教科書/參考書 書評
教科書/參考書 書評
大學部必修課教科書及參考書籍
|| 線性代數 | 高等微積分 | 代數 | 常微分及偏微分方程 | 複變 | 機率 | 幾何(曲線、曲面論) ||
進階參考書籍
|| 拓樸 | 分析 | 偏微分方程 | 微分幾何 | 多複變及黎曼面 | 代數幾何 | 離散數學 | 統計 ||
|
線性代數
|
|
| Principles of Mathematical Analysis | Rudin |
| Introduction to calculus and analysis | Richard Courant, Fritz John |
| A first course in real analysis | Murray H. Protter, Charles B. Morrey |
| Elementary classical analysis | Jerrold E. Marsden, Michael J. Hoffman |
| Modern Algebra | John R.Durbin |
|
Abstract Algebra
|
John B.Fraleigh |
|
Algebra
|
Michael Artin |
|
Topics in Algebra
|
I. N. Herstein |
|
Basic Algebra
|
Nathan Jacobson |
| Algebra | Vander Waerden |
| Algebra | Serge Lang |
| Ordinary differential equations | V. I. Arnold. |
| Differential equations, dynamical systems, and linear algebra | Morris W. Hirsch, Stephen Smale |
| Differential equations | Paul Blanchard, Robert L. Devaney, Glen R. Hall |
| Ordinary differential equations | E.L. Ince |
| An introduction to partial differential equations | Walter A. Strauss |
| Complex analysis : an introduction to the theory of analytic functions of one complex variable | Lars V. Ahlfors |
| The theory of functions | E. C. Titchmarsh |
| Introduction to complex analysis | Nevanlinna |
| Real and complex analysis | Rudin |
| Functions of one complex variable | Conway |
| A First Course in Probability | Sheldon Ross |
| Elementary Probability Theory with Stochastic Processes | Kai Lai Chung ( 鍾開萊 ) |
| An Introduction to Probability and Its Applications | W. Feller |
| Probability : Theory and Examples | Richard Durret |
| Probability with Martingales | David Williams |
| A Course in Probability Theory | Kai Lai Chung ( 鍾開萊 ) |
| Probability Theory | S.R.S. Varadhan |
| Stochastic Processes | Sheldon Ross |
|
幾何 (曲線
、曲面論)
|
|
| Differential geometry of curves and surfaces | Manfredo P. do Carmo |
| Lectures on classical differential geometry | Dirk Jan Struik |
| Differential geometry in the large | Heinz Hopf ; with a preface by S.S. Chern |
| Elementary differential geometry | B. O'Neill |
| 初等微分幾何講稿 | 黃武雄 |
| Topology; a first course | James R. Munkres |
| Basic topology | M.A. Armstrong |
| Algebraic topology | Allen Hatcher |
| Topology from the differentiable viewpoint | John W. Milnor |
| Differential topology | Morris W. Hirsch |
| Morse Theory | J﹒Milnor |
| Differential Forms in Algebraic Topology | Raoul Bott, Loring W. Tu |
| Topology of Fiber Bundles | Norman Steenrod |
| Real analysis | H.L. Royden |
| Measure and integral : an introduction to real analysis | Richard L. Wheeden and Antoni Zygmund |
| Real analysis : modern techniques and their applications | Gerald B. Folland |
| Functional analysis | Peter D. Lax |
| Topics in nonlinear functional analysis | L. Nirenberg |
| Methods of mathematical physics | R. Courant and D. Hilbert |
| Partial Differential Equations | Lawrence C. Evans |
| Partial Differential Equations | F. John |
| Elliptic partial differential equations of second order | David Gilbarg, Neil S. Trudinger |
| Second order parabolic differential equations | Gary M. Lieberman |
| Lectures on elliptic and parabolic equations in Holder spaces | N.V. Krylov |
| Riemannian Geometry | Manfredo P. do Carmo |
| A Comprehensive Introduction to Differential Geometry | Michael Spivak |
| Riemannian geometry and geometric analysis | Jurgen Jost |
| Notes on Differential Geometry | Noel J. Hicks |
| Riemannian Geometry | S. Gallot, D. Hulin, J. Lafontaine |
| Modern Geometry--Methods and Applications | B.A. Dubrovin, A.T. Fomenko, S.P. Novikov |
| Comparison Theorems in Riemannian Geometry | Jeff Cheeger, David G. Ebin |
| Nonlinear Analysis on Manifolds, Monge Ampere Equations | Thierry Aubin |
| Foundations of differential manifolds and Lie groups | F.Warner |
| Differential Geometry, Lie Groups, and Symmetric Spaces | Sigurdur Helgason |
| Geometric Measure Theory | L. Simon |
| Introductions to Riemann surfaces | Springer |
| 緊黎曼曲面引論 | 伍鴻熙 |
| Lectures on Riemann Surfaces | Gunning |
| Complax Manifolds | Kunihiko Kodaira ( 小平邦彥) , James Morrow |
| Principles of Algebraic Geometry | Phillip Griffith, Joseph Harris |
| The Red Book of Varieties and Schemes | David Munford |
| Algebraic Geometry | Robin Hartshorne |
| Introduction to Grothendieck Duality Theory | Allen Altman, Steven Kleiman |
| Compact Complex Surfaces | W. Barth, C. Peters, A. Van de Ven |
| Birational Geometry of Algebraic Varieties | Janos Kollar, Shigefumi Mori |
| Elements of Discrete Mathematics 2nd Edition | 劉炯朗 Liu, C.-L. (Chung Laung) |
| Invitation to Discrete Mathematics | Jiri Matousek, Jaroslav Nesetril |
| Combinatorics : topics, techniques, algorithms | Cameron, Peter J. (Peter Jephson), 1947- |
| A Course in Combinatorics 2nd Edition | J.H. van Lint, R.M. Wilson |
| Introduction to Graph Theory 2nd Edition | Douglas B. West |
| Combinatorial Optimization：Algorithms and Complexity | Christos H. Papadimitriou, Kenneth Steiglitz |
| Introduction to Algorithms 2nd Edition | Thomas H. Cormen |
| Introduction to algorithms: a creative approach | Udi Manber |
| The design and analysis of computer algorithms | Alfred V. Aho, John E. Hopcroft, Jeffrey D. Ullman |
| Elementary Statistics – a step by step approach | Bluman |
| Mathematical Statistics and Data Analysis | John A. Rice |
| Statistics for Experimenters | George E. P. Box, William G. Hunter, J. Stuart Hunter |
| Statistics | David Freedman, Robert Pisani, Roger Durves |
| Linear Statistical Inference and its Applications (Second Edition) | C. Radhakrishna Rao |
| Statistical Inference. 2nd edition | Casella, G. and Berger, R. L. |
| A First Course In Multivariate Statistics | Bernard Flury, Springe 2 |
| Mathematical Statistics and Data Analysis, 2nd Edition | Rice, John A |
| Mathematical Statistics with applications, 6th edition | Dennis D. Wackerly, William Mendenhall Ⅲ, Richard L. Scheaffer |
来源http://www.math.ntu.edu.tw/prospective2/riki.php?id=%E5%8F%83%E8%80%83%E6%9B%B8%E6%9B%B8%E8%A9%95%E4%B8%AD%E6%96%87%E7%89%88&CID=1#diff_eq