# 國立臺灣大學數學系常用教科書列表與簡評

|| 分析/方程 | 代數/數論 | 幾何/拓樸 | 計算/應用 | 機率/統計 | 離散數學 ||

*分類中依第一作者姓氏字母排序。

*尚未提供書評的書籍，會在尾端加註記號

### 分析/方程

#### 微積分/分析/實分析（參考書評）

• Richard Courant, Fritz John Introduction to calculus and analysis
• Gerald B. Folland Real analysis: modern techniques and their applications
• Peter D. Lax Functional analysis *
• Jerrold E. Marsden, Michael J. Hoffman Elementary classical analysis
• Elliott H. Lieb, Michael Loss Analysis*
• Louis Nirenberg Topics in nonlinear functional analysis *
• Murray H. Protter, Charles B. Morrey A first course in real analysis
• Halsey L. Royden Real analysis
• Walter Rudin Principles of Mathematical Analysis
• Elias M. Stein, Rami Shakarchi Princeton Lectures in Analysis, 1-4 *
• Richard L. Wheeden, Antoni Zygmund Measure and integral: an introduction to real analysis *

#### 常微分方程（參考書評）

• Vladimir I. Arnold Ordinary differential equations
• Paul Blanchard, Robert L. Devaney, Glen R. Hall Differential equations
• William E. Boyce, Richard C. DiPrima Elementary differential equations and boundary value problems
• Morris W. Hirsch, Stephen Smale Differential equations, dynamical systems, and linear algebra
• Edward L. Ince Ordinary differential equations

#### 偏微分方程（參考書評）

• Lawrence C. Evans Partial Differential Equations
• David Gilbarg, Neil S. Trudinger Elliptic partial differential equations of second order
• Fritz John Partial Differential Equations
• Nicolai V. Krylov Lectures on elliptic and parabolic equations in Holder spaces *
• Gary M. Lieberman Second order parabolic differential equations *
• Walter A. Strauss An introduction to partial differential equations

#### 複變 （參考書評）

• Lars V. Ahlfors Complex analysis : an introduction to the theory of analytic functions of one complex variable
• John B. Conway Functions of one complex variable
• Lars HormanderAn Introduction to Complex Analysis in Several Variables
• Rolf H. Nevanlinna Introduction to complex analysis
• Walter Rudin Real and complex analysis
• Elias M. Stein, Rami Shakarchi Princeton Lectures in Analysis 2, Complex Analysis
• Edward C. Titchmarsh The theory of functions
• Edmund T. Whittaker, George N. Watson A Course of Modern Analysis

### 代數/數論

#### 代數（參考書評）

• Michael Artin Algebra
• David S. Dummit, Richard M. Foote Abstract Algebra
• John R.Durbin Modern Algebra
• John B.Fraleigh Abstract Algebra
• Israel N. Herstein Topics in Algebra
• Nathan Jacobson Basic Algebra
• 康明昌 《近世代數》
• Serge Lang Algebra
• Vander Waerden Algebra *

#### 代數幾何（參考書評）

＊也可參考複代數幾何

• Allen Altman, Steven Kleiman Introduction to Grothendieck Duality Theory
• Robin Hartshorne Algebraic Geometry
• David Munford The Red Book of Varieties and Schemes

#### 數論（參考書評）

• Kazuya Kato, Nobushige Kurokawa, Takeshi Saito Number Theory 1: Fermat’s Dream, Number Theory 2: Introduction to Class Field Theory
＝加藤和也、黑川信重、斎藤毅《數論I》《數論II》（大陸簡中版）
• J. P. Serre A course in arithmetic
• Joseph H. Silverman, John T. Tate Rational Points on Elliptic Curves
• 從交換代數、代數幾何、代數數論到自守表現論的一份書單與評述（謝銘倫老師）
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### 幾何/拓樸

#### 一般幾何（參考書評）

• David Hilbert, Stephan Cohn-Vossen Geometry and the Imagination

#### 微分幾何（參考書評）

• Thierry Aubin Nonlinear Analysis on Manifolds, Monge Ampere Equations
• Manfredo P. do Carmo Differential geometry of curves and surfaces *
• Manfredo P. do Carmo Riemannian Geometry
• Jeff Cheeger, David G. Ebin Comparison Theorems in Riemannian Geometry
• Boris A. Dubrovin, Anatoly T. Fomenko, Sergei P. Novikov Modern Geometry--Methods and Applications
• Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine Riemannian Geometry
• Sigurdur Helgason Differential Geometry, Lie Groups, and Symmetric Spaces
• Noel J. Hicks Notes on Differential Geometry *
• Heinz Hopf (prefaced by S.S. Chern) Differential geometry in the large *
• 黃武雄 《初等微分幾何講稿》 *
• Jurgen Jost Riemannian geometry and geometric analysis
• Barrett O'Neill Elementary differential geometry *
• Leon Simon Geometric Measure Theory
• Michael Spivak A Comprehensive Introduction to Differential Geometry, 1-5
• Dirk Jan Struik Lectures on classical differential geometry *
• Frank W. Warner Foundations of differential manifolds and Lie groups *

#### 拓樸（參考書評）

• Mark A. Armstrong Basic topology
• Raoul Bott, Loring W. Tu Differential Forms in Algebraic Topology
• Allen Hatcher Algebraic topology
• Morris W. Hirsch Differential topology
• John W. Milnor Topology from the differentiable viewpoint
• John W. Milnor Morse Theory
• James R. Munkres Topology a first course
• Norman Steenrod Topology of Fiber Bundles

#### 黎曼面/複代數幾何（參考書評）

＊也可參考代數幾何

• W. Barth, C. Peters, A. Van de Ven Compact Complex Surfaces
• Phillip Griffith, Joseph Harris Principles of Algebraic Geometry
• Robert C. Gunning Lectures on Riemann Surfaces
• Kunihiko Kodaira (小平邦彥), James Morrow Complax Manifolds
• Janos Kollar, Shigefumi Mori Birational Geometry of Algebraic Varieties
• George S. Springer Introductions to Riemann surfaces
• 伍鴻熙《緊黎曼曲面引論》

### 計算/應用

• Richard Courant, David Hilbert Methods of mathematical physics

### 機率/統計

#### 機率（參考書評）

• Kai Lai Chung (鍾開萊) Elementary Probability Theory with Stochastic Processes
• Kai Lai Chung (鍾開萊) A Course in Probability Theory
• Richard Durret Probability : Theory and Examples
• William Feller An Introduction to Probability and Its Applications
• Sheldon Ross A First Course in Probability
• Sheldon Ross Stochastic Processes
• S. R. Srinivasa Varadhan Probability Theory
• David Williams Probability with Martingales

#### 統計（參考書評）

• Allan G. Bluman Elementary Statistics: a step by step approach
• John A. Rice Mathematical Statistics and Data Analysis
• George E. P. Box, William G. Hunter, J. Stuart Hunter Statistics for Experimenters
• David Freedman, Robert Pisani, Roger Durves Statistics
• C. Radhakrishna Rao Linear Statistical Inference and its Applications, 2nd edition
• George Casella, Roger L. BergerStatistical Inference, 2nd edition
• Bernard Flury A First Course In Multivariate Statistics
• John A Rice Mathematical Statistics and Data Analysis, 2nd edition
• Dennis D. Wackerly, William Mendenhall Ⅲ, Richard L. Scheaffer Mathematical Statistics with applications, 6th edition

### 離散數學

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• Alfred V. Aho, John E. Hopcroft, Jeffrey D. Ullman The design and analysis of computer algorithms

• Peter J. Cameron Combinatorics : topics, techniques, algorithms

• Thomas H. Cormen Introduction to Algorithms 2nd edition

• Chung Laung Liu (劉炯朗) Elements of Discrete Mathematics, 2nd edition

• Jacobus H. van Lint, Richard M. Wilson A Course in Combinatorics, 2nd edition

• Udi Manber Introduction to algorithms: a creative approach

• Jiri Matousek, Jaroslav Nesetril
Invitation to Discrete Mathematics

• Christos H. Papadimitriou, Kenneth Steiglitz Combinatorial Optimization：Algorithms and Complexity

• Douglas B. West Introduction to Graph Theory, 2nd edition
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