University of Texas at Austin, Fall 2022:

Math 341: Linear algebra and matrix theory (55415)

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:
Saad Slaoui. Email: slaouis () utexas.edu
For details on office hours, see syllabus.

Meeting times:
Tuesdays and Thursdays, 9:30am - 11:00am, PMA 5.116.

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

Website:
http://users.oden.utexas.edu/~pgm/Teaching/2022_M341/

Syllabus:
Pdf.

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 - 30%: There will be 11 homeworks assigned. They are (typically) due on Thursdays and will be submitted via canvas. Your 9 best homework scores will each contribute 3.33% to your grade. (In other words, your two worst scores do not count at all.)
• Section exam 1 - 20%: On Thursday October 6, in class.
• Section exam 2 - 20%: On Thursday November 17, in class.
• Final exam - 30%: Saturday, December 10.

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 run in person, and 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. Note that taking photos of handwritten work does not work very well - the text is hard to read. In general, late homeworks will not receive credit. However, we will drop your two lowest homework scores when calculating grades.

Schedule:

Week:	Homework:	Material covered:
1 (Aug 22)		Chapter 1: Vectors and matrices.
2 (Aug 29)	HW1 due Thu.	Chapter 1: Vectors and matrices.
3 (Sep 5)	HW2 due Thu.	Chapter 1: Vectors and matrices. Chapter 2: Systems of linear equations.
4 (Sep 12)	HW3 due Thu.	Chapter 2: Systems of linear equations.
5 (Sep 19)	HW4 due Thu.	Chapter 2: Systems of linear equations.
6 (Sep 26)	HW5 due Thu.	Chapter 3: Determinants and eigenvalues. Tuesday class will be held via zoom.
7 (Oct 3)		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.
8 (Oct 10)	HW6 due Mon Oct 17.	Chapter 3: Determinants and eigenvalues. Chapter 4: Vector spaces.
9 (Oct 17)	HW7 due Thu.	Chapter 4: Vector spaces.
10 (Oct 24)	HW8 due Thu.	Chapter 4: Vector spaces.
11 (Oct 31)	HW9 due Thu.	Chapter 4: Vector spaces. Chapter 5: Linear transformations.
12 (Nov 7)	HW10 due Thu.	Chapter 5: Linear transformations. Chapter 6: Orthogonality. Lecture on Section 6.1 (except Gram-Schmidt).
13 (Nov 14)		Chapter 6: Orthogonality. Lecture on Section 6.2. Lecture on the Gram-Schmidt process. Slides. Section exam 2 on Thursday in class. Exam. Solutions.
(Nov 28)		Thanksgiving. No classes.
14 (Nov 28)	HW11 due Sun.	Chapter 6: Orthogonality.
Final week (Dec 5)		Final exam on Saturday December 10, 1pm - 3pm. Exam. Solutions.