| | 類別資料分析 Categorical Data Analysis 需先修過之課程: 數理統計(一)教材 An introduction to Categorical Data Analysis, 2007, by Alan Agresti (二)參考書 Categorical Data Analysis, 2nd edition, 2002, by Alan Agresti. (三)課程大綱 -
Two-way contingency tables: odds ratio, relative risk, sampling distribution, testing goodness-of-fit, testing independence, testing symmetry, Fisher's exact test. -
Binary response models: logit, probit, extreme-value models, loglinear models, logistic regression. -
Models for ordinary variables -
Multinomial response models -
Repeated categorical response models |  | 應用多變量分析 Applied Multivariate Statistical Analysis 需先修過之課程: 線性代數, 數理統計 (一)教材 Applied Multivariate Statistical Analysis (6th Ed.), 2007, by R.A. Johnson and D.W. Wichern. (二)課程介紹 介紹各種常用之多變量分析統計方法 (三)課程大綱 -
Multivariate Normality -
Multivariate ANOVA -
Multidimensional Scaling -
Principal Components -
Factor Analysis -
Covariance Structure Models -
Canonical Correlation Analysis -
Discriminant Analysis -
Cluster Analysis |  | 時間數列(一) Time Series Analysis (I) 需先修過之課程: 線性代數, 數理統計, 迴歸分析 (一)教材 Time Series Analysis: Univariate and Multivariate Methods (2nd edition), 2005, by William W. S. Wei. (二)課程介紹 介紹時間數列資料的統計分析方法 (三)課程大綱 1. Overview 綜觀
2. Multivariate Normal and Regression 多變量常態分配與廻歸
3. Fundamental Concepts 基本觀念
4. Stationary Time Series Models 穩定時間數列模式
5. Nonstationary Time Series Models 非穩定時間數列模式
6. Forecasting 預測
7. Model Identification 模式確認
8. Parameter Estimation, Diagnostic Checking and Model Selection 參數估計, 診斷檢查及模式選取
9. Seasonal Time Series Models 季節時間數列模式
10. Intervention Analysis and Outlier Detection 介入分析與極端值的探測 |  | 高等數理統計(一) Advanced Mathematical Statistics (I) 需先修過之課程: 機率, 數理統計 (一)教材 Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I (2nd edition), 2001, by P.J. Bickel and K.A. Doksum. (二)參考書 Theory of Point Estimation, 1983, by E.L. Lehmann. (三)課程內容 Studying advanced topics in Mathematical Statistics (四)課程大 綱 1. Review of Probability
2. Introduction to Decision Theory
3. Statistical Models: Exponential Families and Group Families.
4. Sufficiency: summarizing data without losing information.
5. Minimum Variance Unbiased Estimation
6. Information Inequality: A useful lower bound for the variance of an estimator.
7. Large Sample Theory: Maximum likelihood (and related) estimators are approximately optimal in large samples.
8. Bayes Estimation
9. Admissibility
10. Minimax Estimation
11. Shrinkage Estimation |  | 高等數理統計(二) Advanced Mathematical Statistics (II) 需先修過之課程: 高等數理統計(一) (一)教材 Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I (2nd edition), 2001, by P.J. Bickel and K.A. Doksum. (二)參考書 Theory of Point Estimation, 1983, by E.L. Lehmann. 數理統計學, 1994, 楊明宗、劉應興合著 (三)課程內容 Studying advanced topics in Mathematical Statistics (四)課程大 綱 -
Introduction to Decision Theory -
Bayes Decision Rules -
Admissibility and Complete Classes -
Minimax Decision Rule -
Neyman-Pearson Lemma (N-P Lemma) -
Most Powerful Test (MP Test) -
Uniformly Most Powerful Test (UMP Test) -
Monotone Likelihood Ratio Property (MLR property) -
Uniformly Most Powerful Unbiased Test (UMPU Test) -
Locally Best Test -
Confidence Sets -
Duality Between Testing and Interval Estimation -
Generalized Likelihood Ratio Test (GLRT) -
Limit Theorem for the Likelihood Ratio Statistic -
Other topics: Multivariate Normal, Multivariate Central Limit Theorem, Analysis of Discrete Data, Introduction to Nonparametric Methods, Introduction to Linear Models. | | 應用統計 Applied Statistics 需先修過之課程: 迴歸分析, 實驗設計 (一)教材 Practical Regression and Anova using R, 1999, by J.J. Faraway. (二)課程內容 Studying advanced topics in regression and experimental design (三)課程大 綱 1. Estimation 2. Inference 3. Error in Predictors 4. Generalized Least Squares 5. Testing for Lack of Fit 6. Diagnostics 7. Transformation 8. Scale Changes, Principal Components and Collinearity 9. Variable Selection 10. Analysis of Covariance 11. ANOVA 高等工程數學(一) Advanced Engineering Mathematics (I) | (一)教材 Advanced Engineering Mathematics, Third Edition, 2006, by D. G. Zill and M. R. Cullen (二)課程大綱 1. Series Solutions of Linear Equations
2. Orthogonal Functions and Fourier Series
3. Boundary-Value Problems in Rectangular Coordinates |  | 高等工程數學(二) Advanced Engineering Mathematics (II) | (一)教材 Advanced Engineering Mathematics, Third Edition, 2006, by D. G. Zill and M. R. Cullen (二)課程大綱 1. Boundary-Value Problems in Other Coordinate Systems
2. Integral Transform Method
3. Numerical Solutions of Partial Differential Equations | | 高等微分方程 Advanced Differential Equations | (一)教材 A first Course in Differential Equations with Modeling Applications, 8th edition, 2004, Dennis G. Zill (二)參考書 Differential Equations and Boundary Value Problems---3rd edition
Authors: Nagle, Saff and Snider (三)課程 介紹 1. Modeling with First-Order Differential Equations
2. Modeling with Higher-Order Differential Equations
3. Series Solutions of Linear Equations
4. Numerical Solutions of Ordinary Differential Equations (四)課程大綱 1. Linear Models
2. Nonlinear Models
3. Modeling with Systems of Differential Equations
4. Spring/Mass Systems
5. Linear Models: Boundary-Value Problems
6. Solutions about Ordinary Points
7. Solutions about Singular Points
8. Runge-Kutta methods |  | 連續振動學 Vibration of Continuous System (一)教材 Vibration of Continuous System, 楊立杰 (二)課程大綱 1. Transverse Vibrations of Strings
2. Londitudinal and Torsional Vibrations of Bars (or Rods)
3. Beam Vibration
4. Membrances
5. Plates
6. Shells
7. Arbitrary body 彈性力學 Elasticity | (一)教材 Theory of Elasticity, S.P. Timoshenko & J.N. Goodier, McGraw-Hill. (二)參考書 Mathematical Theory of Elasticity, I.S. Sokolnikoff. (三)課程 介紹 This course presents several aspects of the theory of elasticity from a unified point of view and to indicate, along with the familiar methods of solution of the field equations of elasticity, some newer general methods of solution of the two-dimensional problems (四)課程大綱 1. INTRODUCTION
2. PLANE STRESS AND PLANE STRAIN
3.TWO-DIMENSIONAL PROBLEMS IN RECTANGULAR COORDINATES
4. TWO-DIMENSIONAL PROBLEMS IN POLAR COORDINATES
5. TWO-DIMENSIONAL PROBLEMS IN CURVILINEAR COORDINATES
6. TORSION
7. BENDING OF BARS |  | 動力系統 Dynamical System (一)教材 Dynamical Systems: Differential equations, maps and chaotic behavior, 1992
Author: D. K. Arrowsmith (二)參考書 1. Introduction To MATLAB 7 For Engineers by William J. Palm III
2. A first course in Differential Equations with Modeling Applications by D. G. Zill (三)課程 介紹 1. Introduction
2. Linear System
3. Non-linear systems in the plane
4. Flows on non-planar phase spaces
5. Applications (四)課程大綱 1.Autonomous equations
2. Autonomous systems in the plane
3. Flows and evolution
4. Phase portraits for canonical systems in the plane
5. The evolution operator
6. Affine system
7. n-Dimensional system
8. First integrals
9. Poincare-Bendixson theory
10. Poincare maps and Hamiltonian flows 混沌與碎形 (一)教材 Encounters with chaos, 1992, by Denny Gulick (二)參考書 An introduction to chaotic dynamical systems, 2nd edition, 2003, by Robert Devane (三)課程內容 Intrducing examples of chaos (四)課程大綱 1. basics about dynamical systems: fixed points, periodic points, basins, dense orbits.
2. Canter set
3. tent function
4. logistic functions
5. Baker function
6. Henon map 泛函分析 Functional Analysis (一)教材 自編教材 (二)參考書 1. J.B.Conway, A Course in Functional Analysis.
2. M.M.Day, Normed Linear Spaces.
3. N.Dunford and J.T.Schwartz, Linear Operators.
4. C.Goffman and G.Pedrick, First Course in Functional Analysis.
5. P.R.Halmas, Introduction to Hilbert Spaces and the Theory of Spectral Multiplicity.
6. L.V.Kantorovich and G.P.Akilov, Functional Analysis in Normed Spaces.
7. J.L.Kelley and I.Namioka, Linear Topological Spaces.
8. E.Kreyszig, Introductory Functioal Analysis with Applications.
9. L.A.Liusternik and V.J.Sovolev, Elements of Functional Analysis.
10. D.G.Luenberger, Optimization by Vector Space Methods.
11. M.A.Naimark, Normed Algebras.
12. W.Rudin, Functional Analysis.
13. A.E.Taylor and D.C.Lay, Introduction to Functional Analysis.
14. Jan van Tiel, Convex Analysis:An Intrductory Text.
15. K.Yosida, Functional Analysis.
16. E.Zeidler, Nonlinear Functional Analysis. (三)課程大綱 1. Banach Spaces:
Definitions and Basic Properties; The L^p-spaces; Other Examples of Banach Spaces;
Finite-Dimensionality; Bounded Linear Transformation; Consequences of Baire
Theorem; Applications to Fourier Analysis.
2. Hilbert Spaces:
Basic Definitions and Properties; Projection Theorem; Riesz Representation Theorem;
Orthonormal Sets; Trigonometric Series.
3. The Hahn-Banach Theorem:
Analytic Form of the Hahn-Banach Theorem; Geometric Form of the Hahn-Banach
Theorem; Some Applications of the Hahn-Banach Theorem.
4. Dual Spaces:
Reflexivility; Examples of Dual Spaces; Weak Topology and Weak* Topology;
Minimum Norm Problems. 無母數統計 Nonparametric Statistics | (一)教材 Applied Nonparametric Statistics ,2000 , by W. W. Daniel. (二)參考書 Practical Nonparametric Statistics,3rd edition, 2006, by W.J. Conover. (三)課程內容 介紹無母數統計學之理論及其應用 (四)課程大綱 1. Introduction
2. Procedures that utilize data from a single sample
3. Procedures that utilize data from two independent
4. Procedures that utilize data from two related samples
5. Chi-square tests of independence and homogeneity
6. Goodness-of-fit tests | | 最優化理論 Optimization (一)教材 Constrained Optimization in the Calculus of Variations and Optimal Control Theory
by John Gregory & Cantian Lin, Van Nostrand Reinhold, 1992 (二)參考書 Kirk D. E., Optimal Control Theory, Prentice-Hall, 1970 (三)課程內容 1. The Basic Theory of the Calculus of Variations
2. Optimal Control
3. Unconstrained Reformulations
4. Numerical Theory (四)課程大綱 1. The Free Problems
2. The Equality Constrained Problems
3. The Inequality Constrained Problems
4. Newton's Method
5. Critical Point Conditions
6. The Minimum Time Problems
7. The Optimal Control Problems
8. Constrained Calculus of Variations Problems
9. Kuhn-Tucker Reformulation
10. Kuhn-Tucker Method 計算理論與方法 Computation Theory and Method (一)教材 Boundary Element techniques, C.A. Brebbia, J.C. Tells and L.C. Wrobel,
Springer-Verlag (二)參考書 Boundary Elements An Introductory Course, C.A. Brebbia and J. Dominguez,
McGraw-Hill. (三)課程內容 The purpose of this course is to present a comprehensive and up-to-date
treatment of the boundary element method (B.E.M.) (四)課程大綱 1. APPROXIMATE METHODS
2. POTENTIAL PROBLEMS
3. INTERPOLATION FUNCTIONS
4. ELASTOSTATICS
5. BOUNDARU INTEGRAL FORMULATION FOR INELASTIC PROBLEMS
6. APPLICATION OF THE B.E.M. 離散動力系統 Discrete Dynamical System (一)教材 Encounters with chaos by Denny Gulick (二)參考書 An introduction to chaotic dynamical systems
by Robert Devaney (三)課程內容 Intrducing examples of chaos (四)課程大綱 1. basics about dynamical systems: fixed points, periodic points, basins, dense orbits.
2. Canter set
3. tent function
4. logistic functions
5. Baker function
6. Henon map
7. Julia sets 高等科學計算 Advanced Scientific Computation (一)教材 Introduction to Numerical Analysis, Second Edition by Kendall E. Atkinson (二)參考書 1. Elementary Numerical Analysis by Kendall E. Atkinson
2. Scientific Computation an Introduction with Parallel Computing by Gene Golub & James M. Ortega
3. Introduction to Scientific Computing by Charles F. Van Loan (三)課程內容 This course is given to strengthen the ability of students in numerical analysis and with the ability in using MATLAB to do numerical computing. The ability of do programming by MATLAB will be given first and the rest of the course will be given to discuss several important issues in numerical analysis and scientific computing. Some parallel issues will be discussed too. (四)課程大綱 1. Programming by MATLAB
2. Interpolation Theory
3. Linear Algebra & Numerical Solution of Systems of Linear Equations
4. Parallel and Vector Computing 微方特論 Topics in ordinary differential equations (一)教材 Systems of Ordinary Differential Equations: An Introduction
by Jack L. Goldberg & Arthur J. Schwartz (二)參考書 Differential Equations A first Course
by Martin M. Guterman & Zbigniew H. Nitecki (三)課程內容 本課程強調將線性代數概念帶進系統微分方程計算的各種性質及解 (四)課程大綱 Chapter 1: Vectors and Matrices
Chapter2 : Linear Homogeneous Systems and Eigenvectors
Chapter 3: Linear Systems and Root Vectors
Chapter4: Applications of the Theory of the Homogeneous Equations
Chapter 5: Higher Order Equations
Chapter 6: An Introduction to the Theory of Analytic Differential Systems
Chapter 7: Two Dimensional Autonomous Systems: An Introduction to the Qualitative Theory of Differential Equations 高等複變分析 Advanced Complex Analysis | (一)教材 Advanced Engineering Mathematics, Erwin Kreyszig, Wiley. (二)參考書 Complex Variables and Applications, James Ward Brown and Ruel V. Churchill, McGraw Hill. (三)課程內容 無 (四)課程大綱 1. Complex Numbers and Functions
2. Complex Integration
3. Power Series, Taylor Series
4. Laurent Series, Residue Integration
5. Conformal Mapping
6. Complex Analysis and Potential Theory | | 數值專題 Special Topics in Numerical Analysis | (一)教材 Linear Algebra and Linear Operators in Engineering with Applications in Mathematics. (二)參考書 Optimization---Foundations and Applications, Ronald E. Miller (三)課程內容 1. Solution of Linear and Nonlinear
2. Solvability of Linear Algebraic Equations
3. The Eigenproblem
4. Linear Integral Operators in a Hilbert Space
5. Linear Differential Operators in a Hilbert Space (四)課程大綱 1. Synopsis
2. Solvability Theorem
3. Hilbert-Schmidt Operators
4. The Adjoint Operators
5. Green's Function
6. Spectral Theory | | 偏微分方程 Partial Differential Equations | (一)教材 Beginning partial Differential equations By O'Neil (二)參考書 無 (三)課程內容 無 (四)課程大綱 1. First Order Partial Differential Equations
2. Linear Second Order Partial Differential Equations.
3. Element of Fourier Analysis
4. The Wave Equation
5. The Heat Equation
6. Dirichlet and Neumann Problems
| | 天體力學 Celestial Mechanics | (一)教材 無 (二)參考書 Introdution to Hamiltonian dynamical systems and N-body problem, by Meyer (三)課程內容 介紹Nbody problem (四)課程大綱 Kepler law
restricted three body problem | | 高等機率論 Advanced Probability Theory | (一)教材 Probability and Computing, by M. Mitzenmacher and E. Upfal (二)參考書 無 (三)課程內容 The emphasis in this course is on the probabilistic techniques and paradigms. (四)課程大綱 1. events and probability.
2. discrete random variables and expectation.
3. moments and deviations.
4. Chernoff bounds.
5. balls, bins, and random graphs.
6. the probabilistic method.
| | 高等數值線性代數 Advanced Matrix Computation | (一)教材 Introduction to Scientific Computing 2nd Ed. by Charles F. Van Loan (二)參考書 1. 數值線性代數徐樹方、高立、張平文 編著, 北京大學出版社
2. Introduction to Numerical Analysis, second edition, by Kendall E. Atkinson (三)課程內容 This course will introduce some problems in numerical linear algebra, including the linear systems, least square problem, and some eigenvalue problems. These problems occurs in scientific computation, and students usually need the make clear distinction between theoretical and real computation. Some exercises in MATLAB are required for students to work out, and some theoretical proof will be given too. (四)課程大綱 1. Introduction
2. Direct Solutions of Linear system of equation
3. Sensitivity analysis of linear system of equations
4. The least square problem
5. Iteration method of linear system of equations
6. Eigenvalue problems
| | 高等統計品質管制 Advanced Statistical Quality Control | (一)教材 書名：品質管理觀念、理論和方法 作者：傅和彥、黃士韜 書局：前程書局 (二)參考書 書名：品質管理整合性思維 作者：李友錚、賀力行 書局：前程書局 (三)課程內容 1.使學生瞭解統計品質管理的基礎理論與實務技術。 2.使學生熟悉品統計品質管理的方法和應用。 3.培養學生建立品統計品質的觀念和理念。 (四)課程大綱 1. 品質之意義與演變
2.品質成本
3.PDCA循環
4.QC七大手法
5.統計製程管制與管制圖
6.服務品質
7.抽樣方法與檢驗
8.全面品質管理與品管圈
9.品質活動和國家品質獎
10.可靠度
11.ISO制度
12.田口式品管
13.SPC and TQM國外期刊導讀
14.期末心得報告
|  | 大樣本理論 Large Sample Theory | (一)教材 上課筆記 (二)課程內容 介紹大樣本之理論架構及其衍生之重要結果 (三)課程大綱 1. Modes of convergence
2. Laws of large numbers
3. Central limit theorems
4. Pearson's chi-square
5. Asymptotic theory of extreme order statistics
6. Asymptotic normality of the MLE
7. The Cramer-Rao lower bound
8. Asymptotic efficiency | |
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