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
02 
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 
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)
 
指定閱讀
There are thirty lecture notes in total. 
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
  矩陣的四種乘法與反矩陣,以及高斯-喬登消去法 
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
  課程介紹 
第1週
  課程介紹 
第1週
  課程介紹 
第1週
  Lecture #1 The Geometry of Linear Algebra ;<br>
Lecture #2 Matrix Multiplication and Inverse 
第1週
  Introduction 
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2週
  lecture #3 Elimination with Matrix 
第3週
  向量空間 
第3週
  Quiz #1
lecture #4 Space and Subspace 
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
  行列式的性質與其幾何意義 
第8週
  lecture #9 determinants 
第9週
  期中考 
第9週
  Mid-term Exam 
第二週
  Lecture #3 Elimination with Matrix <br> Lecture #4 LDU Decomposition and Cholesky Decomposition 
第10週
  投影矩陣以及最小平方法 
第10週
  lecture #10 projections onto subspace
lecture #11 projection matrix & least square 
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
  特徵值、特徵向量與對角化 
第13週
  lecture #15 diagonalization & spectral theorem
lecture #16 positive definite matrices 
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
  共變異數矩陣與多元常態分配  
第15週
  lecture #18 applications in linear algebra- covariance matrix
lecture #19 applications in linear algebra- multivariate normal distribution 
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