1) 数学是什么？
1, What is mathematics [Courant]
2, Induction and Analogy in mathematics [Polya]
2) 直观几何学，对称，几何之代数
1, Geometry and the Imagination [Hilbert]
2, Symmetry [Weyl]
3, Geometric Algebra [E. Artin]
3) 实与复变函数及其微积分
1, Differential and Integral Calculus [Courant]
2, Complex Analysis [Alfors]
3, A Course of Mordern Analysis [Whittaker & Watson]
4)初等代数拓扑与黎曼面
Algebraic Topology: A first course [W. Fulton]
5) 十九世纪的数学
1, Development of mathematics in the 19th century [F Klein]
2, On Riemanns theory of algebraic function [F Klein]
6) 希尔伯特-柯朗
1, Methods of mathematical physics, Vol 1, [Courant Hilbert]
2, 泛函分析与希尔伯特空间(初步即可)
7) 流形的拓扑与几何
1, 现代几何学卷一，卷二
2, 从微分观点看拓扑[Milnor]
3 , Morse Theory[Milnor]
4, 时空的大尺度结构[Hawking-Ellis]
5 , S. S. Chern 内在证明之原文
6, Geometry and topology of 3-manifold [Thurston]
7, Perelman 原文
8) 群表示论
1, The Classical Groups [Weyl]
2, Representation theory: A first course [W. Fulton]
3, Lectures on exceptional Lie groups [Adams]
9) 抽象代数学基础
1, Basic Notions of Algebra [Shafarevich]
2, Algebra [M. Artin]
10) 代数几何
Principle of Algebraic Geometry [G. H. ]
11) 上同调及其推广
1, 现代几何学卷三
2, Characteristic classes [Milnor]
3, Differential form in algebraic topology [Bott]
4, K-theory [Atiyah]
12) 量子场论与几何
Quantum Fields and Strings: A Course for Mathematicians. Volume 1&2 [Deligne Witten etc. ]
