成大數學系研究所課程總覽

課程地圖:大學部研究所

各領域修課建議:分析代數幾何機率與統計計算與應用數學

課程查詢系統

編號 課程碼 屬性碼 課程名稱 Course Name
1 L150310 Math6002 分析通論(一) General Analysis I
2 L150320 Math6101 分析通論(二) General Analysis II
3 L170210 Math6102 泛函分析(一) Functional Analysis I
4 L170310 Math6008 偏微分方程(一) Partial Differential Equations I
5 L170320 Math6103 偏微分方程(二) Partial Differential Equations II
6 L182500 Math6104 積分方程 Integral Equation
7 C146100 Math5204 傅立葉分析與應用 Fourier Analysis and Applications
8 L150410 Math6003 代數通論(一) General Algebra I
9 L150420 Math6201 代數通論(二) General Algebra II
10 L153200 Math6005 高等線性代數 Advanced Linear Algebra
11 L162500 Math6206 密碼學 Cryptography
12 L167110 Math6202 數論(一) Number Theory I
13 L167120 Math6203 數論(二) Number Theory II
14 L167200 Math6204 有限域 Finite Fields
15 L167300 Math6205 代數編碼理論 Algebraic Coding Theory
16 L167400 Math7202 表示理論 Representation Theory
17 L167500 Math7203 同調代數 Homological Algebra
18 L167610 Math7204 李群和李代數(一) Lie Groups and Lie Algebras I
19 L167620 Math7205 李群和李代數(二) Lie Groups and Lie Algebras II
20 L167710 Math7206 交換代數(一) Commutative Algebra I
21 L167720 Math7207 交換代數(二) Commutative Algebra II
22 L170200 Math7201 環論 Ring Theory
23 L154800 Math6006 微分幾何導論 Introduction to Differential Geometry
24 L164300 Math6301 代數拓樸導論 Introduction to Algebraic Topology
25 L161400 Math7301 黎曼幾何 Riemannian Geometry
26 L168500 Math7303 雙曲幾何 Hyperbolic Geometry
27 L168600 Math7304 代數幾何 Algebraic Geometry
28 L174620 Math7305 代數幾何(二) Algebraic Geometry
29 L171400 Math7302 辛幾何 Symplectic Geometry
30 L184500 Math7307 摩斯理論 Morse Theory
31 L150210 Math6001 機率論(一) Probability I
32 L155600 Math6401 隨機過程 Stochastic Processes
33 L168700 Math6402 數理統計 Mathematical Statistics
34 L168800 Math6403 線性模式 Linear Model
35 L150710 Math5800 數值分析(一) Numerical Analysis I
36 L167900 Math5802 快速計算方法 Fast Computational Method
37 L168000 Math6504 科學計算 Scientific Computing
38 L168100 Math6505 作業研究 Operations Research
39 L168200 Math5804 最佳化理論 Theory of Optimization
40 L168300 Math6507 計算複雜度理論 Computational Complexity
41 L168400 Math6508 應用數學導論 Introduction to Applied Mathematics
42 L182200 Math6509 不連續有限元素法 Discontinuous Galerkin Finite Element Methods
43 L170910 Math6501 數值偏微分方程(一) Numerical Analysis for Partial Differential Equations I
44 L170920 Math6502 數值偏微分方程(二) Numerical Analysis for Partial Differential Equations II
45 L167800 Math7501 數值線性代數 Numerical Linear Algebra
46 L166500 Math7502 線性控制系統與計算方法 Numerical Methods for Linear Control Systems
47 L183600 Math7503 最佳化與數學模式 Optimization and Mathematical Models
48 L153800 Math5806 電磁理論的數學架構 Mathematical Structure of Electro-Magnetic Field Theory
49 L184200 Math6106 氣體動力學方程及其相關主題 Kinetic Equations and Related Topics
50 L184300 Math6511 邊界元素法 Boundary Element Method
51 L168900 Math5807 應用數學(一) Applied Mathematics I
52 L184100 Math6512 應用數學(二) Applied Mathematics II
53 L169000 Math5808 經典力學的數學方法 Mathematical Methods of Classical Mechanics
54 L160600 Math6007 專題討論 Mathematics Colloquium

課程名稱分析通論(一)General Analysis I
課程簡介本課程討論在R^n上的Lebesgue測度和實函數Lebesgue積分理論。The Theory of Lebesgue on R^n, Lebesgue Integration on R^n.

課程名稱分析通論(二)General Analysis II
課程簡介本課程接續(一)的內容,主要討論微分理論和抽象空間中的測度。Lebesgue Differentiation Theory, L^p Spaces, Maximal Functions, Abstract Measures.

課程名稱泛函分析(一)Functional Analysis I
課程簡介本課程介紹泛函分析的基本要素。我們將著重Sobolev空間及線性算子理論。我們將討論Hahn-Banach theorem, principle of uniform boundedness 及 open mapping theorem。我們也將討論Riesz theory及Fredholm theory。We study some basic elements of functional analysis including some operator theory. The main objects in this course are Sobolev spaces and linear operators. We will discuss the Hahn-Banach theorem, the principle of uniform boundedness and open mapping theorem. Also, Riesz theory and Fredholm theory will also be discussed.

課程名稱偏微分方程(一)Partial Differential Equations I
課程簡介本課程學習偏微分方程的概念與基本類型以及它們的屬性。討論邊界問題,傅立葉級數,調和函數。研究Green等式和Green函數,在空間的波,在空間及平面的邊界,一般特徵值問題,與波分佈的想法。We study the concepts and basic types of PDE, and their properties. Then we discuss boundary problems, Fourier Series, and Harmonic Funtions. Next we investigate the ideas of Green`s Identities and Green`s Functions, Waves in Space, Boundaries in the Plane and in Space, General Eigenvalue Problems, and Distributions.

課程名稱偏微分方程(二)Partial Differential Equations II
課程簡介本課程學習空間中波的概念和基本類型,包括氫原子,及其性質。然後我們討論在平面與空間的邊界及一些特別函數,一般特徵值問題和分佈,包括到目前為止我們所學習過的偏微分方程的基本解以及傅立葉變換。最後,我們調查了一些物理現象,如散射問題,連續譜,衝擊波和光孤子。We study the concepts and basic types of Waves in Space, including Hydrogen Atom, and their properties. Then we discuss, Boundaries in the Plane and in Space and some special functions involved, General Eigenvalue Problems, and Distributions, including the fundamental solutions for the PDEs we have learnt so far and Fourier transform. Finally we investigate some physical phenomena like scattering problems, continuous spectrum, shock waves, and solitons.

課程名稱積分方程Integral Equation
課程簡介本課程介紹數學物理中的線性積分方程. 本課程將以泛函分析為工具來作一有系統的分析。 主題包含:Abel 積分方程,Riesz 理論,Fredholm 理論,積分變換,Hilbert空間中的有界算子理論。In the course, we are mainly concerned with linear integral equations arising from mathematical physics. Tools from functional analysis will also be included to enable a systematical analysis. Topics included are: Abel integral equation, Riesz Theory, Fredholm theory, integral transformations, bounded linear operators in Hilbert spaces.

課程名稱傅立葉分析與應用CALCULUS ON MANIFOLDS
課程簡介許多大自然的現象具有週而復始的規律,即週期現象,由此誘發了偏微分方程的研究。為了求方程的解,Fourier 分析是個重要且不可或缺的工具。這門課是以一個學期為考量,針對理工科系高年級學生而設計的,內容涵蓋Fourier分析與偏微分方程的基本知識與應用。Many phenomena in nature have the feature of periodic occurence. And thus Fourier analysis is useful in solving problems arising from physics or engineering. In addition to the techniques of solving differential equations, the theoretical aspect is also emphasized in this course so that students can benefit from the study of the idea underlying the subject.

課程名稱代數通論(一)General Algebra I
課程簡介群同構定理,群作用,西羅定理,阿貝爾群基本定理,若爾當-赫爾德定理,p-群,冪零群,可解群。Basic concepts, the isomorphism theorems for groups, group actions, Sylow theorems, fundamental theorem of abelian groups, Jordan-Holder theorem, p-groups, nilpotent and solvable groups.

課程名稱代數通論(二)General Algebra II
課程簡介多項式環,環同態,環同構定理,唯一分解整環,歐幾里得整環,主要理想整環,體擴張,代數擴張,分裂體,伽羅瓦理論基本定理,有限群表現理論。Basic concepts, polynomial rings, ring homomorphisms, isomorphism theorems of rings, unique factorization domains, principal ideal domains and Euclidean domains, field extensions, algebraic extensions, splitting fields, Fundamental theorem of Galois theory, representation theory of finite groups.

課程名稱高等線性代數Advanced Linear Algebra
課程簡介向量空間和多重線性變換,張量,對稱和外代數。Vector spaces and multilinear transformations, tensor, symmetric and exterior algebra.

課程名稱密碼學Cryptography
課程簡介密碼學是在研究秘密通訊的方法,本學期將介紹現代密碼學的理論以及所需要的數學知識。Cryptography is the study of techniques for secure communication. In this course we will introduce modern cryptography and mathematical theory invoved.

課程名稱數論(一)Number Theory I
課程簡介各種主題的代數和解析數論和算術幾何。Various topics in algebraic and analytic number theory and arithmetic geometry.

課程名稱數論(二)Number Theory II
課程簡介各種主題的代數和解析數論和算術幾何。Various topics in algebraic and analytic number theory and arithmetic geometry.

課程名稱有限域Finite Fields
課程簡介有限域的結構,它們的分類和應用。Structures of finite fields, their classification and applications.

課程名稱代數編碼理論Algebraic Coding Theory
課程簡介有限域及其在編碼理論的應用。Finite fields and their application to coding theory.

課程名稱表示理論Representation Theory
課程簡介各種群和(李)代數的表示。Representations of various groups and (Lie) algebra.

課程名稱同調代數Homological Algebra
課程簡介復體和導出範疇,同調和上同調理論。Complexes and derived categories, homology and cohomology theory.

課程名稱李群和李代數(一)Lie Groups and Lie Algebras I
課程簡介李群和李代數及其表示,單李群和代數的分類。Lie groups and Lie algebra, classification of simple Lie groups and algebras and their representations.

課程名稱李群和李代數(二)Lie Groups and Lie Algebras I
課程簡介李群和李代數及其表示,單李群和代數的分類。Lie groups and Lie algebra, classification of simple Lie groups and algebras and their representations.

課程名稱交換代數(一)Commutative Algebra I
課程簡介本課程主題包含Noetherian環以及它們的模,Hilbert基底定理,Noether正則化定裡,Hilbert零點定理,局部化,理想分解定理,維度定理,以及一些重要的交換環介紹。The main topics of this course consist of Noetherian rings and modules, Hilbert basis theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs and normal domains, and dimension theory.

課程名稱交換代數(二)Commutative Algebra II
課程簡介本課程包含基本的同調代數理論,環及模的完備化,以及一些來自於代數幾何的相關概念:微分算子,完全正交環,Gorenstein環,Cohen-Macaulay環及他們的模。此外,一些關於組合交換代數及tight closure的基本理論也會被介紹。In this course, more advanced topics in commutative algebra will be discussed including basic homological algebras, completions of rings and modules, regular local rings, derivation and differentials, complete intersections, Gorenstein rings, Cohen--Macaulay rings and modules. Some topics in combinatorial commutative algebra and tight closure theory will also be discussed.

課程名稱環論Ring Theory
課程簡介環以及相關理論,交換和非交換環, 模。Rings and related theory, commutative and noncommutative rings, modules.

課程名稱微分幾何導論Introduction to Differential Geometry
課程簡介這是微分幾何的入門課程。其中涉及的主題包括光滑流形和光滑映射,正切和餘切束,向量場,微分形式,流形上的積分,de Rham上同調,映射度和指標,以及進一步的應用。This is the introductory course on differential geometry. Among the topics covered are smooth manifolds and smooth maps, the tangent and cotangent bundles, vector fields and differential forms, integration on manifolds, de Rham cohomology, degrees and indices, and further applications.

課程名稱代數拓樸導論Introduction to Algebraic Topology
課程簡介代數拓樸運用代數工具來處理拓樸問題。這門課是代數拓樸的入門課,探討同倫論與同調論。題材包括基本群、覆疊空間、奇異同調、相對同調、胞腔同調、切除以及Mayer-Vietoris序列。若時間允許,將涵蓋上同調及龐加萊對偶性。Algebraic topology uses algebraic tools to study topological problems. In this introductory course, we discuss homotopy theory and homology theory. Topics include fundamental groups, covering spaces, singular homology, relative homology, cellular homology, excision, and Mayer-Vietoris sequences. If time permits, we will cover other topics such as cohomology and Poincare duality.

課程名稱黎曼幾何Riemannian Geometry
課程簡介這門課的目的是探討黎曼流形。題材包括黎曼度量、聯絡、測地線、曲率、Jacobi場、完備性與Hopf–Rinow定理、Cartan–Hadamard定理等。This course is devoted to studying Riemannian manifolds. Topics will include Riemannian metrics, connection, geodesics, curvature, Jacobi fields, completeness and Hopf–Rinow Theorem, Cartan–Hadamard Theorem, etc.

課程名稱雙曲幾何Hyperbolic Geometry
課程簡介介紹二維和三維的實雙曲流形和/或二維的複雙曲流形。Two and three dimensional real hyperbolic manifolds and/or two dimensional complex hyperbolic manifolds.

課程名稱代數幾何Algebraic Geometry
課程簡介代數幾何探討多項式方程組的解集及其幾何結構。這門課的主要目的是引進代數幾何裡的一些重要概念。題材包括曲體、態射與有理映射、維度以及平滑性。若時間允許,將涵蓋概形論的基本概念。Algebraic geometry studies the zero sets of polynomials and their geometric structures. The main goal of this course is to introduce some of the important ideas of algebraic geometry. Specifically, we will explore the following topics: varieties, morphisms and rational maps, dimension, and smoothness. If time permits, basic notions in scheme theory will also be discussed.

課程名稱代數幾何(二)Algebraic Geometry II
課程簡介這門課將探討概形論與層上同調。題材包括層、概形、分離態射與真態射、平坦性、平滑態射與平展態射、Cech上同調以及Serre對偶。This course will deal with scheme theory and sheaf cohomology. Topics will include sheaves, schemes, separated and proper morphisms, flatness, smooth and etale morphisms, Cech cohomology, and Serre duality.

課程名稱辛幾何Symplectic Geometry
課程簡介本課程旨在介紹辛幾何。辛流形在數學和物理的許多領域中自然產生,局部結構單純,但擁有豐富的整體結構。我們計劃由辛向量空間開始,學習辛流形和接觸流形以及辛群作用的基礎,再視學生的背景和興趣,探討如等變上同調,J-holomorphic曲線等進一步主題。This course is intended as an introduction to symplectic geometry. Symplectic manifolds arise naturally in many areas of mathematics and physics. They are very simple locally but have a rich global structure. We plan to begin with the basics on symplectic vector spaces, symplectic and contact manifolds, symplectic quotients, followed by further topics subject to the backgrounds and interests of the students such as equivariant cohomology, J-holomorphic curves, etc.

課程名稱摩斯理論Probability I
課程簡介摩斯理論是從近乎任意的數值函數中提取拓樸信息的有力工具。 本課程將涵蓋摩斯理論的基礎知識,並提及摩斯理論一些很好的應用。Morse theory is a powerful tool to extract topological information from a nearly arbitrary numerical function. This course will cover the basics of the theory and some of its very nice applications.

課程名稱機率論(一)Probability I
課程簡介機率測度,大數法則,中央極限定理,隨機游動,Martingale,Ergodic理論,布朗運動。Probability measure, Law of Large Number, Central Limit Theorem, Random walk, Martingale, Ergodic Theory, Brownian Motion.

課程名稱隨機過程Stochastic Processes
課程簡介伯努力定理,馬可夫鏈,普松過程,再生過程。Bernoulli Processes, Mankov chains, Poisson Processes, Renewal Processes.

課程名稱數理統計Mathematical Statistics
課程簡介機率空間,統計模式之建構,參數化,統計推論,大樣本理論。Probability Space, Statistical Modeling, Parameterized, Statistical Inference, Large Sample Theory.

課程名稱線性模式Linear Model
課程簡介代數矩陣,多變量常態分配,線性迴歸,變異數分析,共軛變異數分析。Matrix Algebra, Multi-normal distribution, Linear regression, Analysis of Variance, Analysis of Covariance.

課程名稱數值分析(一)Numerical Analysis I
課程簡介本課程涵蓋數值分析的主要概念,包括:實數系與浮點數系統,精確度,準確度和誤差分析,高維的求根方法和收斂性分析,線性系統數值方法,數值微分方程,以及相關的穩定性分析與數值方法。This course covers main concepts of numerical analysis, including: real number system v.s. floating number system, precision, accuarcy and error analysis, higher dimensional root finding methods and convergence analysis, numerical methods for linear systems, numerical differential equations, and related stability analysis.

課程名稱快速計算方法Fast Computational Method
課程簡介本課程介紹快速計算方法的理論並透過程式語言的實作來了解此類方法快在哪裡的精髓。課程中將介紹快速排序法、快速富立葉轉換、快速波瓦松求解器、幾何及代數多重網格法、快速多重極方法等等。The theory of fast computational methods are introduced. Students could understand the essence through the implementation in programming languages. Several methods will be illustrated, such as quick sort, fast Fourier transform, fast Poisson solver, geometry and algebraic multigrid method, fast multipole method, etc.

課程名稱科學計算Scientific Computing
課程簡介本課程將介紹不同領域的科學計算,如流體力學、分子動力學、電磁學、動態系統等等。學生將從本課程中學到基本的科學計算方法並體驗科學的美及計算的力量。Scientific computings in various fields are introduced, for example, fluid dynamics, molecular dynamics, electro-magnetic computation, dynamical system, etc.. Students will learn the basic methods of scientific computing, realize the power of computing, and experence the beauty of sciences.

課程名稱作業研究Operations Research
課程簡介線性規劃、Simplex Method、對偶理論、運輸問題、網路最佳化、整數規劃。Linear Programming, Simplex Method, Duality, Transportation problem, Network Optimization, Integer Programming.

課程名稱最佳化理論Theory of Optimization
課程簡介本課程主要介紹半無限維線性規劃問題與其對偶問題、強對偶定理、最佳解的基本性質及演算法、二次半無限維規劃問題與其對偶問題、解二次半無限維規劃問題的演算法、無限維線性規劃問題及其演算法。This curriculum mainly introduce the semi-infinite Linear programming problems and its dual problem, strong duality theorem, basic properties of optimal solution and algorithms, quadratic semi-infinite programming problems and its dual problems, algorithms for quadratic semi-infinite programming problems, infinite Linear programming problem and its algorithms.

課程名稱計算複雜度理論Computational Complexity
課程簡介Turing Machine、計算複雜度分類(P, NP, coNP)、組合優化演算法分析(背包問題、機器排程、頂點集覆蓋問題、最大割問題)、半正定近似算法。Turing Machine、Complexity Classes、Algorithms for Combinatorial Optimizaiton(Knapsack problem, machine scheduling, vertex conver, max cut) 、Semidefinite Relaxation.

課程名稱應用數學導論Introduction to Applied Mathematics
課程簡介矩陣線性系統的模組與數學結構、平衡系統結構、拉格朗日對偶、最小平方估計與Kalman Filter、平衡微分方程組、Laplace方程、變分法。Matrix Linear System (Modeling and Mathematical Structure), Structure of Equilibrium, Lagrange Duality, Least Squares and the Kalman Filter, Differential Equations of Equilibrium, Laplace Equations, Calculus of Variation.

課程名稱不連續有限元素法Discontinuous Galerkin Finite Element Methods
課程簡介本課程目的在簡介以不連續有限元方法(Discontinuous Galerkin Methods)解偏微分方程。不連續有限元方法是有限元素法的一種,但是他同時擁有限體積法的一些特色。和傳統的連續有限元素法不同,不連續有限元方法使用的函數空間在每個元素中是連續的,但是元素間是不連續的,因此以DG離散得到的方程式是局部的。這個特性,使得不連續有限元方法非常適合在非結構性網格上發展高精度數值方法,同時也非常適合平行計算。 這門課程,我們會先給數值偏微分方程以及有限元素法簡短的介紹,接著介紹如何使用不連續有限元方法對不同類型偏微分方程求解,討論數值穩定性、一致性、收斂性以及誤差估計。實做部分主要以MATLAB範例程式讓學生了解方法的效果。

This course gives an introduction to the Discontinuous Galerkin methods. The discontinuous Galerkin method is a special class of the finite element methods and the method combines features of the finite element and finite volume methods. Unlike traditional continuous Galerkin method, the DG method works over a trial space of functions that are continuous in each element but discontinuous across edges and thus the resulting equations are local to the generating element. The method provides a practical framework for the development of high-order accurate methods using unstructured grids and is well suited for parallel computing. We will give a short introduction to the numerical partial differential equations and finite element methods, and introduce discontinuous Galerkin methods for equations of various types and discuss how these discrete problems can be solved efficiently. We will address mathematical questions related to the concepts of consistency, stability, convergence, and error estimation. Programs written in MATLAB will be used to demonstrate examples.

課程名稱數值偏微分方程(一)Numerical Analysis for Partial Differential Equations I
課程簡介本課程為數值偏微分方程的入門課程。主要在教導學生如何發展有限差分法對偏微分方程求解,同時分析數值方法的穩定性與收斂性。本課程中將教授有限差分法解各種不同類型問題包含:橢圓方程問題、擴散方程問題、對流方程問題。This course provides an introduction to solve partial differential equations numerically. The course covers the finite difference approximation, elliptic equations, Fourier analysis of linear PDEs, diffusion equations, advection equations.

課程名稱數值偏微分方程(二)Numerical Analysis for Partial Differential Equations II
課程簡介本課程為數值偏微分方程的進階課程。主要在教導學生如何設計發展有限元素法、有限體積法或是邊界元素法對特定類型偏微分方程求解,同時分析數值方法的穩定性與收斂性。This course is an advanced course for numerical partial differential equations. The course aims to provide students with understanding of solving partial differential equations with finite element methods, finite volume methods or boundary elements.

課程名稱數值線性代數Numerical Linear Algebra
課程簡介本課程的目的是學習數值線性代數的一些基本知識,特別是線性系統的數值解算器和最小二乘問題。課程內容包括了基本的矩陣分析,線性系統的敏感性分析,一般線性系統的LU分解,高斯消去法和準確性分析,正交化和最小二乘問題的迭代修正,線性系統的數值迭代解法:標準分裂迭代法,Jacobi和Gauss-Seidel方法,SOR與Krylov法。The purpose of this course is to learn some elementary knowledge related to the numerical linear algebra, especially, numerical solvers for the linear systems and least squares problems. The course covers basic matrix analysis, sensitivity analysis of linear systems, LU factorization and general linear systems, Gaussian elimination and iterative refinement for accuracy, orthogonalization and least squares problems, iterative methods for linear systems: standard splitting iteration, Jacobi and Gauss-Seidel methods, SOR and Krylov-based methods.

課程名稱線性控制系統與計算方法Numerical Methods for Linear Control Systems
課程簡介本課程內容包括了以下幾個控制問題之計算的研究主題: 系統辨識,系統實現與最小實現,系統的可控性、可觀測性與可最小化性,卡爾曼分解,極點配置問題,觀測器與控制器的設計,列亞波若夫與雷卡迪方程的數值解,卡爾曼濾波器的數值實驗等。The course plans to contain several topics of the computation for control problems, including: system identifications, realizations and minimal realization, controllability、observability、minimality, Kalman decomposition, pole assignment problems,design on observers and controllers,numerical solutions for Lyapunov and Riccati equations, experimental evaluations for Kalman filters.

課程名稱最佳化與數學模式Optimization and Mathematical Models
課程簡介本課程介紹如何將一個複雜系統加以量化成為數學模式,並利用數學求解最佳解或平衡解。求解最佳化系統牽涉到處理不等式組,包括線性、非線性、隨機和動態的。我們將講解線性規劃、線性錐規劃、計算複雜度理論、網路、固定點理論與對局論。搭配數學理論所介紹的複雜系統都是完全實務的,包括 美國空軍的飲食平衡問題、民航機飛行員排班問題、交通運輸規劃的 Braess 悖論、對局論的 Nash 平衡解等等。學生將學到最佳化理論、數學建模、以及使用數學去分析問題和解決問題的能力。This is an introductory course to translate a complex system into a kind of mathematical model, and to find the optimal solution or the equilibrium solution of the model. Solving an optimization problem requires to deal with systems of inequalities, including linear, nonlinear, dynamical, and stochastic. We will be focused on linear programming, linear conic programming, the theory of computational complexity, networks, the fixed point theory and the game theory. All models to be introduced are real world problems, including the diet problem faced by the US Air Force, the crew scheduling problem from the airline company, Braess Paradox in transportation, Nash equilibrium in game theory, etc. We expect students to learn from this course the theory of optimization, skill of modeling, and the capability of using mathematical analysis to resolve practical problems.

課程名稱電磁理論的數學架構Mathematical Structure of Electro-Magnetic Field Theory
課程簡介在這個課程中,我們將介紹電磁理論的數學架構和某些相關 的主題. 我們將討論 微分形式(Differential Forms), 外微分(Exterior Derivative), 李微分(Lie Derivative),主纖維叢(Principal Fiber Bundles), 主纖維叢上的連絡 (Connections on Principal Bundles) , 拉格朗日泛函(Lagrangian Functional), 陳省身特性類(Chern Characteristic Class), 勞侖茲力(Lorentz Force), 馬克士威方程組 (Maxwell Equations). 我們可能會進一步討論自旋(spinor)和狄拉克方程。 In this course, we introduce the mathematical structure of Electro-magnetic Field Theory and certain related topics. We will discuss Differential Forms, Exterior Derivative, Lie Derivative, Principal Bundles, Connections, Lagrangian Functional, Chern Characteristic Class, Lorentz Force, and Maxwell Equations. We probably will discuss Spinors and Dirac Equation.

課程名稱氣體動力學方程及其相關主題Kinetic Equations and Related Topics
課程簡介本課程將介紹波茲曼方程與藍道方程的數學理論, 其中包含線性化問題與非線性穩定性, 並介紹最近的研究方向. 基本背景要求為高等微積分, 線性代數及大學部微分方程. This course will introduce mathematical theory of the Boltzmann and Landau equations, including linearized problem and nonlinear stability. Moreover, we will introduce some recent research directions. The background of this course is advanced calculus, linear algebra and undergraduate level of DE.

課程名稱邊界元素法Boundary Element Method
課程簡介本課程介紹:(1) 線性偏微分方程與邊界值問題: 拉普拉斯方程、熱傳方程及波方程 (2) 基本解與格林函數 (3) 邊界積分表現法與邊界積分方程. (4) 數值方法 In this course, we will learn about (1) boundary value problems of linear partial differential equation: Laplace equations, heat equations and wave equations; (2) fundamental solutions and Greens function; (3) boundary integral representation and boundary integral equation; (4) numerical schemes;

課程名稱應用數學(一)Applied Mathematics I
課程簡介本課程將介紹一些物理科學與生命科學中的數學問題,以及相關的分析與計算工具,例如:動態系統與穩定性分析,隨機現象與擴散過程,守恆律與微分方程。 This course is aimed to study analytical and computational methods in mathematical problems arising in physical science and life science. For example: dynamical systems and stability analysis, stochastic phenomena and diffusion process, conservation laws and differential equations.

課程名稱應用數學(二)Applied Mathematics II
課程簡介本課程將介紹一些社會科學與資訊科學中的數學問題,以及相關的分析與計算工具,例如:線性系統與線性規劃,傅立葉分析與訊號處理,統計方法與資料分析。 This course is aimed to study analytical and computational methods in mathematical problems arising in social science and information science. For example: linear systems and linear programming, Fourier analysis and signal process, statistics and data analysis.

課程名稱經典力學的數學方法Mathematical Methods of Classical Mechanics
課程簡介在這個課程中,我們將介紹經典力學的數學方法和某些相關的主題. 我們將討論牛頓力學(動量守恆,角動量守恆,能量守恆)和Lagrangian力學(Euler-Lagrangian 方程,Noether’s 定理,李群,微分方程的微擾理論,Euler方程和剛體運動)。我們將會進一步討論陀螺運動的細節。 In this course, we discuss the mathematical methods of Classical Mechanics and certain related topics. We will discuss Newtoniann Mechanics (Conservation of Momentum, Angular Momentum, and Energy) and Lagrangian Mechanics (Euler-Lagrangian Equations, Noether’s Theorem, Lie Groups, Perturbation Theory of Differential Equations, Euler Equation and the motion of Rigid Bodies). We will furthermore discuss the motion of Top in details.

課程名稱專題討論Mathematics Colloquium
課程簡介將安排一系列的演講,讓學生透過演講增廣見聞,並認識更多類型的數學。Will arrange a variety of talks. Learn to be open-minded and enjoy all kinds of Mathematics.