Math 403/503, Fall 2022

Course information

Meeting times: T,Th from 10:30–11:45am
Textbook: Axler, Linear algebra done right, 3rd
Homework: View homework problems
Office hours: TBA, and by appointment

Course description

Linear algebra evolved from the study of linear equations. It now encompasses the study of any objects that may be added and rescaled (vector spaces). The subject lies at the heart of both pure and applied math. In this course we will build upon the matrix theory you have seen in the past to explore the theoretical foundations of the subject.

Anticipated learning outcomes

  • Possess and exhibit a working knowledge of linear algebra content
  • Read and write proofs in linear algebra
  • Explore mathematical questions and appreciate abstract mathematics

Rough plan

  • Weeks 1-5: Vector spaces and linear mappings (chapters 1, 2, 3)
  • Weeks 6-10: Eigenvalues/vectors and orthogonality (chapters 3, 5, 6)
  • Weeks 11-15: Spectral theory and determinants (chapters 7, 8, 10)

Course format

The course will be delivered through synchronous remote class sessions. Each session will include a mixture of student questions on previous material, discussion of new material, and group problem solving.


Attendance and participation 20%

Please attend remote class sessions, be prepared to ask questions and discuss the material, and collaborate with your peers on group activities. You may miss a few class sessions without penalty, but additional absences must be documented. Each session will feature one or more “U-Pruv” problems which must be completed collaboratively and submitted as a group.

Homework 50%

Homework assignments will be given each week and collected the following week. Students enrolled in Math 503 may be asked to complete additional problems. You are encouraged to collaborate with your peers, and you are welcome to use online resources when you are stuck (please reference). But please keep in mind that you must always fully understand your solutions and most importantly write them in your own words.

Quizzes 30%

We will have three take-home quizzes to be completed individually. Students enrolled in Math 503 may be asked to complete additional problems. The quizzes will take place during the 5th week, 10th week, and finals week.


This syllabus is subject to change. I may make refinements and updates during the first few weeks of the semester. While I don’t expect any substantial changes, please allow for some flexibility. I will give notice before making any changes to the syllabus.