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

線性代數

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)

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

參考書評)
  • 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