Course Syllabus
Math 496 - Linear Algebra II
Spring 2026

Textbook:

The Course: This course will continue the formal study of linear algebra. We will focus on the investigation of Vector Space and Linear Transformation between them. We will study theoretical concepts like eigenvalues, singular value decomposition, and canonical forms as well as their applications. We will also learn computational techniques like LU decomposition, Gram-Schmidt procedure, numerical techniques for finding some eigenvalues.

Participation, Presentations, and Projects: Each student is expected to be a productive member of the class. This means you should expect to attend each class period and be prepared to discuss the material. Excessive absence or unpreparedness will result in deduction of points in this area. Occasionally students will present homework solutions to the rest of the class. Each student will be given a particular problem to solve individually or in pairs and present to the class. The student will be expected to understand their solution well enough to be very clear, use proper terminology, and answer questions. All of these aspects of the class will be worth 10% of your final grade.

Homework: You will be assigned weekly homework assignments to be turned in most class periods. You are allowed and indeed encouraged to work on your homework with other people, however what you turn in should be your own understanding of how to do the problems and should not just be a copy of someone else's work. Your homework must follow the homework guidelines given in class. The homework for the course will be worth 16% of your total grade.

Quizzes: Most weeks that do not include an exam will have a short quiz. The quiz will cover the most recent material from the class and should take no longer than 10-15 minutes. Although these quizzes cannot be made up except in extreme circumstances, one quiz will be dropped so missing one quiz will not greatly affect your grade. All the quizzes will each be worth 20% towards your final grade.

Exams: There will be two period-long midterms which will occur on Mar. 13 and Apr. 17. The material it will cover will be announced on the website and in class at least a week ahead of time. Make-up exams will not be given. If you have a legitimate excuse you may use your final exam score to make up for missing exam scores. Each midterm will be worth 16% of your grade.
There will be a comprehensive 2 hour final given on Monday, May 18 at 11 AM. The final is worth 22% of your grade.

Learning Outcomes: Upon completion of this class students should be able to:

• understand the theory of vector spaces and transformations between them
• to know and be able to correctly apply theorems of the course
• understand the importance of abstraction in algebra
• be able to write clear, coherent and correct proofs of more complicated theorems

Disability: For accommodations due to a disability please contact me within the first 2 weeks.

Academic Honesty: Cheating and plagiarism are in violation of USD's academic integrity policy and are taken very seriously. Make sure you are aware of this policy.

Have a Good Semester!