Springer大学数学图书：泰勒斯的遗产

图书标准信息

• 作者 [美]安格林、[美]兰贝克 著
• 出版社 清华大学出版社
• 出版时间 2009-11
• 版次 1
• ISBN 9787302214830
• 定价 45.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 327页
• 正文语种 英语

【内容简介】

　　《泰勒斯的遗产》以专题方式讲述数学的历史和数学的哲学（非史论型著作），每个专题相对独立。《泰勒斯的遗产》以数学历史为线索，以数学为内容主体，以数学哲学为引申，易读、易懂，是本科生学习数学过程中非常好的课外读物。

【目录】

Preface
0Introduction
PARTⅠ：HistoryandPhilosophyofMathematics
1EgyptianMathematics
2ScalesofNotation
3PrimeNumbers
4Sumerian-BabylonianMathematics
5MoreaboutMesopotamianMathematics
6TheDawnofGreekMathematics
7PythagorasandHisSchool
8PerfectNumbers
9RegularPolyhedra
10TheCrisisofIncommensurables
11FromHeraclitustoDemocritus
12MathematicsinAthens
13PlatoandAristotleonMathematics
14ConstructionswithRulerandCompass
15TheImpossibilityofSolvingtheClassicalProblems
16Euclid
17Non-EuclideanGeometryandHilbertsAxioms
18Alexandriafrom300BCto200BC
19Archimedes
20Alexandriafrom200BCto500AD
21MathematicsinChinaandIndia
22MathematicsinIslamicCountries
23NewBeginningsinEurope
24MathematicsintheRenaissance
25TheCubicandQuarticEquations
26RenaissanceMathematicsContinued
27TheSeventeenthCenturyinFrance
28TheSeventeenthCenturyContinued
29Leibniz
30TheEighteenthCentury
31TheLawofQuadraticReciprocity
PARTⅡ：FoundationsofMathematics
1TheNumberSystem
2NaturalNumbers(PeanosApproach)
3TheIntegers
4TheRationals
5TheRealNumbers
6ComplexNumbers
7TheFundamentalTheoremofAlgebra
8Quaternions
9QuaternionsAppliedtoNumberTheory
10QuaternionsAppliedtoPhysics
11QuaternionsinQuantumMechanics
12CardinalNumbers
13CardinalArithmetic
14ContinuedFractions
15TheFundamentalTheoremofArithmetic
16LinearDiophantineEquations
17QuadraticSurds
18PythagoreanTrianglesandFermatsLastTheorem
19WhatIsaCalculation?
20RecursiveandRecursivelyEnumerableSets
21HilbertsTenthProblem
22LambdaCalculus
23LogicfromAristotletoRussell
24IntuitionisticPropositionalCalculus
25HowtoInterpretIntuitionisticLogic
26IntuitionisticPredicateCalculus
27IntuitionisticTypeTheory
28GodelsTheorems
29ProofofGSdelsIncompletenessTheorem
30MoreaboutGodelsTheorems
31ConcreteCategories
32GraphsandCategories
33Functors
34NaturalTransformations
35ANaturalTransformationbetweenVectorSpaces
References
Index