The Monty Hall Problem
The Monty Hall Problem

Author: Jason Rosenhouse

Publisher: Oxford University Press

Published: 2009-06-04

Total Pages: 209

ISBN-13: 0199709904

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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.

The Colossal Book of Short Puzzles and Problems
The Colossal Book of Short Puzzles and Problems

Author: Martin Gardner

Publisher: W W Norton & Company Incorporated

Published: 2006

Total Pages: 494

ISBN-13: 9780393061147

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The renowned provocateur of popular math presents a collection of his widely recognized short puzzles--along with a few new ones--that explore chess, physics, probability, and topology, among other topics.

Ask Marilyn
Ask Marilyn

Author: Marilyn Vos Savant

Publisher: Saint Martin's Paperbacks

Published: 1994-01

Total Pages: 333

ISBN-13: 9780312951818

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"Parade" magazine's resident genius compiles the best of her question-and-answer column that logically tackles the mysteries of the universe, brainteasers, and unique insights

The Cauchy-Schwarz Master Class
The Cauchy-Schwarz Master Class

Author: J. Michael Steele

Publisher: Cambridge University Press

Published: 2004-04-26

Total Pages: 320

ISBN-13: 9780521546775

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This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

Mathematical Puzzles and Curiosities
Mathematical Puzzles and Curiosities

Author: Barry R. Clarke

Publisher: Courier Corporation

Published: 2013-06-19

Total Pages: 177

ISBN-13: 048631572X

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Intriguing collection features recreational math, logic, and creativity puzzles. Classic and new puzzles include The Monty Hall Problem, The Unexpected Hanging, The Shakespeare Puzzles, and Finger Multiplication.

The Monty Hall Problem & Other Puzzles
The Monty Hall Problem & Other Puzzles

Author: Ivan Moscovich

Publisher: Robson Books Limited

Published: 2005

Total Pages: 132

ISBN-13: 9781861055965

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Puzzlers will feel fit to be tied - Dog Tied: If Fido is tied to a 10-foot-long rope, and his bone is 15 feet away, how is it possible that he can reach and enjoy his bone without breaking or stretching the rope? (And yes - the rope IS tied to something.) There's fun in finding the answer to this and other cool number-based problems. Dust off your mathematics and get solving. The intriguing enigmas include questions on interstellar communications, ancient geometry (Pythagoras and Plato), and even traffic patterns in gridlock city. Or play the grasshopper jumping game. It's all fascinating.

Introduction to Probability
Introduction to Probability

Author: Joseph K. Blitzstein

Publisher: CRC Press

Published: 2014-07-24

Total Pages: 599

ISBN-13: 1466575573

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Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Games for Your Mind
Games for Your Mind

Author: Jason Rosenhouse

Publisher: Princeton University Press

Published: 2020-11-24

Total Pages: 348

ISBN-13: 0691200343

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A lively and engaging look at logic puzzles and their role in mathematics, philosophy, and recreation Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself. In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt Gödel's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data. Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the "Hardest Logic Puzzle Ever," metapuzzles, paradoxes, and the logic puzzles in detective stories.

The Monty Hall Problem
The Monty Hall Problem

Author: Rob Deaves

Publisher: Lulu Enterprises Uk Limited

Published: 2007-01

Total Pages: 80

ISBN-13: 9781847530783

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This short book explores the Monty Hall dilemma, a well known mathematical puzzle. The original problem, the controversy surrounding it and its solution are discussed. Further, the boundaries of the problem are expanded to consider prior knowledge and host intention. This book should be of interest to those who enjoy problem solving.

Taking Sudoku Seriously
Taking Sudoku Seriously

Author: Jason Rosenhouse

Publisher: Oxford University Press

Published: 2012-01-19

Total Pages: 227

ISBN-13: 0199913153

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Packed with more than a hundred color illustrations and a wide variety of puzzles and brainteasers, Taking Sudoku Seriously uses this popular craze as the starting point for a fun-filled introduction to higher mathematics. How many Sudoku solution squares are there? What shapes other than three-by-three blocks can serve as acceptable Sudoku regions? What is the fewest number of starting clues a sound Sudoku puzzle can have? Does solving Sudoku require mathematics? Jason Rosenhouse and Laura Taalman show that answering these questions opens the door to a wealth of interesting mathematics. Indeed, they show that Sudoku puzzles and their variants are a gateway into mathematical thinking generally. Among many topics, the authors look at the notion of a Latin square--an object of long-standing interest to mathematicians--of which Sudoku squares are a special case; discuss how one finds interesting Sudoku puzzles; explore the connections between Sudoku, graph theory, and polynomials; and consider Sudoku extremes, including puzzles with the maximal number of vacant regions, with the minimal number of starting clues, and numerous others. The book concludes with a gallery of novel Sudoku variations--just pure solving fun! Most of the puzzles are original to this volume, and all solutions to the puzzles appear in the back of the book or in the text itself. A math book and a puzzle book, Taking Sudoku Seriously will change the way readers look at Sudoku and mathematics, serving both as an introduction to mathematics for puzzle fans and as an exploration of the intricacies of Sudoku for mathematics buffs.