The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (Sterling Milestones)

Miles Reid, Balazs Szendroi

Geometry Provides A Whole Range Of Views On The Universe, Serving As The Inspiration, Technical Toolkit And Ultimate Goal For Many Branches Of Mathematics And Physics. This Book Introduces The Ideas Of Geometry, And Includes A Generous Supply Of Simple Explanations And Examples. The Treatment Emphasises Coordinate Systems And The Coordinate Changes That Generate Symmetries. The Discussion Moves From Euclidean To Non-euclidean Geometries, Including Spherical And Hyperbolic Geometry, And Then On To Affine And Projective Linear Geometries. Group Theory Is Introduced To Treat Geometric Symmetries, Leading To The Unification Of Geometry And Group Theory In The Erlangen Program. An Introduction To Basic Topology Follows, With The Möbius Strip, The Klein Bottle And The Surface With G Handles Exemplifying Quotient Topologies And The Homeomorphism Problem. Topology Combines With Group Theory To Yield The Geometry Of Transformation Groups,having Applications To Relativity Theory And Quantum Mechanics. A Final Chapter Features Historical Discussions And Indications For Further Reading. With Minimal Prerequisites, The Book Provides A First Glimpse Of Many Research Topics In Modern Algebra, Geometry And Theoretical Physics. The Book Is Based On Many Years' Teaching Experience, And Is Thoroughly Class-tested. There Are Copious Illustrations, And Each Chapter Ends With A Wide Supply Of Exercises. Further Teaching Material Is Available For Teachers Via The Web, Including Assignable... Leer más…

Hodgkin, Luke Howard

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwasizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader. Leer más…

K. Lee Lerner And Brenda Wilmoth Lerner, Editors

Cover Page......Page 1 Title Page - Volume 1......Page 3 Title Page - Volume 2......Page 4 ISBN 0787694223......Page 5 Volume 1: A–L......Page 6 Volume 2: M–Z......Page 7 Architectural Math......Page 8 Cartography......Page 9 Domain and Range......Page 10 Functions......Page 11 Inverse......Page 12 Multiplication......Page 13 Perspective......Page 14 Ratio......Page 15 Scientific Notation......Page 16 Topology......Page 17 Zero-Sum Games......Page 18 Introduction......Page 19 List of Advisors and Contributors......Page 21 ACKNOWLEDGMENTS......Page 22 A Brief History of Discovery and Development......Page 23 SPORTS AND FITNESS ADDITION......Page 25 FINANCIAL ADDITION......Page 26 POKER, PROBABILITY, AND OTHER USES OF ADDITION......Page 27 USING ADDITION TO PREDICT AND ENTERTAIN......Page 28 Potential Applications......Page 29 Where to Learn More......Page 30 Fundamental Mathematical Concepts and Terms......Page 31 A Brief History of Discovery and Development......Page 34 PERSONAL FINANCES......Page 35 COLLEGE FOOTBALL......Page 36 UPC BARCODES......Page 37 FLYING AN AIRPLANE......Page 38 SKYDIVING......Page 39 CRASH TESTS......Page 40 BUILDING SKYSCRAPERS......Page 41 BUYING LIGHT BULBS......Page 42 ART......Page 43 FINGERPRINT SCANNERS......Page 44 TELEPORTATION......Page 45 Where to Learn More......Page 46 A Brief History of Discovery and Development......Page 48 CREDIT CARD FRAUD DETECTION......Page 49 ENCRYPTION AND ENCRYPTION DEVICES......Page 50 INTERNET DATA... Leer más…

David Wells, David G. Wells

A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The "Primes is in P" algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more Leer más…

Clifford A Pickover; Netlibrary, Inc

Archimedes to Hawking takes the reader on a journey across the centuries as it explores the eponymous physical laws--from Archimedes' Law of Buoyancy and Kepler's Laws of Planetary Motion to Heisenberg's Uncertainty Principle and Hubble's Law of Cosmic Expansion--whose ramifications have profoundly altered our everyday lives and our understanding of the universe. Throughout this fascinating book, Clifford Pickover invites us to share in the amazing adventures of brilliant, quirky, and passionate people after whom these laws are named. These lawgivers turn out to be a fascinating, diverse, and sometimes eccentric group of people. Many were extremely versatile polymaths--human dynamos with a seemingly infinite supply of curiosity and energy and who worked in many different areas in science. Others had non-conventional educations and displayed their unusual talents from an early age. Some experienced resistance to their ideas, causing significant personal anguish. Pickover examines more than 40 great laws, providing brief and cogent introductions to the science behind the laws as well as engaging biographies of such scientists as Newton, Faraday, Ohm, Curie, and Planck. Throughout, he includes fascinating, little-known tidbits relating to the law or lawgiver, and he provides cross-references to other laws or equations mentioned in the book. For several entries, he includes simple numerical examples and solved problems so that readers can have a hands-on understanding of the... Leer más…

David M. Burton

The History of Mathematics: An Introduction , Sixth Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools. Elegantly written in David Burton’s imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics’ greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Sixth Edition a valuable resource that teachers and students will want as part of a permanent library. Leer más…

Jessika Sobanski

Visual Math has been designed to allow learners to "see" why math makes sense. By combining logical math concepts with pictures, previously unclear images will fade and math will suddenly click for you. Pictures, graphs, and diagrams help you understand math questions in the areas of number concepts and properties, fractions and decimals, ratios and proportions, percents, algebra, geometry, and much more. Designed especially for students who have difficulty with conventional math rules, this book gives you step-by step instructions with pictures to help you solve math problems. Leer más…

Uta C. Merzbach, Carl B. Boyer; Isaac Asimov (Foreword)

Main subject categories: • History of mathematics • Mathematics of ancient Egypt • Mathematics of ancient Europe • Mathematics of medieval Europe • Mathematics of ancient China • Mathematics of medieval China • Mathematics of ancient India • Mathematics of medieval IndiaThe updated new edition of the classic and comprehensive guide to the history of mathematicsFor more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs.• Distills thousands of years of mathematics into a single, approachable volume• Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present• Includes up-to-date references and an extensive chronological table of mathematical and general historical developments.Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it. Leer más…

Erwin Kreyszig, In Collaboration With Herbert Kreyszig And Edward J. Norminton

Small error at SEC 1.1(Basic Concepts: Modeling), EXAMPLE 3: *c is missing in y'=0.2( )e^0.2t. The tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the following topics at great depth differential equations, partial differential equations, Fourier analysis, vector analysis, complex analysis, and linear algebra/differential equations. Leer más…

Steven H. Strogatz

A world-class mathematician and regular contributor to the __New York Times__ hosts a delightful tour of the greatest ideas of math, revealing how it connects to literature, philosophy, law, medicine, art, business, even pop culture in ways we never imaginedDid O.J. 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... Leer más…

Clifford Alan Pickover

Math’s infinite mysteries and beauty unfold in this follow-up to the best-selling The Science Book. Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems. Leer más…

Glendinning, Paul

Paul Glendinning is Professor of Applied Mathematics at the University of Manchester. He was founding Head of School for Mathematics at the combined University of Manchester and has published over fifty academic articles and an undergraduate textbook on chaos theory. Both simple and accessible, Math in Minutes is a visually led introduction to 200 key mathematical concepts. Each concept is described by means of an easy-to-understand illustration and a compact, 200-word explanation. Concepts span all of the key areas of mathematics, including Fundamentals of Mathematics, Sets and Numbers, Geometry, Equations, Limits, Functions and Calculus, Vectors and Algebra, Complex Numbers, Combinatorics, Number Theory, and more. From the Trade Paperback edition. MATHEMATICS Leer más…

Clifford A. Pickover

From Witch Doctors to Robot Surgeons, 250 Milestones in the History of MedicineFollowing his hugely successful The Math Book and The Physics Book, Clifford Pickover now chronicles the advancement of medicine in 250 entertaining, illustrated landmark events. Touching on such diverse subspecialties as genetics, pharmacology, neurology, sexology, and immunology, Pickover intersperses “obvious” historical milestones—the Hippocratic Oath, general anesthesia, the Human Genome Project—with unexpected and intriguing topics like “truth serum,” the use of cocaine in eye surgery, and face transplants. Leer más…

Clifford A. Pickover

Following the hugely successful __The Science Book__ and __The Math Book__ comes a richly illustrated chronology of physics, containing 250 short, entertaining, and thought-provoking entries. In addition to exploring such engaging topics as dark energy, parallel universes, the Doppler effect, the God particle, and Maxwell's demon, the book's timeline extends back billions of years to the hypothetical Big Bang and forward trillions of years to a time of “quantum resurrection.” Like the previous titles in this series, __The Physics Book__ helps readers gain an understanding of major concepts without getting bogged down in complex details. Leer más…

Ian Stewart; David Tall; Oxford University Press

The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows... Leer más…

Richard J. Brown (Ed.)

From Rubik's cubes to Godel's incompleteness theorem, everything mathematical explained, with colour illustrations, in half a minute. Maths is enjoying a resurgence in popularity. So how can you avoid being the only dinner guest who has no idea who Fermat was, or what he proved? The more you know about Maths, the less of a science it becomes. 30 Second Maths takes the top 50 most engaging mathematical theories, and explains them to the general reader in half a minute, using nothing more than two pages, 200 words and one picture. Read at your own pace, and discover that maths can be more fascinating than you ever imagined. ** Review '[30-Second Maths] unveils the wonder of mathematics, touching on ideas from the Mobius strip to infinity with clear, entertaining and delightfully concise explanations.' -- New Scientist About the Author Richard Brown is Director of Undergraduate Studies at the Department of Mathematics, Johns Hopkins University. Formats : EPUB Leer más…

Jim Libby

"Where are we ever going to use this?" Every high school math student has asked this question. Often teachers themselves aren't sure how to respond. One answer is that higher mathematics learned in high school will be essential to learning yet more at the college level. A more satisfactory answer calls for an awareness of how math is applied in many specific areas. Written primarily for teachers, this book presents hundreds of practical applications for mathematics--from baseball statistics to the theory of relativity--that can be understood by anyone with a knowledge of high school algebra, geometry and trigonometry. Leer más…

Dk, Mike Goldsmith

In this clever guide, young readers previously daunted by algebra, logic, algorithms, and all things math will discover they are better at it than they thought. __How to be a Math Genius__ explores the math brain and demonstrates to readers that they use math skills all the time — they just don't know it yet. Packed with math activities and puzzles, compelling stories of math geniuses, math facts and stats, and more, __How to be a Math Genius__ makes the dreaded subject of math both engaging and relevant. Leer más…

David J Acheson

Calculus is the key to much of modern science and engineering. It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn...In __The Calculus Story__, David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step-by-step treatment, he demonstrates how to start doing calculus, from the very beginning. Leer más…