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Number Theory: A Very Short Introduction
- Very Short Introductions
- ナレーター: Al Kessel
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The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and listeners of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought.
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Surely You're Joking, Mr. Feynman!
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With his characteristic eyebrow-raising behavior, Richard P. Feynman once provoked the wife of a Princeton dean to remark, "Surely you're joking, Mr. Feynman!" But the many scientific and personal achievements of this Nobel Prize-winning physicist are no laughing matter. Here, woven with his scintillating views on modern science, Feynman relates the defining moments of his accomplished life.
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Fractals
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From the contours of coastlines to the outlines of clouds, and the branching of trees, fractal shapes can be found everywhere in nature. In this Very Short Introduction, Kenneth Falconer explains the basic concepts of fractal geometry, which produced a revolution in our mathematical understanding of patterns in the 20th century, and explores the wide range of applications in science, and in aspects of economics.
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Games are everywhere: Drivers maneuvering in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. The supermarket's price for corn flakes is decided by playing an economic game. This Very Short Introduction offers a succinct tour of the fascinating world of game theory, a groundbreaking field that analyzes how to play games in a rational way.
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あらすじ・解説
Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the "building blocks" of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no one has ever been able to resolve them.
But number theory has also recently become of great practical importance - in the area of cryptography, where the security of your credit card, and indeed of the nation's defense, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed other spectacular developments, such as Andrew Wiles's proof of "Fermat's last theorem" (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction, Robin Wilson introduces the main areas of classical number theory, both ancient and modern. Drawing on the work of many of the greatest mathematicians of the past, such as Euclid, Fermat, Euler, and Gauss, he situates some of the most interesting and creative problems in the area in their historical context.