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常用教科書列表與簡評

Common Mathematics Textbooks & Reviews — NTU Department of Mathematics

＊書目依作者姓氏字母排序 · Sorted by first author's last name
＊＊標題後標注 * 者尚無書評 · Books marked * have no review yet

分析／方程
Analysis / Equations

代數／數論
Algebra / Number Theory

幾何／拓樸
Geometry / Topology

計算／應用
Computation / Applied

機率／統計
Probability / Statistics

離散數學
Discrete Mathematics

微積分／實分析　Calculus / Real Analysis

Courant & John — Introduction to Calculus and Analysis [書評 Book Review]
Folland — Real Analysis: Modern Techniques and Their Applications [書評 Book Review]
Lax —Functional Analysis*
Lieb & Loss —Analysis*
Marsden & Hoffman —Elementary Classical Analysis [書評 Book Review]
Nirenberg —Topics in Nonlinear Functional Analysis*
Protter & Morrey — A First Course in Real Analysis [書評 Book Review]
Royden —Real Analysis [書評 Book Review]
Rudin —Principles of Mathematical Analysis [書評 Book Review]
Stein & Shakarchi — Princeton Lectures in Analysis, Vols. 1, 2, 3, 4 *
Wheeden & Zygmund —Measure and Integral: An Introduction to Real Analysis*

常微分方程　Ordinary Differential Equations

Arnold —Ordinary Differential Equations [書評 Book Review]
Blanchard, Devaney & Hall — Differential Equations [書評 Book Review]
Boyce & DiPrima —Elementary Differential Equations and Boundary Value Problems [書評 Book Review]
Hirsch & Smale —Differential Equations, Dynamical Systems, and Linear Algebra [書評 Book Review]
Ince —Ordinary Differential Equations [書評 Book Review]

偏微分方程　Partial Differential Equations

Evans —Partial Differential Equations [書評 Book Review]
Gilbarg & Trudinger —Elliptic Partial Differential Equations of Second Order [書評 Book Review]
John —Partial Differential Equations [書評 Book Review]
Krylov —Lectures on Elliptic and Parabolic Equations in Hölder Spaces*
Lieberman —Second Order Parabolic Differential Equations *
Strauss — An Introduction to Partial Differential Equations [書評 Book Review]

複變分析　Complex Analysis

Ahlfors —Complex Analysis [書評 Book Review]
Conway —Functions of One Complex Variable [書評 Book Review]
Hörmander — An Introduction to Complex Analysis in Several Variables [書評 Book Review]
Nevanlinna —Introduction to Complex Analysis [書評 Book Review]
Rudin —Real and Complex Analysis [書評 Book Review]
Stein & Shakarchi —Princeton Lectures in Analysis 2: Complex Analysis [書評 Book Review]
Titchmarsh —The Theory of Functions [書評 Book Review]
Whittaker & Watson — A Course of Modern Analysis [書評 Book Review]

線性代數　Linear Algebra

Hoffman & Kunze — Linear Algebra, 2nd ed. [書評 Book Review]

抽象代數　Abstract Algebra

Artin — Algebra [書評 Book Review]
Dummit & Foote — Abstract Algebra [書評 Book Review]
Durbin — Modern Algebra [書評 Book Review]
Fraleigh — A First Course in Abstract Algebra [書評 Book Review]
Herstein — Topics in Algebra [書評 Book Review]
Jacobson — Basic Algebra [書評 Book Review]
康明昌 — 《近世代數》[書評 Book Review]
Lang — Algebra [書評 Book Review]
van der Waerden — Algebra *

代數幾何　Algebraic Geometry

Altman & Kleiman — Introduction to Grothendieck Duality Theory [書評 Book Review]
Hartshorne — Algebraic Geometry [書評 Book Review]
Mumford — The Red Book of Varieties and Schemes [書評 Book Review]

數論　Number Theory

Kato, Kurokawa & Saito — Number Theory 1 & 2（數論 I、II） [書評 Book Review]
Serre — A Course in Arithmetic [書評 Book Review]
Silverman & Tate — Rational Points on Elliptic Curves [書評 Book Review]
謝銘倫 — 從交換代數到自守表現論書單 ↗

一般幾何　General Geometry

Hilbert & Cohn-Vossen — Geometry and the Imagination [書評 Book Review]

微分幾何　Differential Geometry

Aubin — Nonlinear Analysis on Manifolds, Monge–Ampère Equations [書評 Book Review]
Cheeger & Ebin — Comparison Theorems in Riemannian Geometry [書評 Book Review]
do Carmo — Differential Geometry of Curves and Surfaces *
do Carmo — Riemannian Geometry [書評 Book Review]
Dubrovin, Fomenko & Novikov — Modern Geometry—Methods and Applications [書評 Book Review]
Gallot, Hulin & Lafontaine — Riemannian Geometry [書評 Book Review]
Helgason — Differential Geometry, Lie Groups, and Symmetric Spaces [書評 Book Review]
Hicks — Notes on Differential Geometry *
Hopf — Differential Geometry in the Large *
黃武雄 — 《初等微分幾何講稿》 *
Jost — Riemannian Geometry and Geometric Analysis [書評 Book Review]
O'Neill — Elementary Differential Geometry *
Simon — Geometric Measure Theory [書評 Book Review]
Spivak — A Comprehensive Introduction to Differential Geometry, Vols. 1–5 [書評 Book Review]
Struik — Lectures on Classical Differential Geometry *
Warner — Foundations of Differentiable Manifolds and Lie Groups *

拓樸　Topology

Armstrong — Basic Topology [書評 Book Review]
Bott & Tu — Differential Forms in Algebraic Topology [書評 Book Review]
Hatcher — Algebraic Topology [書評 Book Review]
Hirsch — Differential Topology [書評 Book Review]
Milnor — Topology from the Differentiable Viewpoint [書評 Book Review]
Milnor — Morse Theory [書評 Book Review]
Munkres — Topology: A First Course [書評 Book Review]
Steenrod — The Topology of Fibre Bundles [書評 Book Review]

黎曼面／複代數幾何　Riemann Surfaces / Complex Algebraic Geometry

Barth, Peters & Van de Ven — Compact Complex Surfaces [書評 Book Review]
Griffiths & Harris — Principles of Algebraic Geometry [書評 Book Review]
Gunning — Lectures on Riemann Surfaces [書評 Book Review]
Kodaira & Morrow — Complex Manifolds [書評 Book Review]
Kollár & Mori — Birational Geometry of Algebraic Varieties [書評 Book Review]
Springer — Introduction to Riemann Surfaces [書評 Book Review]
伍鴻熙 — 《緊黎曼曲面引論》 [書評 Book Review]

數理方法　Methods of Mathematical Physics

Courant & Hilbert — Methods of Mathematical Physics, Vols. 1–2 [書評 Book Review]

機率論　Probability Theory

Chung（鍾開萊） — Elementary Probability Theory with Stochastic Processes [書評 Book Review]
Chung（鍾開萊） — A Course in Probability Theory [書評 Book Review]
Durrett — Probability: Theory and Examples*
Feller — An Introduction to Probability Theory and Its Applications [書評 Book Review]
Ross — A First Course in Probability; [書評 Book Review]
Ross — Stochastic Processes [書評 Book Review]
Varadhan — Probability Theory [書評 Book Review]
Williams — Probability with Martingales [書評 Book Review]

統計學　Statistics

Bluman — Elementary Statistics: A Step by Step Approach [書評 Book Review]
Box, Hunter & Hunter — Statistics for Experimenters [書評 Book Review]
Casella & Berger — Statistical Inference, 2nd ed. [書評 Book Review]
Flury — A First Course in Multivariate Statistics [書評 Book Review]
Freedman, Pisani & Purves — Statistics [書評 Book Review]
Rao — Linear Statistical Inference and Its Applications, 2nd ed. [書評 Book Review]
Rice — Mathematical Statistics and Data Analysis, 2nd ed. [書評 Book Review]
Wackerly, Mendenhall & Scheaffer — Mathematical Statistics with Applications, 6th ed. [書評 Book Review]

離散數學與演算法　Discrete Mathematics & Algorithms

Aho, Hopcroft & Ullman — The Design and Analysis of Computer Algorithms [書評 Book Review]
Cameron — Combinatorics: Topics, Techniques, Algorithms [書評 Book Review]
Cormen et al. — Introduction to Algorithms, 2nd ed. [書評 Book Review]
Liu（劉炯朗） — Elements of Discrete Mathematics, 2nd ed. [書評 Book Review]
Manber — Introduction to Algorithms: A Creative Approach [書評 Book Review]
Matoušek & Nešetřil — Invitation to Discrete Mathematics [書評 Book Review]
Papadimitriou & Steiglitz — Combinatorial Optimization: Algorithms and Complexity [書評 Book Review]
van Lint & Wilson — A Course in Combinatorics, 2nd ed. [書評 Book Review]
West — Introduction to Graph Theory, 2nd ed. [書評 Book Review]

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