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The Monty Hall Problem

The Monty Hall Problem
Author: Rob Deaves
Publisher: Lulu Enterprises Uk Limited
Total Pages: 80
Release: 2007-01
Genre: Games
ISBN: 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.


The Monty Hall Problem

The Monty Hall Problem
Author: Jason Rosenhouse
Publisher: Oxford University Press
Total Pages: 209
Release: 2009-06-04
Genre: Mathematics
ISBN: 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 Cauchy-Schwarz Master Class

The Cauchy-Schwarz Master Class
Author: J. Michael Steele
Publisher: Cambridge University Press
Total Pages: 320
Release: 2004-04-26
Genre: Mathematics
ISBN: 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.


The Monty Hall Problem & Other Puzzles

The Monty Hall Problem & Other Puzzles
Author: Ivan Moscovich
Publisher: Robson Books Limited
Total Pages: 132
Release: 2005
Genre: Games & Activities
ISBN: 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.


The Monty Hall Problem

The Monty Hall Problem
Author: Jason Rosenhouse
Publisher: Oxford University Press
Total Pages: 209
Release: 2009-06-04
Genre: Mathematics
ISBN: 0195367898

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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.


Ask Marilyn

Ask Marilyn
Author: Marilyn Vos Savant
Publisher: Saint Martin's Paperbacks
Total Pages: 333
Release: 1994-01
Genre: Reference
ISBN: 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 Monty Hall Dilemma

The Monty Hall Dilemma
Author: Donald Granberg
Publisher:
Total Pages: 218
Release: 2014-12-09
Genre:
ISBN: 9780996100809

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A cognitive illusion occurs when the obvious answer to a thought question turns out to be incorrect. Psychological reality conflicts with objective reality. The Monty Hall Dilemma is a cognitive illusion par excellence originating in the "Let's Make a Deal" television game show in which a contestant selects one of three doors hoping that it hides the grand prize (like a new car!). After an initial guess has been made, host Monty Hall reveals a consolation prize (like a goat!) behind one of the other doors. The contestant's dilemma is whether to stay with the first choice or switch to the remaining unchosen door. Popular PARADE magazine columnist, Marilyn vos Savant, writing about the Monty Hall dilemma, received thousands of letters from readers most of whom contested her surprising solution to this dilemma. Knowing about cognitive illusions in general (several are presented here) and the Monty Hall Dilemma in particular should alert readers to the possibility that ordinary reasoning and common sense don't always apply even though people have a tendency to stick with their initial hunches.


One Thousand Exercises in Probability

One Thousand Exercises in Probability
Author: Geoffrey Grimmett
Publisher: Oxford University Press
Total Pages: 452
Release: 2001-05-24
Genre: Business & Economics
ISBN: 9780198572213

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This guide provides a wide-ranging selection of illuminating, informative and entertaining problems, together with their solution. Topics include modelling and many applications of probability theory.


Introduction to Probability

Introduction to Probability
Author: Joseph K. Blitzstein
Publisher: CRC Press
Total Pages: 599
Release: 2014-07-24
Genre: Mathematics
ISBN: 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.


Simulations in Swift 5

Simulations in Swift 5
Author: Beau Nouvelle
Publisher: Apress
Total Pages: 151
Release: 2019-10-25
Genre: Computers
ISBN: 148425337X

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Design and implement simulations using Apples Swift Playgrounds. Computer simulations are used to replicate the physical systems we see all around us. They help us solve problems by performing experiments that may otherwise be impossible in the real world. This book uses simulations to solve counter-intuitive logic puzzles, create procedural artworks, and build habitats for digital lifeforms. To help you create your own simulations using the Swift programming language, this book is filled with projects that you can easily follow along with. All you need is a Mac with the latest version of Xcode installed. All projects are written in Xcode’s Playgrounds. This keeps the process simple. No need to setup an Apple account, or learn anything further about building apps. Simulations are used in many areas within computer science and yet, barely anyone is teaching them. Sure, the fundamentals are in algorithm design, but simulations are a step above that. Usually when writing an algorithm you have a specific outcome in mind. However, when you create a simulation, the system you are modelling can be far more unpredictable than sorting a list, or navigating a maze. Simulations in Swift 5 will guide you through all of this. What You'll Learn Simulate situations with advanced algorithms to solve advanced problems Incorporate real-world physics into simulated problems Predict biological and other systems behavior and the outcome of events based on presented factors Who This Book Is For Swift programmers interested in tackling fun projects in Swift involving advanced algorithms and factors