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※ [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)
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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)
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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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