Duelling Idiots And Other Probability Puzzlers

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Duelling Idiots and Other Probability Puzzlers

Paul J. Nahin
Duelling Idiots and Other Probability Puzzlers Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 300 pages
File Size : 46,5 Mb
Release : 2012-07-22
Category : Mathematics
ISBN : 9781400843046

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Duelling Idiots and Other Probability Puzzlers by Paul J. Nahin Pdf

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.

Duelling Idiots and Other Probability Puzzlers

Paul J. Nahin
Duelling Idiots and Other Probability Puzzlers Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 300 pages
File Size : 50,7 Mb
Release : 2012-07-22
Category : Mathematics
ISBN : 9780691155005

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Duelling Idiots and Other Probability Puzzlers by Paul J. Nahin Pdf

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

Paul Nahin
Digital Dice Book PDF

Author : Paul Nahin
Publisher : Princeton University Press
Page : 288 pages
File Size : 44,7 Mb
Release : 2013-03-24
Category : Mathematics
ISBN : 9781400846115

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Digital Dice by Paul Nahin Pdf

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.

Will You Be Alive 10 Years from Now?

Paul J. Nahin
Will You Be Alive 10 Years from Now Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 249 pages
File Size : 51,5 Mb
Release : 2014
Category : Mathematics
ISBN : 9780691156804

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Will You Be Alive 10 Years from Now? by Paul J. Nahin Pdf

A collection of stimulating probability puzzles from bestselling math writer Paul Nahin 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.

Digital Dice

Paul J. Nahin
Digital Dice Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 288 pages
File Size : 54,5 Mb
Release : 2013-03-24
Category : Computers
ISBN : 9780691158211

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Digital Dice by Paul J. Nahin Pdf

Some probability problems are so difficult that they stump the smartest mathematicians. This text shows readers how to get numerical answers to difficult probability problems without having to solve complicated mathematical questions.

The Monty Hall Problem

Jason Rosenhouse
The Monty Hall Problem Book PDF

Author : Jason Rosenhouse
Publisher : Oxford University Press
Page : 208 pages
File Size : 48,5 Mb
Release : 2009-06-04
Category : Mathematics
ISBN : 0199709904

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The Monty Hall Problem by Jason Rosenhouse Pdf

Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

Will You Be Alive 10 Years from Now?

Paul J. Nahin
Will You Be Alive 10 Years from Now Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 249 pages
File Size : 47,5 Mb
Release : 2019-11-12
Category : Mathematics
ISBN : 9780691196367

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Will You Be Alive 10 Years from Now? by Paul J. Nahin Pdf

"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"--

Hot Molecules, Cold Electrons

Paul J. Nahin
Hot Molecules Cold Electrons Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 232 pages
File Size : 46,6 Mb
Release : 2022-05-10
Category : Science
ISBN : 9780691207841

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Hot Molecules, Cold Electrons by Paul J. Nahin Pdf

An entertaining mathematical exploration of the heat equation and its role in the triumphant development of the trans-Atlantic telegraph cable Heat, like gravity, shapes nearly every aspect of our world and universe, from how milk dissolves in coffee to how molten planets cool. The heat equation, a cornerstone of modern physics, demystifies such processes, painting a mathematical picture of the way heat diffuses through matter. Presenting the mathematics and history behind the heat equation, Hot Molecules, Cold Electrons tells the remarkable story of how this foundational idea brought about one of the greatest technological advancements of the modern era. Paul Nahin vividly recounts the heat equation’s tremendous influence on society, showing how French mathematical physicist Joseph Fourier discovered, derived, and solved the equation in the early nineteenth century. Nahin then follows Scottish physicist William Thomson, whose further analysis of Fourier’s explorations led to the pioneering trans-Atlantic telegraph cable. This feat of engineering reduced the time it took to send a message across the ocean from weeks to minutes. Readers also learn that Thomson used Fourier’s solutions to calculate the age of the earth, and, in a bit of colorful lore, that writer Charles Dickens relied on the trans-Atlantic cable to save himself from a career-damaging scandal. The book’s mathematical and scientific explorations can be easily understood by anyone with a basic knowledge of high school calculus and physics, and MATLAB code is included to aid readers who would like to solve the heat equation themselves. A testament to the intricate links between mathematics and physics, Hot Molecules, Cold Electrons offers a fascinating glimpse into the relationship between a formative equation and one of the most important developments in the history of human communication.

The Logician and the Engineer

Paul J. Nahin
The Logician and the Engineer Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 245 pages
File Size : 50,6 Mb
Release : 2017-04-04
Category : Biography & Autobiography
ISBN : 9780691176000

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The Logician and the Engineer by Paul J. Nahin Pdf

Third printing. First paperback printing. Original copyright date: 2013.

Transients for Electrical Engineers

Paul J. Nahin
Transients for Electrical Engineers Book PDF

Author : Paul J. Nahin
Publisher : Springer
Page : 189 pages
File Size : 44,7 Mb
Release : 2018-07-05
Category : Technology & Engineering
ISBN : 9783319775982

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Transients for Electrical Engineers by Paul J. Nahin Pdf

This book offers a concise introduction to the analysis of electrical transients aimed at students who have completed introductory circuits and freshman calculus courses. While it is written under the assumption that these students are encountering transient electrical circuits for the first time, the mathematical and physical theory is not ‘watered-down.’ That is, the analysis of both lumped and continuous (transmission line) parameter circuits is performed with the use of differential equations (both ordinary and partial) in the time domain, and the Laplace transform. The transform is fully developed in the book for readers who are not assumed to have seen it before. The use of singular time functions (unit step and impulse) is addressed and illustrated through detailed examples. The appearance of paradoxical circuit situations, often ignored in many textbooks (because they are, perhaps, considered ‘difficult’ to explain) is fully embraced as an opportunity to challenge students. In addition, historical commentary is included throughout the book, to combat the misconception that the material in engineering textbooks was found engraved on Biblical stones, rather than painstakingly discovered by people of genius who often went down many wrong paths before finding the right one. MATLAB® is used throughout the book, with simple codes to quickly and easily generate transient response curves.

Ants, Bikes, and Clocks

William Briggs
Ants Bikes and Clocks Book PDF

Author : William Briggs
Publisher : SIAM
Page : 174 pages
File Size : 41,9 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 0898717914

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Ants, Bikes, and Clocks by William Briggs Pdf

Mathematics educators agree that problem solving is one of the essential skills their students should possess, yet few mathematics courses or textbooks are devoted entirely to developing this skill. Supported by narrative, examples, and exercises, Ants, Bikes, and Clocks: Problem Solving for Undergraduates is a readable and enjoyable text designed to strengthen the problem-solving skills of undergraduate students. The book, which provides hundreds of mathematical problems, gives special emphasis to problems in context, often called story problems or modeling problems, that require mathematical formulation as a preliminary step. Both analytical and computational approaches, as well as the interplay between them, are included.

How to Fall Slower Than Gravity

Paul J. Nahin
How to Fall Slower Than Gravity Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 318 pages
File Size : 50,7 Mb
Release : 2021-11-23
Category : Crafts & Hobbies
ISBN : 9780691229171

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How to Fall Slower Than Gravity by Paul J. Nahin Pdf

An engaging collection of intriguing problems that shows you how to think like a mathematical physicist Paul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Always entertaining, the problems range from ancient catapult conundrums to the puzzling physics of a very peculiar material called NASTYGLASS—and from dodging trucks to why raindrops fall slower than the rate of gravity. The questions raised may seem impossible to answer at first and may require an unexpected twist in reasoning, but sometimes their solutions are surprisingly simple. Nahin’s goal, however, is always to guide readers—who will need only to have studied advanced high school math and physics—in expanding their mathematical thinking to make sense of the curiosities of the physical world. The problems are in the first part of the book and the solutions are in the second, so that readers may challenge themselves to solve the questions on their own before looking at the explanations. The problems show how mathematics—including algebra, trigonometry, geometry, and calculus—can be united with physical laws to solve both real and theoretical problems. Historical anecdotes woven throughout the book bring alive the circumstances and people involved in some amazing discoveries and achievements. More than a puzzle book, this work will immerse you in the delights of scientific history while honing your math skills.

The Improbability Principle

David J. Hand
The Improbability Principle Book PDF

Author : David J. Hand
Publisher : Scientific American / Farrar, Straus and Giroux
Page : 288 pages
File Size : 55,7 Mb
Release : 2014-02-11
Category : Mathematics
ISBN : 9780374711399

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The Improbability Principle by David J. Hand Pdf

In The Improbability Principle, the renowned statistician David J. Hand argues that extraordinarily rare events are anything but. In fact, they're commonplace. Not only that, we should all expect to experience a miracle roughly once every month. But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of "miracle" is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough. Together, these constitute Hand's groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective. An irresistible adventure into the laws behind "chance" moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it's in the world of business and finance or you're merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

Exploring University Mathematics with Python

Siri Chongchitnan
Exploring University Mathematics with Python Book PDF

Author : Siri Chongchitnan
Publisher : Springer Nature
Page : 521 pages
File Size : 55,8 Mb
Release : 2024-01-05
Category : Computers
ISBN : 9783031462702

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Exploring University Mathematics with Python by Siri Chongchitnan Pdf

This book provides a unique tour of university mathematics with the help of Python. Written in the spirit of mathematical exploration and investigation, the book enables students to utilise Python to enrich their understanding of mathematics through: Calculation: performing complex calculations and numerical simulations instantly Visualisation: demonstrating key theorems with graphs, interactive plots and animations Extension: using numerical findings as inspiration for making deeper, more general conjectures. This book is for all learners of mathematics, with the primary audience being mathematics undergraduates who are curious to see how Python can enhance their understanding of core university material. The topics chosen represent a mathematical overview of what students typically study in the first and second years at university, namely analysis, calculus, vector calculus and geometry, differential equations and dynamical systems, linear algebra, abstract algebra and number theory, probability and statistics. As such, it can also serve as a preview of university mathematics for high-school students. The prerequisites for reading the book are a familiarity with standard A-Level mathematics (or equivalent senior high-school curricula) and a willingness to learn programming. For mathematics lecturers and teachers, this book is a useful resource on how Python can be seamlessly incorporated into the mathematics syllabus, assuming only basic knowledge of programming.