Haskell emerged in the last decade as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvellous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures.This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others.

    joyfully shows you how to make nature's numbers dance."--Bill Nye (the science guy)The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the "mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike."A positively joyful exploration of mathematics."-Publishers Weekly, starred review"Each [trick] is more dazzling than the last."-Physics World

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    Theoretical, yet applied. Statistics for Business and Economics, Eleventh Edition, gives you the best of both worlds. Using a rich array of applications from a variety of industries, McClave/Sincich/Benson clearly demonstrates how to use statistics effectively in a business environment.The book focuses on developing statistical thinking so the reader can better assess the credibility and value of inferences made from data. As consumers and future producers of statistical inferences, readers are introduced to a wide variety of data collection and analysis techniques to help them evaluate data and make informed business decisions. As with previous editions, this revision offers an abundance of applications with many new and updated exercises that draw on real business situations and recent economic events. The authors assume a background of basic algebra.

    Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all, this is an excellent work, of equally high value for both student and teacher." Zentralblatt f�r Mathematik

    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.

    Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics — profusely illustrated — include: Mathematical Models, Elementary Concepts of Graph Theory, Transportation Problems, Connection Problems, Party Problems, Digraphs and Mathematical Models, Games and Puzzles, Graphs and Social Psychology, Planar Graphs and Coloring Problems, and Graphs and Other Mathematics. A useful Appendix covers Sets, Relations, Functions, and Proofs, and a section devoted to exercises — with answers, hints, and solutions — is especially valuable to anyone encountering graph theory for the first time. Undergraduate mathematics students at every level, puzzlists, and mathematical hobbyists will find well-organized coverage of the fundamentals of graph theory in this highly readable and thoroughly enjoyable book.

    A Key Strength Of This Text Is Zill'S Emphasis On Differential Equations As Mathematical Models, Discussing The Constructs And Pitfalls Of Each. The Third Edition Is Comprehensive, Yet Flexible, To Meet The Unique Needs Of Various Course Offerings Ranging From Ordinary Differential Equations To Vector Calculus. Numerous New Projects Contributed By Esteemed Mathematicians Have Been Added. Key Features O The Entire Text Has Been Modernized To Prepare Engineers And Scientists With The Mathematical Skills Required To Meet Current Technological Challenges. O The New Larger Trim Size And 2-Color Design Make The Text A Pleasure To Read And Learn From. O Numerous NEW Engineering And Science Projects Contributed By Top Mathematicians Have Been Added, And Are Tied To Key Mathematical Topics In The Text. O Divided Into Five Major Parts, The Text'S Flexibility Allows Instructors To Customize The Text To Fit Their Needs. The First Eight Chapters Are Ideal For A Complete Short Course In Ordinary Differential Equations. O The Gram-Schmidt Orthogonalization Process Has Been Added In Chapter 7 And Is Used In Subsequent Chapters. O All Figures Now Have Explanatory Captions. Supplements O Complete Instructor'S Solutions: Includes All Solutions To The Exercises Found In The Text. Powerpoint Lecture Slides And Additional Instructor'S Resources Are Available Online. O Student Solutions To Accompany Advanced Engineering Mathematics, Third Edition: This Student Supplement Contains The Answers To Every Third Problem In The Textbook, Allowing Students To Assess Their Progress And Review Key Ideas And Concepts Discussed Throughout The Text. ISBN: 0-7637-4095-0

    Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation — Classical Theory; Fourier Approximation — Modern Theory; and Exponential Approximation.

    But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. "Here's Looking at Euclid "is a rare gem that brings the beauty of math to life.

    CONTAINS MCQ'S

    With it has come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It should be a valuable resource for statisticians and anyone interested in data mining in science or industry. The book's coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting—the first comprehensive treatment of this topic in any book. Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie wrote much of the statistical modeling software in S-PLUS and invented principal curves and surfaces. Tibshirani proposed the Lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, and projection pursuit.

    This well-organized text defines the role of the general dentist as a member of the surgical management team. Basic techniques of evaluation, diagnosis, and medical management are presented in explicit detail that allows the reader to immediately apply these methods to practice. It provides information on the basic oral surgery procedures that the general practitioner encounters, as well as an overview of oral and maxillofacial surgery procedures performed by the specialist. All surgical techniques are well illustrated so readers can visualize key surgical concepts.Authored by well-known, respected practitioners and contributors in the field of OMS, drawing on their wealth of clinical expertise.Two-color format highlights key concepts and makes information easy to follow.Appendices provide valuable reference sections, including useful examples of prescriptions, postoperative instructions, an informed consent form, and current instrument pricing.A new chapter focuses on facial esthetic surgery, which is often included in a comprehensive treatment plan to complement restorative, prosthetic, and orthodontic treatment.Basic and advanced preprosthetic procedures have been combined into one complete chapter so readers can easily turn to procedures of interest.Enhanced and improved illustrations throughout more accurately depict key concepts and techniques, and many photos have been replaced with new, high-quality images.The chapter on facial neuropathology has been completely revised to present the most up-to-date information on this topic.