duelling idiots and other probability puzzlers princeton puzzlers

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Duelling Idiots And Other Probability Puzzlers

Author : Paul J. Nahin
ISBN : 9781400843046
Genre : Mathematics
File Size : 24. 98 MB
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What are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of twenty-one puzzles, Paul Nahin challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper, and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the workings of probability. Over the years, Nahin, a veteran writer and teacher of the subject, has collected these and other favorite puzzles designed to instruct and entertain math enthusiasts of all backgrounds. If idiots A and B alternately take aim at each other with a six-shot revolver containing one bullet, what is the probability idiot A will win? What are the chances it will snow on your birthday in any given year? How can researchers use coin flipping and the laws of probability to obtain honest answers to embarrassing survey questions? The solutions are presented here in detail, and many contain a profound element of surprise. And some puzzles are beautiful illustrations of basic mathematical concepts: "The Blind Spider and the Fly," for example, is a clever variation of a "random walk" problem, and "Duelling Idiots" and "The Underdog and the World Series" are straightforward introductions to binomial distributions. Written in an informal way and containing a plethora of interesting historical material, Duelling Idiots is ideal for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.

Digital Dice

Author : Paul J. Nahin
ISBN : 9781400846115
Genre : Mathematics
File Size : 39. 37 MB
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Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women. The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem. Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.

Chases And Escapes

Author : Paul J. Nahin
ISBN : 0691125147
Genre : Mathematics
File Size : 66. 94 MB
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Traces the development of modern pursuit theory, from its classical analytical beginnings to the present day, and provides challenging puzzles with solutions, anecdotes, and entertaining facts, in a first comprehensive history of a fascinating area of mathematics.

In Praise Of Simple Physics

Author : Paul J. Nahin
ISBN : 9781400880515
Genre : Science
File Size : 86. 21 MB
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Physics can explain many of the things that we commonly encounter. It can tell us why the night is dark, what causes the tides, and even how best to catch a baseball. With In Praise of Simple Physics, popular math and science writer Paul Nahin presents a plethora of situations that explore the science and math behind the wonders of everyday life. Roaming through a diverse range of puzzles, he illustrates how physics shows us ways to wring more energy from renewable sources, to measure the gravity in our car garages, to figure out which of three light switches in the basement controls the light bulb in the attic, and much, much more. How fast can you travel from London to Paris? How do scientists calculate the energy of an atomic bomb explosion? How do you kick a football so it stays in the air and goes a long way downfield? Nahin begins with simpler problems and progresses to more challenging questions, and his entertaining, accessible, and scientifically and mathematically informed explanations are all punctuated by his trademark humor. Readers are presumed to have some background in beginning differential and integral calculus. Whether you simply have a personal interest in physics' influence in the world or you're an engineering and science student who wants to gain more physics know-how, this book has an intriguing scenario for you. In Praise of Simple Physics proves that if we look carefully at the world around us, physics has answers for the most astonishing day-to-day occurrences.

Will You Be Alive 10 Years From Now

Author : Paul J. Nahin
ISBN : 9781400848379
Genre : Mathematics
File Size : 22. 55 MB
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What are the chances of a game-show contestant finding a chicken in a box? Is the Hanukkah dreidel a fair game? Will you be alive ten years from now? These are just some of the one-of-a-kind probability puzzles that acclaimed popular math writer Paul Nahin offers in this lively and informative book. Nahin brings probability to life with colorful and amusing historical anecdotes as well as an electrifying approach to solving puzzles that illustrates many of the techniques that mathematicians and scientists use to grapple with probability. He looks at classic puzzles from the past--from Galileo's dice-tossing problem to a disarming dice puzzle that would have astonished even Newton--and also includes a dozen challenge problems for you to tackle yourself, with complete solutions provided in the back of the book. Nahin then presents twenty-five unusual probability puzzlers that you aren't likely to find anywhere else, and which range in difficulty from ones that are easy but clever to others that are technically intricate. Each problem is accompanied by an entertaining discussion of its background and solution, and is backed up by theory and computer simulations whenever possible in order to show how theory and computer experimentation can often work together on probability questions. All the MATLAB® Monte Carlo simulation codes needed to solve the problems computationally are included in the book.With his characteristic wit, audacity, and insight, Nahin demonstrates why seemingly simple probability problems can stump even the experts.

Number Crunching

Author : Paul J. Nahin
ISBN : 1400839580
Genre : Mathematics
File Size : 65. 17 MB
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How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished. Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions. Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.

Mrs Perkins S Electric Quilt

Author : Paul J. Nahin
ISBN : 1400833469
Genre : Mathematics
File Size : 22. 13 MB
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What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many ways math and physics combine to create something vastly more powerful, useful, and interesting than either is by itself. In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems--some three dozen in all--that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end. Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class--and anyone who enjoys popular math books.

The Science Of Radio

Author : Paul J. Nahin
ISBN : 0387951504
Genre : Computers
File Size : 26. 58 MB
Format : PDF
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The Science of Radio explains the working and charts the development of the ordinary AM radio receiver, which has become an integral part of our lives in the 80 years since its invention. As well as showing the reader the growth of technology in this century, the story of AM radio can provide a unique insight into the basics of electrical engineering, making the primary concepts and applications visual and comprehensible. Taking a "top down" approach to the subject, Nahin starts with a broad overview of radio as a sociological and technological phenomenon, then describes specific advances in research that made radio possible, moving through deeper levels of technical detail as the story progresses. Readers will see how various concepts and theories are combined to achieve specific practical results. And the book's "just in time" method of introducing mathematical and physical theory only as needed to understand a topic, helps readers gain a firm grasp of often elusive material. By focusing specifically on the workings of AM radio, The Science of Radio offers both a fascinating history of radio as an information and entertainment medium and a practical, applications-oriented introduction to electrical engineering. This second edition, written the same witty and accessible style as the first, also includes illustrative examples based on the popular MATLAB and Electronics Workbench programs now commonly used in engineering courses, as well as new technical material on differential amplifiers, more end-of-chapters problems, and additional historical discussion. About the author Paul J. Nahin is Professor of Electrical Engineering at the University of New Hampshire, and is the author of Oliver Heaviside: Sage In Solitude (IEEE Press); Time Machines: Time Travel In Physics, Metaphysics And Science Fiction, (AIP Press); and An Imaginary Tale; The Story Of The Square Root Of Minus One, (Princeton University Press).

When Least Is Best

Author : Paul J. Nahin
ISBN : 9781400841363
Genre : Mathematics
File Size : 61. 31 MB
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What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows look like in the future? Why do soap bubbles have a shape that gives them the least area? By combining the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more. Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot. Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, When Least Is Best is full of fascinating examples and ready-to-try-at-home experiments. This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics.

Trigonometric Delights

Author : Eli Maor
ISBN : 9781400846757
Genre : Mathematics
File Size : 36. 31 MB
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Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights. ? Maor, whose previous books have demystified the concept of infinity and the unusual number "e," begins by examining the "proto-trigonometry" of the Egyptian pyramid builders. He shows how Greek astronomers developed the first true trigonometry. He traces the slow emergence of modern, analytical trigonometry, recounting its colorful origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, we see trigonometry at work in, for example, the struggle of the famous mapmaker Gerardus Mercator to represent the curved earth on a flat sheet of paper; we see how M. C. Escher used geometric progressions in his art; and we learn how the toy Spirograph uses epicycles and hypocycles. Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor--but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name "the witch of Agnesi." The book is richly illustrated, including rare prints from the author's own collection. Trigonometric Delights will change forever our view of a once dreaded subject.

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