※ [本文轉錄自 NomarFan 看板] 作者: lakerfan (紅襪邁向世界冠軍) 看板: NomarFan 標題: 好書 (數學) 時間: Wed Aug 11 22:38:40 2004 微積分 Calculus: One and Several Variables - Salas Calculus and Analytic Geometry - Thomas Calculus I & II - Apostol 線代 Introduction to Linear Algebra - Strang Linear Algebra - Friedberg (條列許多定理) Linear Algebra... - Strang (涵蓋一些Friedberg所沒有的數值方法,比第一本多些證明) Linear Algebra - Hoffman (需要一點代數知識) Advanced Linear Algebra - Roman (需要些代數知識) --------------------------------------------------------- 高微 Mathematical Analysis - Apostol (條列許多定理) Elementary Classical Analysis - Marsden Principles of Mathematical Analysis - Rudin (經典之作) Functions of Several Variables - Fleming (講多變數很好的書) 代數 Topics in Algebra - Herstein Abstract Algebra - Herstein (內容跟上一本差不多,只略去線代) A First Course in Abstract Algebra - Fraleigh Algebra - Hungerford (稍微進階) Algebra - Lang (既深且廣,進階用書) 數論 An introduction to the theory of numbers - Niven An Introduction To The Theory Of Numbers - Hardy (經典之作) 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 (密碼學) Introduction to Cryptography - Buchmann (密碼學) Cryptography: Theory and Practice - Stinson (密碼學) 微方(ODE) Differential Equations - Blanchard Differential equations, dynamical systems... - Hirsch Theory Of Ordinary Differential Equations - Coddington, Levinson Ordinary differential equations - Arnold (經典之作) 機率 A First Course in Probability - Ross Introduction to Probability Theory - Hoel, Port, Stone (行文簡潔,証明典雅) An Introduction to Probability Theory... vol 1,2 - Feller (經典之作) Stochastic Processes - Ross A First / Second Course in Stochastic Processes - Karlin Introduction to Stochastic Processes - Cinlar Brownian Motion and Stochastic Calculus - Karatzas (稍微進階) 統計 Introduction to Mathematical Statistics - Hogg & Craig A First Course in Mathematical Statistics - Roussas An introduction to Probability and Statistics - Rohatgi Statistical Inference - Casella (稍微進階) Mathematical Statistics: Basic Ideas... - Bickel (稍微進階) ---------------------------------------------------------- 實變 Real Analysis - Royden Real and Complex analysis - Rudin (經典之作) Measure theorey - Halmos Measure and Integral - Wheeden and Zygmund 複變 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 (經典之作) Complex analysis - Ahlfors (經典之作) 拓樸 Topology - Munkres (入門首選) Basic Topology - Armstrong (比上一本有趣些) General Topology - Kelly (全是定理證明,不錯的參考書) Topological spaces : from distance to neighborhood - Buskes 微分幾何 Differential Geometry of Curves and Surfaces - Carmo Notes on Differential Geometry - Hicks Lectures on Classical Differential Geometry - Struik Differential geometry in the large - Hopf 微分幾何講義 - 陳省身 (經典之作) 代數幾何 Undergraduate Algebraic Geometry - Reid Algebraic curves : an introduction... - Fulton Algebraic Geometry - Hartshorne (經典之作) Algebraic curves and Riemann surfaces - Miranda Introduction to elliptic curves and modular forms - Koblitz The arithmetic of elliptic curves - Silverman 組合 泛論性的書 Introduction to Combinatorial Mathematics - C.L.Liu Combinatorics : topics... - Cameron (其futher reading值得參考) A Course in Combinatorics - Lint (稍微進階) Enumerative Combinatorics vol 1,2 - Stanley (稍微進階) Handbook of Combinatorics - Graham (厚厚兩本參考用書,像字典) 圖論 Graph Theory - Diestel Modern Graph Theory - Bollobas Introduction to Graph Theory - West Algebraic Graph Theory - Godsil (稍微進階) 組合最佳/優化 Combinatorial Optimization：Algorithms... - Papadimitriou 演算法及資料結構 Data Structures and Algorithm Analysis in... - Weiss Data Structures & Program Design in... - Kruse Fundamentals of Data Structures in.. - Horowitz (據說歷代版本中,以pascal最好) http://www.nist.gov/dads/ (資結與演算法的網路字典) Introduction to Algorithms - Cormen (以方法為主的書) Computer Algorithm - Horowitz (以方法為主的書) Algorithms in... Part 1~5 - Sedgewick (以方法為主) Introduction to Algorithms... - Manber (以分析為主的書) Introduction to the Analysis of Algorithms - Sedgewick (以分析為主) Algorithms and Complexity - Wilf (薄薄一本,分析導向,對方法著墨較少) Computers and Intractability... - Garey (講NP的書,進階級) Randomized Algorithms - Motwani (講randomized的書,進階級) The Art of Computer Programming vol 1~3 - Knuth (經典之作) Selected papers on analysis of algorithms - Knuth (適合數學愛好者) 其他 http://directory.google.com/Top/Computers/ (這裡可以找到許多課程投影片) 數值分析 泛論 Numerical analysis - Burden (主要在講數值上的微方跟線代) http://lib-www.lanl.gov/numerical/bookcpdf.html 數值線性代數/矩陣計算 Topics in matrix analysis - Horn Introduction to Numerical Linear Algebra and Optimisation - Ciarlet Matrix Computations - Golub 計算理論 Introduction to the Theory of Computation - Sipser Introduction to Automata Theory... - Hopcroft Introduction to Languages... - Martin 一些比較深的書,是後來慢慢增補上去的, 所以標題好像應該改成"入門到進階"才對 :) 另,疏漏之處,請大家補上來吧 2003/10/09 --

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