M341: Linear algebra and matrix theory, Spring 2024

University of Texas at Austin, Spring 2024:

Math 341: Linear algebra and matrix theory (53755 & 53760)

Instructor:
Gunnar Martinsson. Email: pgm () oden.utexas.edu
Office hours: Mondays 1:00pm - 1:50pm; Fridays 4:00pm - 4:50pm. Via zoom - see canvas for link.

TA:
Abhishek Koparde. Email ak48945 () utexas.edu
For details on office hours, see syllabus.

Meeting times:
53755: Tuesdays and Thursdays, 8:00am - 9:30am, PMA 5.114.
53760: Tuesdays and Thursdays, 9:30am - 11:00am, PMA 5.114.

Text book:
Elementary Linear Algebra by Stephen Andrilli and David Hecker, 5th edition.

Website:
http://users.oden.utexas.edu/~pgm/Teaching/2024_M341/

Syllabus:
pdf for 53755, pdf for 53760.

Description:
This course covers a variety of topics within linear algebra and matrix theory. It is also intended to help develop skills at constructing and writing mathematical proofs. Specific topics to be covered include vectors and matrices, systems of linear equations and Gaussian elimination, eigenvalues and eigenvectors, determinants, vector spaces, linear transformations, and orthogonality.

Examination:
The syllabus provides the definitive statement of grading policies. In brief, the grade will be based on the following components:

Homeworks - 27%: There will be 11 homeworks, one per week except for the exam weeks (see below). They are typically due on Thursdays and will be submitted via canvas. Your 9 best homework scores will each contribute 3% to your grade. (In other words, your two worst scores do not count at all.) You get participation credit for any graded problem with an honest attempt.
Class quizzes (participation) - 10%: About once a week, there will be a brief quiz in class. Anyone answering all questions will get full credit.
Section exam 1 - 15%: On Thursday February 22, in class.
Section exam 2 - 15%: On Thursday March 28, in class.
Section exam 3 - 10%: On Thursday April 18, in class.
Final exam - 23%: Thursday, May 2.

Homeworks should be individual work, but you are allowed to discuss the problems with your classmates and to work collaboratively. In contrast, the exams will be run in person, and should be worked individually. They will all be closed notes/books exams.

Homework logistics:
Homeworks will be assigned most weeks, and will be submitted through Canvas. The preferred format is to upload your work as a single PDF. For best legibility, please type your work, or write it by hand and then scan using a flatbed scanner. If your homework is unreasonably hard to read, you may lose points. In general, late homeworks will not receive credit. However, we will drop your two lowest homework scores when calculating grades.

Tentative schedule:

Week:
Homework:
Material covered:

1 (Jan 15) HW 1 due Jan 25. Chapter 1: Vectors and matrices.

2 (Jan 22) HW 2 due Feb 1. Chapter 1: Vectors and matrices.

3 (Jan 29) HW 3 due Feb 8. Chapter 1: Vectors and matrices.
Chapter 2: Systems of linear equations.

4 (Feb 5) HW 4 due Feb 15. Chapter 2: Systems of linear equations.

5 (Feb 12)
Chapter 2: Systems of linear equations.

6 (Feb 19) HW 5 due March 2. Chapter 3: Determinants and eigenvalues.
Section exam 1 on Thursday in class.
The exam covers Chapters 1 and 2 in the book (not 3).
Exam. Solutions. Mean = 67.7. Median = 65.

7 (Feb 26) HW 6 due March 7. Chapter 3: Determinants and eigenvalues.

8 (March 4) HW 7 due March 21. Chapter 3: Determinants and eigenvalues.
Chapter 4: Vector spaces.

(March 11)
Spring break. No classes.

9 (March 18)
Chapter 4: Vector spaces.

10 (March 25) HW 8 due April 7. Chapter 4: Vector spaces.
Section exam 2 on Thursday in class.
The exam covers material through Section 4.2.
Exam. Solutions. Mean = 79. Median = 85.5.

11 (April 1) HW 9 due April 11. Chapter 4: Vector spaces.
Chapter 5: Linear transformations.

12 (April 8) HW 10 due April 21. Chapter 5: Linear transformations.

13 (April 15) HW 11 due April 28. Chapter 6: Orthogonality.
Lecture on Section 6.1.
Lecture on Section 6.2 (except Gram-Schmidt).
Lecture on the Gram-Schmidt process.
Slides.
Section exam 3 on Thursday in class (only half of the lecture).
The exam covers material through Chapter 5.

14 (April 22)
Chapter 6: Orthogonality.

Final week (April 29)
Final exam on Thursday May 2.

Week:	Homework:	Material covered:
1 (Jan 15)	HW 1 due Jan 25.	Chapter 1: Vectors and matrices.
2 (Jan 22)	HW 2 due Feb 1.	Chapter 1: Vectors and matrices.
3 (Jan 29)	HW 3 due Feb 8.	Chapter 1: Vectors and matrices. Chapter 2: Systems of linear equations.
4 (Feb 5)	HW 4 due Feb 15.	Chapter 2: Systems of linear equations.
5 (Feb 12)		Chapter 2: Systems of linear equations.
6 (Feb 19)	HW 5 due March 2.	Chapter 3: Determinants and eigenvalues. Section exam 1 on Thursday in class. The exam covers Chapters 1 and 2 in the book (not 3). Exam. Solutions. Mean = 67.7. Median = 65.
7 (Feb 26)	HW 6 due March 7.	Chapter 3: Determinants and eigenvalues.
8 (March 4)	HW 7 due March 21.	Chapter 3: Determinants and eigenvalues. Chapter 4: Vector spaces.
(March 11)		Spring break. No classes.
9 (March 18)		Chapter 4: Vector spaces.
10 (March 25)	HW 8 due April 7.	Chapter 4: Vector spaces. Section exam 2 on Thursday in class. The exam covers material through Section 4.2. Exam. Solutions. Mean = 79. Median = 85.5.
11 (April 1)	HW 9 due April 11.	Chapter 4: Vector spaces. Chapter 5: Linear transformations.
12 (April 8)	HW 10 due April 21.	Chapter 5: Linear transformations.
13 (April 15)	HW 11 due April 28.	Chapter 6: Orthogonality. Lecture on Section 6.1. Lecture on Section 6.2 (except Gram-Schmidt). Lecture on the Gram-Schmidt process. Slides. Section exam 3 on Thursday in class (only half of the lecture). The exam covers material through Chapter 5.
14 (April 22)		Chapter 6: Orthogonality.
Final week (April 29)		Final exam on Thursday May 2.