IE 5034: Linear Algebra and its Applications, Fall 2013

Instructor: Ling-Chieh Kung
Department of Information Management
National Taiwan University

Note. This course is typically taught by Professor Argon Chen in the Graduate Institute of Industrial Engineering. When I was a master student, I took this course from Professor Chen and really enjoyed studying this subject. That is why when Professor Chen is on leave for Fall 2013, I teach this course for him. As Professor Chen's course materials are excellent and I have to prepare for my own courses, I will mostly follow the materials prepared by him. However, all the errors are mine.

Linear algebra is not only the most useful mathematical tool but also an exciting subject that is full of surprises. To be able to appreciate its beauty and actually use it in practice is the goal of this class.

This is an elective course offered in the Graduate Institute of Industrial Engineering in National Taiwan University. The target "customers" of this course are graduate and senior students, though junior students may still enroll. If there are available seats, all students who want to enroll in or audit this course are welcome.

Basic information

Instructor	Ling-Chieh Kung (孔令傑) E-mail: lckung(AT)ntu.edu.tw Office: Room 413, Management Building II Tel: 02-3366-1176.
Teaching assistants	工工碩二張富皓. 工工碩二沈子欣 (shenzixin2008@126.com).
Syllabus	Syllabus
Lectures	9:10am-12:10pm, Tuesday. Room 404, Core Subjects Classroom Building (普通大樓).
Office hour	The instructor's office hour: 9:10am-11:10am, Wednesday or by appointment. Room 413, Management Building II (管理學院二號館). The teaching assistants' office hour: 3pm-5pm and 7pm-9pm, Monday. Room: 455, Engineering Building (工學院綜合大樓).
Prerequisites	Calculus: "Calculus I" and "Calculus II" for the first-year NTU students, or equivalent. Statistics: A one-semester or one-year introductory Statistics course.
Textbook	Gilbert Strang, 2006, Linear Algebra and its Applications, 4th edition, Thomson. 歐亞書局: 02-8912-1188.
References	Applied Multivariate Statistical Analysis by R. Johnson and D. Wichern. Convex Optimization by S. Boyd and L. Vandenberghe.
On-line resources	The textbook author's MIT open course website. To check grades: CEIBA. To download materials: This website. To discuss: the bulletin board "NTUIM-lckung" on PTT.

Tentative plan

We will follow the textbook to introduce the theory of Linear Algebra. Some applications contained in the textbook will be discussed when we see them. We will also introduce some important applications of Linear Algebra in the fields of Multivariate Statistical Analysis, Optimization, Game Theory, etc. When the materials are not covered in the textbook, the instructor will provide relevant handouts.

Theory:
1. Chapter 1: Matrices and Guassian Elimination.
2. Chapter 2: Vector spaces and Linear Equations.
3. Chapter 3: Orthogonality.
4. Chapter 4: Determinants.
5. Chapter 5: Eigenvalues and Eigenvectors.
6. Chapter 6: Positive Definite Matrices.
Applications:
1. Principal Component Analysis.
2. Singular Value Decomposition (Appendix A).
3. Linear Programming (Chapter 8).
4. Nonlinear Programming.
5. Game Theory (Chapter 8).

Schedule

Week	Lecture Date	Topics
1	2013/9/10	Overview and Sections 1.1-1.5
2	2013/9/17	Sections 1.6-1.7, Linear Programming, Section 2.1
3	2013/9/24	Sections 2.1-2.4
4	2013/10/1	Sections 2.4-2.6
5	2013/10/8	Sections 2.6-3.1
6	2013/10/15	Sections 3.1-3.3
7	2013/10/22	Sections 3.3-3.4
8	2013/10/29	Sections 4.1-4.4
9	2013/11/5	Midterm exam
		(In class, three-hour, close-book)
10	2013/11/12	Sections 5.1-5.3
11	2013/11/19	Sections 5.4-5.5
12	2013/11/26	Sections 5.6-6.2
13	2013/12/3	Sections 6.3
14	2013/12/10	Linear Programming
15	2013/12/17	Nonlinear Programming
16	2013/12/24	Principal component analysis
17	2013/12/31	Project presentations
18	2014/1/7	Final exam
		(In class, three-hour, close-book, comprehensive)

Homework

Problems	Release Date	Due Date
Homework 1	2013/9/10	2013/9/17
Homework 2	2013/9/17	2013/9/24
Homework 3	2013/9/24	2013/10/1
Homework 4	2013/10/1	2013/10/8
Homework 5	2013/10/8	2013/10/15
Homework 6	2013/10/15	2013/10/22
Homework 7	2013/10/22	2013/10/29
Homework 8	2013/10/31	No due date.
Homework 9	2013/11/13	2013/11/19
Homework 10	2013/11/19	2013/11/26
Homework 11	2013/11/27	2013/12/3
Homework 12	2013/12/3	2013/12/10
Homework 13	2013/12/11	2013/12/17
Homework 14	2013/12/18	2013/12/24

Images of exercises adopted from the textbook can be found on CEIBA.

Exams

Problems	Solution
Midterm	Solution
Final	Solution

Project

Project description
Suggestions for formatting your report
Important dates:
- By December 2, 2013: Inform the instructor about team formattion.
- December 3, 2013: The number of teams will be announced.
- December 31, 2013: Project presentations.

Grading

Breakdown

Quiz: 0%.
Homework: 30%.
Project: 20%.
Class participation: 5%.
Two exams: 45% (one of the following two plans will be chosen to maximize your grades):
- Plan 1: midterm 20% and final 25%.
- Plan 2: midterm 15% and final 30%.

Conversion rule

The final letter grades will be given according to the following conversion rule:

Letter	Range	Letter	Range	Letter	Range
A+	[90, 100]	B+	[77, 80)	C+	[67, 70)
A	[85, 90)	B	[73, 77)	C	[63, 67)
A-	[80, 85)	B-	[70, 73)	C-	[60, 63)

Policies

Office hour	You are welcome to my office hour to ask me any question. You may ask me to clarify some concepts, give hints for homework problems, or discuss the final project. In fact, discussions not related to Linear Algebra are also welcome. If you don't want to come in the designated time, feel free to send me an e-mail to schedule a meeting. You are also welcome to the TAs' office to ask questions, particularly those about homework.
Class participation	We do not require one to attend all the lectures. If you have something more important to do, feel free to drop a class. Nevertheless, as communication skills are essential for almost everyone, we encourage class participation and include it in evaluating each student. In other words, class participation is not just sitting in the classroom. During lecture time or office hour, you are more than welcome to ask or answer questions and provide comments. You are also encouraged to use the course bulletin board on PTT or send me e-mails at any time. These will not only give you a good participation grade but also significantly help your learning.
Homework	Homework will be assigned roughly once per week. To submit homework, please put a hard copy of your work into the homework box in front of Room 455 (the TAs' lab) of the Engineering Building by the due time (typically 8:30am on Tuesday). No submission in class. No late submission. The lowest two homework grades will be dropped (i.e., you may skip two homework if you want). The TAs will grade homework and regrade them upon request. If you have a regrading request, please contact the TAs directly (e.g., in their office hour).
Project	Please form a team of five to eight students and apply the knowledge learned in this semester to solve a self-selected problem. Each team will make a 15-minute presentation and submit a report no more than 15 pages. All team members must be in class for the team to present.
Exams	Both the two exams will be in-class and close-book. Cheating will result in severe penalty. The final exam is comprehensive: It covers everything taught in this semester.