泰勒斯的遺產

前言

　　在學校教書多年，當學生（特別是本科生）問有什么好的參考書時，我們所能推薦的似乎除了教材還是教材，而且不同教材之間的差別并不明顯、特色也不鮮明。所以多年前我們就開始醞釀，希望為本科學生引進一些好的參考書，為此清華大學數學科學系的許多教授與清華大學出版社共同付出了很多心血?！　∵@里首批推出的十余本圖書，是從Springer出版社的多個系列叢書中精心挑選出來的。在叢書的籌劃過程中，我們挑選圖書最重要的標準并不是完美，而是有特色并包容各個學派（有些書甚至有爭議，比如從數學上看也許不夠嚴格），其出發(fā)點是希望我們的學生能夠吸納百家之長；同時，在價格方面，我們也做了很多工作，以使得本系列叢書的價格能讓更多學校和學生接受，使得更多學生能夠從中受益?！　”鞠盗袌D書按其定位，大體有如下四種類型（一本書可以屬于多類，但這里限于篇幅不能一一介紹）。

內容概要

本書以專題方式講述數學的歷史和數學的哲學（非史論型著作），每個專題相對獨立。全書以數學歷史為線索以數學為內容主體，以數學哲學為引申，易讀、易懂，是本科生學習數學過程中非常好的課外讀物。

書籍目錄

Preface0 IntroductionPART Ⅰ: History and Philosophy of Mathematics　1 Egyptian Mathematics　2 Scales of Notation　3 Prime Numbers　4 Sumerian-Babylonian Mathematics　5 More about Mesopotamian Mathematics　6 The Dawn of Greek Mathematics　7 Pythagoras and His School　8 Perfect Numbers　9 Regular Polyhedra　10 The Crisis of Incommensurables　11 From Heraclitus to Democritus　12 Mathematics in Athens　13 Plato and Aristotle on Mathematics　14 Constructions with Ruler and Compass　15 The Impossibility of Solving the Classical Problems　16 Euclid　17 Non-Euclidean Geometry and Hilbert's Axioms　18 Alexandria from 300 BC to 200 BC　19 Archimedes　20 Alexandria from 200 BC to 500 AD　21 Mathematics in China and India　22 Mathematics in Islamic Countries　23 New Beginnings in Europe　24 Mathematics in the Renaissance　25 The Cubic and Quartic Equations　26 Renaissance Mathematics Continued　27 The Seventeenth Century in France　28 The Seventeenth Century Continued　29 Leibniz　30 The Eighteenth Century　31 The Law of Quadratic ReciprocityPART Ⅱ: Foundations of Mathematics　1 The Number System　2 Natural Numbers (Peano's Approach)　3 The Integers　……ReferencesIndex

章節(jié)摘錄

　　Pythagoras and His School　　Pythagoras （570-500 BC） was born in Samoa, a Greek island off the coast of what is now Turkey. According to ancient sources （Iamblichus, Porphyry and Diogenes Liberties）, he traveled and studied in the Persian empire, which extended then from northern Greece to the Indus Valley and included ancient Mesopotamia. We know （Plimpton 322） that the Babyloni- ans understood what is now called the theorem of Pythagoras, although the latter may have given the first proof. Pythagoras may have learned the theory of Pythagorean triangles from the Babylonians.　 According to the above mentioned sources, Pythagoras also studied under the Zoroastrian priests, the so-called Magi. However, judging from his belief in reincarnation and his vegetarianism, it is more likely that he was influenced by Hindu tradition. Even his mathematics has an Indian flavour.　 About 525 BC, Pythagoras emigrated to Croton （modern Crotone） in southern Italy, where he founded a society, half-way between a political party and a religious cult, which came to be known as the Pythagorean Brotherhood. Some members of this society were admitted to an inner circle consisting of the so-called mathematicians.　 The word mathematics was in fact introduced by Pythagoras. The first part of this word is an old Indo-European root, related to the English word mind. The modern meaning of mathematics is due to Aristotle.

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