課程大綱

課程資訊

課程名稱

管理數學
Mathematics for Management

開課學期

105-1

授課對象

財務金融學系

授課教師

黃以達

課號

Fin2009

課程識別碼

703 30500

班次

學分

全/半年

半年

必/選修

必修

上課時間

星期二A,B(18:25~20:10)星期五7,8,9(14:20~17:20)

上課地點

管一102管二206

備註

本課程中文授課,使用英文教科書。週二56堂實習課於管二301教室。先修科目：微積分乙上下。
總人數上限：90人
外系人數限制：20人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/1051Fin2009_02

課程簡介影片

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課程大綱

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課程概述

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!

課程目標

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.

課程要求

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!

預期每週課後學習時數

Office Hours

每週四 14:30~16:30 備註：教研308

指定閱讀

There are thirty lecture notes in total.

參考書目

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)

評量方式
(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 ;<br> 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 <br> 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