to their particular courses. The book is both complete and careful, and it continues to maintain its emphasis on algorithms and applications. Excellent exercise sets allow students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making this the ideal text for preparing students for advanced study.

    It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    So it's not surprising that we persist in thinking that we're in with a chance, whether we're playing the lottery or working out the likelihood of extra-terrestrial life. In Chance, a (not entirely) random selection of the New Scientist's sharpest minds provide fascinating insights into luck, randomness, risk and probability. From the secrets of coincidence to placing the perfect bet, the science of random number generation to the surprisingly haphazard decisions of criminal juries, it will explore these, and many other, tantalising questions.Following on from the bestselling Nothing and Question Everything, this book will open your eyes to the weird and wonderful world of chance - and help you see when some things, in fact, aren't random at all.

    It follows standards-based principles, but also teaches readers ways around problems they are likely to face using (X)HTML.While XHTML is the "current" standard, the book still covers HTML because many people do not yet understand that XHTML is the official successor to HTML, and many readers will still stick with HTML for backward compatibility and simpler/informal Web pages that don't require XHTML compliance.The book teaches basic principles of usability and accessibility along the way, to get users into the mode of developing Web pages that will be available to as many viewers as possible from the start. The book also covers the most commonly used programming/scripting language -- JavaScript -- and provides readers with a roadmap of other Web technologies to learn after mastering this book to add more functionality to their sites.

    It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the students existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research-based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

    It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.