unexpected expectations the curiosities of a mathematical crystal ball

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Unexpected Expectations

Author : Leonard M. Wapner
ISBN : 9781568817217
Genre : Mathematics
File Size : 58. 57 MB
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Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball explores how paradoxical challenges involving mathematical expectation often necessitate a reexamination of basic premises. The author takes you through mathematical paradoxes associated with seemingly straightforward applications of mathematical expectation and shows how these unexpected contradictions may push you to reconsider the legitimacy of the applications. The book requires only an understanding of basic algebraic operations and includes supplemental mathematical background in chapter appendices. After a history of probability theory, it introduces the basic laws of probability as well as the definition and applications of mathematical expectation/expected value (E). The remainder of the text covers unexpected results related to mathematical expectation, including: The roles of aversion and risk in rational decision making A class of expected value paradoxes referred to as envelope problems Parrondo’s paradox—how negative (losing) expectations can be combined to give a winning result Problems associated with imperfect recall Non-zero-sum games, such as the game of chicken and the prisoner’s dilemma Newcomb’s paradox—a great philosophical paradox of free will Benford’s law and its use in computer design and fraud detection While useful in areas as diverse as game theory, quantum mechanics, and forensic science, mathematical expectation generates paradoxes that frequently leave questions unanswered yet reveal interesting surprises. Encouraging you to embrace the mysteries of mathematics, this book helps you appreciate the applications of mathematical expectation, "a statistical crystal ball." Listen to an interview with the author on NewBooksinMath.com.

The Pea And The Sun

Author : Leonard M. Wapner
ISBN : 1568813279
Genre : Mathematics
File Size : 71. 99 MB
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Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

Here S Looking At Euclid

Author : Alex Bellos
ISBN : 9781416596349
Genre : Mathematics
File Size : 58. 12 MB
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Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place." Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct—including the revelation that ants can actually count how many steps they’ve taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games. Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here’s Looking at Euclid is a rare gem that brings the beauty of math to life.

Music

Author : Judith Anderson
ISBN : 075025890X
Genre : Music
File Size : 29. 44 MB
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This series takes a look behind the scenes at a variety of creative and media industries. The books give an overview of the various jobs available and feature first-hand accounts of people working in each industry.

A Short Account Of The History Of Mathematics

Author : Walter William Rouse Ball
ISBN : UOM:39015065517024
Genre : Mathematics
File Size : 25. 13 MB
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Science Technology And The Military

Author : E. Mendelsohn
ISBN : 9789401729581
Genre : History
File Size : 40. 44 MB
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Grave Expectations

Author : C.J. Archer
ISBN :
Genre : Fiction
File Size : 61. 62 MB
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Charlie's life is perfect. She has everything her heart desires. Until it all goes horribly wrong. Charlie and Lincoln return to London to find two supernaturals have been murdered, and Charlie might be next. As if that wasn't bad enough, the man who adopted her has escaped from prison, and the committee members have just learned some news that infuriates them. Now there's talk of sending Charlie away again. Far away. But the worst is yet to come. Charlie is kidnapped and forced to summon one of the murder victims - but she's unable to send him back. With an angry dead supernatural on the loose and the committee determined to get rid of her, Charlie's time with the Ministry of Curiosities, and Lincoln, is in grave danger of coming to an end.

E2

Author : Pam Grout
ISBN : 9781401938901
Genre : Self-Help
File Size : 36. 18 MB
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Don't face reality. Create reality! E-Squared could best be described as a lab manual with simple experiments to prove once and for all that reality is malleable, that consciousness trumps matter, and that you shape your life with your mind. Rather than take it on faith, you are invited to conduct nine 48-hour experiments to prove there really is a positive, loving, totally hip force in the universe. Yes, you read that right. It says prove. The experiments, each of which can be conducted with absolutely no money and very little time expenditure, demonstrate that spiritual principles are as dependable as gravity, as consistent as Newton's laws of motion. For years, you've been hoping and praying that spiritual principles are true. Now, you can know. E-Squared proves the following: There is an invisible energy force or field of infinite possibilities. You impact the field and draw from it according to your beliefs and expectations. You, too, are a field of energy. Whatever you focus on expands. Your connection to the field provides accurate and unlimited guidance. Your thoughts and consciousness impact matter. Your thoughts and consciousness provide the scaffolding for your physical body. You are connected to everything and everyone else in the universe. The universe is limitless, abundant, and strangely accommodating.

The Spirit Catches You And You Fall Down

Author : Anne Fadiman
ISBN : 9780374533403
Genre : Family & Relationships
File Size : 37. 62 MB
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A study in the collision between Western medicine and the beliefs of a traditional culture focuses on a hospitalized child of Laotian immigrants whose belief that illness is a spiritual matter comes into conflict with doctors' methods.

The Taming Of Chance

Author : Ian Hacking
ISBN : 0521388848
Genre : History
File Size : 60. 18 MB
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This book combines detailed scientific historical research with characteristic philosophic breadth and verve.

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