Leonard M. Wapner's Books

Unexpected Expectations

The Curiosities of a Mathematical Crystal Ball

By: Leonard M. Wapner

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Unexpected Expectations

The Curiosities of a Mathematical Crystal Ball

By: Leonard M. Wapner

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.

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Page Count

222

Publisher

CRC Press

Published Date

ISBN 10

1568817215

ISBN 13

9781568817217

The Pea and the Sun

A Mathematical Paradox

By: Leonard M. Wapner

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The Pea and the Sun

A Mathematical Paradox

By: Leonard M. Wapner

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.

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Page Count

233

Publisher

CRC Press

Published Date

ISBN 10

1439864845

ISBN 13

9781439864845

The Pea and the Sun

A Mathematical Paradox

By: Leonard M. Wapner

Write a review Read reviews Take a Quiz Solve Book Puzzle

The Pea and the Sun

A Mathematical Paradox

By: Leonard M. Wapner

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

233

Publisher

CRC Press

Published Date

ISBN 10

1439864845

ISBN 13

9781439864845

Book's by Leonard M. Wapner

Unexpected Expectations

Unexpected Expectations

The Pea and the Sun

The Pea and the Sun

The Pea and the Sun

The Pea and the Sun

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