※ [本文转录自 NomarFan 看板] 作者: lakerfan (红袜迈向世界冠军) 看板: NomarFan 标题: 好书 (数学) 时间: Wed Aug 11 22:38:40 2004 微积分 Calculus: One and Several Variables - Salas Calculus and Analytic Geometry - Thomas Calculus I & II - Apostol 线代 Introduction to Linear Algebra - Strang Linear Algebra - Friedberg (条列许多定理) Linear Algebra... - Strang (涵盖一些Friedberg所没有的数值方法,比第一本多些证明) Linear Algebra - Hoffman (需要一点代数知识) Advanced Linear Algebra - Roman (需要些代数知识) --------------------------------------------------------- 高微 Mathematical Analysis - Apostol (条列许多定理) Elementary Classical Analysis - Marsden Principles of Mathematical Analysis - Rudin (经典之作) Functions of Several Variables - Fleming (讲多变数很好的书) 代数 Topics in Algebra - Herstein Abstract Algebra - Herstein (内容跟上一本差不多,只略去线代) A First Course in Abstract Algebra - Fraleigh Algebra - Hungerford (稍微进阶) Algebra - Lang (既深且广,进阶用书) 数论 An introduction to the theory of numbers - Niven An Introduction To The Theory Of Numbers - Hardy (经典之作) Introduction to Analytic Number Theory - Apostol Algebraic Number Theory - Lang Riemann's zeta function - Edwards Elliptic curves : number theory and cryptography - Washington A Course in Number Theory and Cryptography - Koblitz (密码学) Introduction to Cryptography - Buchmann (密码学) Cryptography: Theory and Practice - Stinson (密码学) 微方(ODE) Differential Equations - Blanchard Differential equations, dynamical systems... - Hirsch Theory Of Ordinary Differential Equations - Coddington, Levinson Ordinary differential equations - Arnold (经典之作) 机率 A First Course in Probability - Ross Introduction to Probability Theory - Hoel, Port, Stone (行文简洁,证明典雅) An Introduction to Probability Theory... vol 1,2 - Feller (经典之作) Stochastic Processes - Ross A First / Second Course in Stochastic Processes - Karlin Introduction to Stochastic Processes - Cinlar Brownian Motion and Stochastic Calculus - Karatzas (稍微进阶) 统计 Introduction to Mathematical Statistics - Hogg & Craig A First Course in Mathematical Statistics - Roussas An introduction to Probability and Statistics - Rohatgi Statistical Inference - Casella (稍微进阶) Mathematical Statistics: Basic Ideas... - Bickel (稍微进阶) ---------------------------------------------------------- 实变 Real Analysis - Royden Real and Complex analysis - Rudin (经典之作) Measure theorey - Halmos Measure and Integral - Wheeden and Zygmund 复变 Introductory complex analysis - Silverman Complex Variables and Applications - Brown, Churchill Basic Complex Analysis - Marsden Functions of one complex variable - Conway The theory of functions - Titchmarsh (经典之作) Complex analysis - Ahlfors (经典之作) 拓朴 Topology - Munkres (入门首选) Basic Topology - Armstrong (比上一本有趣些) General Topology - Kelly (全是定理证明,不错的参考书) Topological spaces : from distance to neighborhood - Buskes 微分几何 Differential Geometry of Curves and Surfaces - Carmo Notes on Differential Geometry - Hicks Lectures on Classical Differential Geometry - Struik Differential geometry in the large - Hopf 微分几何讲义 - 陈省身 (经典之作) 代数几何 Undergraduate Algebraic Geometry - Reid Algebraic curves : an introduction... - Fulton Algebraic Geometry - Hartshorne (经典之作) Algebraic curves and Riemann surfaces - Miranda Introduction to elliptic curves and modular forms - Koblitz The arithmetic of elliptic curves - Silverman 组合 泛论性的书 Introduction to Combinatorial Mathematics - C.L.Liu Combinatorics : topics... - Cameron (其futher reading值得参考) A Course in Combinatorics - Lint (稍微进阶) Enumerative Combinatorics vol 1,2 - Stanley (稍微进阶) Handbook of Combinatorics - Graham (厚厚两本参考用书,像字典) 图论 Graph Theory - Diestel Modern Graph Theory - Bollobas Introduction to Graph Theory - West Algebraic Graph Theory - Godsil (稍微进阶) 组合最佳/优化 Combinatorial Optimization：Algorithms... - Papadimitriou 演算法及资料结构 Data Structures and Algorithm Analysis in... - Weiss Data Structures & Program Design in... - Kruse Fundamentals of Data Structures in.. - Horowitz (据说历代版本中,以pascal最好) http://www.nist.gov/dads/ (资结与演算法的网路字典) Introduction to Algorithms - Cormen (以方法为主的书) Computer Algorithm - Horowitz (以方法为主的书) Algorithms in... Part 1~5 - Sedgewick (以方法为主) Introduction to Algorithms... - Manber (以分析为主的书) Introduction to the Analysis of Algorithms - Sedgewick (以分析为主) Algorithms and Complexity - Wilf (薄薄一本,分析导向,对方法着墨较少) Computers and Intractability... - Garey (讲NP的书,进阶级) Randomized Algorithms - Motwani (讲randomized的书,进阶级) The Art of Computer Programming vol 1~3 - Knuth (经典之作) Selected papers on analysis of algorithms - Knuth (适合数学爱好者) 其他 http://directory.google.com/Top/Computers/ (这里可以找到许多课程投影片) 数值分析 泛论 Numerical analysis - Burden (主要在讲数值上的微方跟线代) http://lib-www.lanl.gov/numerical/bookcpdf.html 数值线性代数/矩阵计算 Topics in matrix analysis - Horn Introduction to Numerical Linear Algebra and Optimisation - Ciarlet Matrix Computations - Golub 计算理论 Introduction to the Theory of Computation - Sipser Introduction to Automata Theory... - Hopcroft Introduction to Languages... - Martin 一些比较深的书,是後来慢慢增补上去的, 所以标题好像应该改成"入门到进阶"才对 :) 另,疏漏之处,请大家补上来吧 2003/10/09 --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 61.230.99.89