課程資訊

Mathematics for Management

105-1

Fin2009

703 30500

02

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1051Fin2009_02

This course is to offer the fundamental tools especially used in finance. In this course, main subjects, such as calculus, linear algebra, and probability models are included. In this course, the materials are based on the required lecture notes. The grade is totally determined by the regular examinations and quizzes.

Notice that: The first class will be on 9/13 Tuesday (5,6) or (11,12) Optional!

Linear Algebra
#1 Multiplication of Matrices, Inverse and Gauss-Jordan Elimination.
#2 LU Decomposition, Cholesky Decomposition and Permutation Matrix.
#3 Vector Space.
#4 Linear Independence, Bases and Dimensions.
#5 Types of Solution in Linear System and Complete Solutions.
#6 Inner Product Space and Norm.
#7 Four Fundamental Subspaces.
#8 Determinants.
#9 Projection Matrix and Least Square Method.
#10 Orthogonal Matrix and Gram-Schmidt Process.
#11 Linear Transformation.
#12 Eigenvalue and Eigenvector.
#13 Diagonalization.
#14 Real Symmetric Matrices and Spectral Theorem.
#15 Positive Definite Matrix and Quadratic Form.
#16 SVD Decomposition and Pseudo Inverse.

Topics of Probability Theory and Statistics
#1 Belief of Equal Chance and Laplace Ideas.
#2 Conditional Probability, Independent Events, and Bayes Ideas.
#3 Random Variables and Probability Distributions.
#4 Functions of Random Variables.
#5 Expectations and Moment Generating Function.
#6 Some Famous Discrete-type Probability Distributions.
#7 Some Famous Continuous-type Probability Distributions.
#8 Random Vectors and Multidimensional Normal Distribution Functions.
#9 Some Famous Inequalities in Probability Theory.
#10 Modes of Convergence in Probability Theory.
#11 Random Sample and Sampling Distributions.
#12 Pivotal Quantity and Confidence Interval.
#13 Some Concepts of Point Estimation.
#14 Variance-Covariance Matrix.
#15 Principal Axis Theorem and Principal Component Analysis.
#16 Techniques of Matrix Algebra for Chi-Square and T Distributions.

Applications in Finance
Topic 1. Portfolio Theory
#1 Diversification and Mean-Variance Decision Principle.
#2 Portfolio Allocation Theory and Separation Theory.

Topic 2. Asset Pricing in Contingent Claims
#1 No Arbitrage Principle and General One-Period Model.
#2 Fundamental Theorems of Asset Pricing.

There will be twelve 80 minutes quizzes at class, one mid-term and one final exam.
Among these you can pick ten of your highest scores as your grades，but all these tests cannot be make-up!

Office Hours

There are thirty lecture notes in total.

1. Gilber Strang: Introduction to linear algebra. (4th edition)
2. MIT Open Course: Linear algebra. (2011 Fall)
3. 張森林 &石百達, 財金數量方法, 初版. 2010, 雙葉書局。
4. Sheldon Ross, A First Course in Probability. ( 8th edition)

(僅供參考)

 No. 項目 百分比 說明 1. Final Exam 30% 2. Quiz 40% 3. The Mid-term Exam 30% 4. Extra Bonus Exam 16% It will be on 1/16 (Optional!)

 課程進度
 週次 日期 單元主題 第1週 lecture #1 The Geometry of Linear Algebra 第1週 lecture #1 The Geometry of Linear Algebra lecture #2 Matrix Multiplication and Inverse 第1週 Lecture #1 The Geometry of Linear Algebra ;
Lecture #2 Matrix Multiplication and Inverse 第1週 課程介紹 第1週 課程介紹 第1週 Introduction 第1週 課程介紹 第1週 lecture #1 The Geometry of Linear Algebra lecture #2 Matrix Multiplication and Inverse 第1週 Introduction 第1週 Introduction 第1週 lecture #1 The Geometry of Linear Algebra lecture #2 Matrix Multiplication and Inverse 第1週 lecture #1: The Geometry of Linear Algebra 第1週 lecture #1 The Geometry of Linear Algebra lecture #2 Matrix Multiplication and Inverse 第1週 矩陣的四種乘法與反矩陣，以及高斯-喬登消去法 第2週 lecture #3 Elimination with Matrix 第2週 lecture#2 Matrix Multiplication and Inverse 第2週 LU分解、喬列斯基分解以及置換矩陣 第3週 Quiz #1 lecture #4 Space and Subspace 第3週 向量空間 第4週 lecture #5 LDU decomposition and Cholesky decomposition 第4週 線性獨立、基底與維度 第5週 Quiz #2 lecture #6 Independence, basis and dimension 第5週 解的行為與線性系統的完整解 第6週 lecture #7 The behavior of solutions for Ax=b 第6週 內積空間與範數 第7週 Quiz #3 lecture #8 The four fundamental subspace 第7週 矩陣的四個基本子空間 第8週 lecture #9 determinants 第8週 行列式的性質與其幾何意義 第9週 Mid-term Exam 第9週 期中考 第二週 Lecture #3 Elimination with Matrix
Lecture #4 LDU Decomposition and Cholesky Decomposition 第10週 lecture #10 projections onto subspace lecture #11 projection matrix & least square 第10週 投影矩陣以及最小平方法 第11週 lecture #12 orthogonal matrices & Gram-Schmielt lecture #13 linear transformation 第11週 正交矩陣與正交化過程 第12週 Quiz #4 lecture #14 eigenvalues and eigenvectors 第12週 線性變換 第13週 lecture #15 diagonalization & spectral theorem lecture #16 positive definite matrices 第13週 特徵值、特徵向量與對角化 第14週 Quiz #5 lecture #17 change basis 第14週 矩陣的正定性與二次式圖形 第15週 lecture #18 applications in linear algebra- covariance matrix lecture #19 applications in linear algebra- multivariate normal distribution 第15週 共變異數矩陣與多元常態分配 第16週 Quiz #5 lecture #20 applications in linear algebra- Chi square distribution and T distribution 第16週 矩陣代數技巧處理卡方分配與T分配 第17週 lecture #21 singular value decomposition lecture #22 left inverse, right inverse & pseudo inverse lecture #23 diversification & optimal portfolio 第17週 風險分散與極佳化投資組合 第1-1週 課程介紹