Math 312 Spring 2018

Instructor: Yuecheng Zhu yuecheng@upenn.edu
Office: DRL 4C7
Office Hours: Tue 9:30 - 10:30 AM, Thu 1 - 2 PM.
TA: Stephen Gillen stepe@math.upenn.edu
Course Guide
• Class meeting: TR    10:30 AM - 12 PM, DRL A2.
• Textbook:  Introduction to Linear Algebra  (5E)  by Gilbert Strang.
• Grades: 30% mid-term, 40% final, 10% attendence, 10% weekly homework, 10% problems 10% attendence.
• Syllabus
• UPenn 3-year Calendar
Problems (10%):
• Problem_sheet
• Each problem is 10 pts. You only need to get 100 pts. Note that the earlier problems are usually easier.
• 1, 2, 13, 16, 17 due on 3/15 ;
• 3, 4, 5, 14, 15 due on 4/11 ;
• 6, 7, 8, 9, 10, 11, 12 due on 4/25 ;
Homework (10%):
• The deadline is 4:30 pm of the due date. You put your homework in Stephen's mailbox directly. His mailbox is located inside the Math Main Office. The Math Main Office is closed at 5pm.
• You have all together five one-day submission extensions. For example, you may submit Homework 2 three days after the due date and Homework 3 two days after the due-date. After that no late homework will be accepted. Use them smartly. In particular, use them if you have big projects due. If you use the submission extension, you should let TA know about it explicily. If there are some very rare cases that you truly need more extensions email me before the deadline. Starting from Homework 3, two of the homework problems will be graded. 50% for the correctness of the two problems, 50% for the completeness.
• Homework 1 (due on 1/25) 1.1: 16; 1.2: 13; 1.3: 7; 2.1: 3; 2.2: 12; 2.3: 1, 13, 25; 2.4: 26, 32; 2.5: 3, 7, 27; 2.6: 1, 5.
• Homework 2 (due on 2/1) 3.1: 23; 3.2: 13, 32; 3.3: 1, 4, 25; 3.4: 2, 11, 16, 20, 26, 32.
• Homework 3 (due on 2/15) 3.5: 2, 5, 24; 4.1: 4, 13, 16, 26; 4.2: 1, 3, 19, 20; 4.3: 1, 4, 12, 21.
• Homework 4 (due on 2/19) 4.4: 1, 3, 18, 21.
• Homework 5 (due on 3/1) 5.1: 1, 8, 11, 18, 29 (Also answer what det P should be), 30; 5.2: 5, 13, 15; 5.3: 18, 23.
• Homework 6 (due on 3/20) 6.1: 6, 16, 21, 33; 6.2: 15 (Compute the diagonalization first), 16, 19, 22, 30, 31; 6.4: 3, 7, 16; 6.5: 4, 12, 16, 36.
• Homework 7 (due on 3/29) 7.1: 3; 7.2: 2, 3, 4, 10, 26; 7.3: 1, 3, 4, 5.
• Homework 8 (due on 4/5) 8.1: 2, 13, 14, 16; 8.2: 10, 11, 15, 24, 16; 8.3: 4, 6, 7.
• Homework 9 (due on 4/12) 9.1: 2, 6, 9, 10, 15; 9.2: 1, 3, 5, 14, 16; 9.3: 7.
• Homework 10 (due on 4/19) 10.1: Review the last two problems of the midterm exam (no submission), 8, 9, 10; 10.3: 1, 2, 9, 11.
Exams (70%):
Schedule:

Date
Topic
Remark
Notes
1/11
1.1 - 1.2

Linear Combinations, the Dot Product
1/15

Martin Luther King, Jr. Day

1/16
1.3 - 2.1

Matrix times a Column Vector
1/18
2.2 - 2.4

From Row Operations to Matrix Multiplications
1/23
2.5 - 2.7

Inverse Matrices, LU Decomposition, Symmetric Matrices
1/25
3.1 - 3.2
Homework 1 due
Vector Spaces and Subspaces, Rank
1/29

Course Selection Period ends

1/30
3.3 - 3.4

Independence, Dimension and Basis
2/1
3.5 - 4.1
Homework 2 due
Four subspaces, Orthogonal Projections
2/6
Recitation

2/8
School closed

2/13
4.2 - 4.3

Orthogonal Projection and Linear Regression
2/15
4.3 - 4.4
Homework 3 due
Linear Regression, Gram-Schmidt
2/16

Drop Period ends

2/19

Homework 4 due

2/20
5.1 - 5.2

Determinants
2/22
Mid-term Exam

2/27
5.2 - 5.3

Cofactor Formula
3/1
6.1 - 6.2
Homework 5 due
Cramer's Rule, Eigenvectors, Diagonalization
3/3 - 3/11

Spring Break

3/13
6.2, 6.4

Diagonalization, Symmetric matrices
3/15
6.5, inner product
Problem 1, 2, 13, 16, 17 due
Positive Definite Matrices, Inner Product
3/20
7.1 - 7.2
Homework 6 due
Singular Value Decomposition
3/22
7.3 - 7.4

Principal Component Analysis
3/27
8.1 - 8.2

Linear Transformation, Change of Bases Formula
3/29
8.2 - 8.3
Homework 7 due
Good Bases for Linear Transformations
3/30

Last day to withdraw

4/3
9.1 - 9.2

Complex Numbers, Hermitian and Unitary Matrices
4/5
9.3
Homework 8 due
Fast Fourier Transform
4/10
10.1

Graphs
4/12
10.2 - 10.3
Homework 9 due
Difference Equations, Markov Matrices
4/13

Problem 3, 4, 5, 14, 15 due

4/17
10.3

Simulation, Markov Chains
4/19
10.7, Review
Homework 10 due
Hill Cipher, review
4/24
Final Exam

4/25

Problem 6, 7, 8, 9, 10, 11, 12 due