The Science and Mathematics behind Everyday Questions

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 1400880513

Category: Science

Page: 272

View: 6643

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.
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The Science and Mathematics Behind Everyday Questions

Author: Paul J. Nahin

Publisher: N.A

ISBN: 9780691178523

Category: Science

Page: 272

View: 5553

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.
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Computational Solutions to Practical Probability Problems

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 0691158215

Category: Computers

Page: 288

View: 1128

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.
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Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 1400843049

Category: Mathematics

Page: 304

View: 8072

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.
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Taming Unruly Computational Problems from Mathematical Physics to Science Fiction

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400839582

Category: Mathematics

Page: 408

View: 5320

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.
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And Other Intriguing Stories of Mathematical Physics

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400833467

Category: Mathematics

Page: 424

View: 8234

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.
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Time Travel in Physics, Metaphysics, and Science Fiction

Author: Paul J. Nahin

Publisher: Springer Science & Business Media

ISBN: 9780387985718

Category: Literary Criticism

Page: 628

View: 5229

Time Machines takes you on an exhilarating journey through the intriguing theories of scientists and the far-flung imaginations of writers. It explores the ideas of time travel from the first account in English literature to the latest theories of physicists such as Kip Thorne and Igor Novikov. This very readable work covers a variety of topics including the history of time travel in fiction; the fundamental scientific concepts of time, spacetime, and the fourth dimension; the speculations of Einstein, Richard Feynman, Kurt Gödel, and others; time travel paradoxes, and much more. For anyone who shares a fascination with time travel, Time Machines is an engrossing study of what writers have imagined and what scientists may some day make possible. "Here's a gem of a book...all peppered with delightful notes...I can't turn a page without finding a jewel."Clifford Stoll, University of California, Berkeley, author of "The Cuckoo's Egg""...I have been struck by the richness and complexity of the tapestry of ideas that Nahin presents...may well remain the most readable and complete treatise on time travel in science and science fiction." Kip S. Thorne, The Feynman Professor of Theoretical Physics, California Institute of Technology"if, like me, you are a child at heart, the real fun lies in the zany stories and wild speculations" Physics World
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The Mathematics of Pursuit and Evasion

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 1400842069

Category: Mathematics

Page: 272

View: 5507

We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day. Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an array of challenging puzzles with their historical background and broader applications. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis. Now with a gripping new preface on how the Enola Gay escaped the shock wave from the atomic bomb dropped on Hiroshima, this book will appeal to anyone interested in the mathematics that underlie pursuit and evasion. Some images inside the book are unavailable due to digital copyright restrictions.
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The Evolution and Science of Ballistics

Author: Mark Denny

Publisher: JHU Press

ISBN: 0801899818

Category: Science

Page: 248

View: 9086

For study or hobby, Their Arrows Will Darken the Sun is an entertaining guide to the world of ballistics.
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How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 1400841364

Category: Mathematics

Page: 392

View: 4355

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.
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With Matlab and Electronics Workbench Demonstration, 2nd edition

Author: Paul J. Nahin

Publisher: Springer Science & Business Media

ISBN: 9780387951508

Category: Computers

Page: 466

View: 4772

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).
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A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and Devilishly Seductive Maneuvers for Computing Nearly 200 Perplexing Definite Integrals From Physics, Engineering, and Mathematics (Plus 60 Challenge Problems with Complete, Detailed Solutions)

Author: Paul J. Nahin

Publisher: Springer

ISBN: 1493912771

Category: Science

Page: 412

View: 3196

What’s the point of calculating definite integrals since you can’t possibly do them all?. What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you.
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The Life, Work, and Times of an Electrical Genius of the Victorian Age

Author: Paul J. Nahin

Publisher: JHU Press

ISBN: 9780801869099

Category: Biography & Autobiography

Page: 318

View: 8101

"A good book by a careful, historically minded engineer... A lively, informative narrative of Heaviside's life and work. Nahin has exhaustively resurveyed archives and contemporary sources and is very much at home in historical discussions of Victorian physics." -- Isis
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Cures Many Mathematical Ills

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400838479

Category: Mathematics

Page: 416

View: 9786

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.
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Preparing for University

Author: Stephen Siklos

Publisher: Open Book Publishers

ISBN: 1783741449

Category: Mathematics

Page: 186

View: 2550

This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.
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The Science Behind the Speed

Author: Diandra Leslie-Pelecky

Publisher: Penguin

ISBN: 1101213949

Category: Sports & Recreation

Page: 304

View: 7644

A physicist explores the science of speed racing and the #1 spectator sport in America, with 75 million fans. Every NASCAR fan—at one time or another—asks the same question: Why isn’t my favorite driver winning? This is your chance to discover how much more there is to NASCAR than “Go fast, turn left and don’t crash.” If you’ve ever wondered why racecars don’t have mufflers, how “bump drafting” works, or what in the world “Let’s go up a pound on the right rear and add half a round of wedge” means, The Physics of NASCAR is for you. In this fast-paced investigation into the adrenaline-pumping world of NASCAR, a physicist with a passion uncovers what happens when the rubber hits the road and 800-horsepower vehicles compete at 190 miles per hour only inches from one another. Diandra Leslie-Pelecky reveals how and why drivers trust the engineering and science their teams literally build around them not only to get them across the finish line in first place, but also to keep them alive. Leslie-Pelecky is a physicist in love with the sport’s beauty and power and is uniquely qualified to explain exactly how physics translates into winning races. Based on the author’s extensive access to race shops, pit crews, crew chiefs and mechanics, this book traces the life cycle of a race car from behind the scenes at top race shops to the track. The Physics of NASCAR takes readers right into the ultra competitive world of NASCAR, from the champion driver’s hot seat behind the detachable steering wheel to the New Zealander nicknamed Kiwi in charge of shocks for the No. 19 car. Diandra Leslie-Pelecky tells her story in terms anyone who drives a car—and maybe occasionally looks under the hood--can understand. How do drivers walk away from serious crashes? How can two cars travel faster together than either car can on its own? How do you dress for a 1800°F gasoline fire? In simple yet detailed, high-octane prose, this is the ultimate thrill ride for armchair speed demons, auto science buffs, and NASCAR fans at every level of interest. Readers, start your engines.
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The Story of √-1

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400833894

Category: Mathematics

Page: 296

View: 6294

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.
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Explaining and Extending the Standard Model

Author: Gordon Kane

Publisher: Cambridge University Press

ISBN: 1107165083

Category: Science

Page: 256

View: 9070

This book is written for students and scientists wanting to learn about the Standard Model of particle physics. Only an introductory course knowledge about quantum theory is needed. The text provides a pedagogical description of the theory, and incorporates the recent Higgs boson and top quark discoveries. With its clear and engaging style, this new edition retains its essential simplicity. Long and detailed calculations are replaced by simple approximate ones. It includes introductions to accelerators, colliders, and detectors, and several main experimental tests of the Standard Model are explained. Descriptions of some well-motivated extensions of the Standard Model prepare the reader for new developments. It emphasizes the concepts of gauge theories and Higgs physics, electroweak unification and symmetry breaking, and how force strengths vary with energy, providing a solid foundation for those working in the field, and for those who simply want to learn about the Standard Model.
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How George Boole and Claude Shannon Created the Information Age

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 0691151008

Category: Computers

Page: 228

View: 4686

Examines how mathematician and philosopher George Boole and electrical engineer Claude Shannon became the fathers of the information age by advancing Boolean logic, and looks at the influence of other factors, including the Turing machine.
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