The nature and power of mathematics
著者
書誌事項
The nature and power of mathematics
Princeton University Press, c1993
- : pbk
- タイトル別名
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Mathematics
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注記
Includes bibliographical references (p. [379]-382) and index
内容説明・目次
内容説明
In this engaging book, Donald Davis explains some of the most fascinating ideas in mathematics to the nonspecialist, highlighting their philosophical and historical interest, their often surprising applicability, and their beauty. The three main topics discussed are non-Euclidean geometry, with its application to the theory of relativity; number theory, with its application to cryptography; and fractals, which are an application in art, among other areas, of early mathematical work on iteration. Other topics include the influence of Greek mathematics on Kepler's laws of planetary motion, and the theoretical work that led to the development of computers. Assuming the reader has some background in basic algebra and geometry, Davis relies on exercises to develop some of the important concepts. These exercises are designed to improve the reader's ability in logic, and enable him or her actually to experience mathematics at increasingly advanced levels.
目次
Preface1Some Greek Mathematics31.1[phi] and Irrational Numbers: An Introduction to Greek Mathematics31.2Euclidean Geometry191.3Greek Mathematics and Kepler422Non-Euclidean Geometry692.1Formal Axiom Systems692.2Precursors to Non-Euclidean Geometry842.3Hyperbolic Geometry1002.4Spherical Geometry1222.5Models of Hyperbolic Geometry1432.6The Geometry of the Universe1603Number Theory1823.1Prime Numbers1823.2The Euclidean Algorithm2083.3Congruence Arithmetic2203.4The Little Fermat Theorem2384Cryptography2494.1Some Basic Methods of Cryptography2494.2Public Key Cryptography2675Fractals2845.1Fractal Dimension2845.2Iteration and Computers3145.3Mandelbrot and Julia sets339Epilogue377Bibliography379Credits383Index385
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