Linear Algebra

Math 524
Spring 2026
Meeting: Tuesday, Thursday 2:00-3:15
NE 278B
San Diego State University
Professor: Mike O'Sullivan
Web page: http://mosullivan.sdsu.edu
Email: mosullivan@sdsu.edu
Office: GMCS #582
Office Hours:
You may make an appointment for another time, or just stop by my office. If I am in and available, we can talk.

Schedule:

First day of class: Tuesday, Jan. 20.
Homework: due on most Thursdays.
Test 1: Vector Spaces and linear maps. Thursday February 26.
Test 2: Eigenvalues, eigenvectors, eigenspaces and Jordan form. Thursday March 26.
Last day of class: Tuesday, May 5.
Final Test: Cumulative, but with a focus on inner product spaces, spectral theorem, singular value decomposition.
Tuesday May 12, 1:00-3:00.

Detailed Information


Syllabus

SCHEDULE
ASSIGNMENTS

Resources

Axler, Linear ALgebra Done Right 4th Edition, Springer.
Required. The pdf linked above is a free download, but I encourage you to get a physical copy, even if it is an earlier edition.

Course Description

This is a second course in linear algebra, building on the more applied SDSU course Math 254: Introduction to Linear Algebra. There is much more emphasis in this course on the theory that undergirds the subject, so it is valuable to have additional background such as Math 245 (Discrete Mathematics) and Math 320 (Introduction to Abstract Algebra) or some other course that uses proof techniques.

Linear Algebra is one of the most widely used and fundamental areas of mathematics. It is an important tool in virtually all physical sciences, in engineering, and in economics and other social sciences. It an important companion to calculus, but the flavor of the subject is different, as you will see in this course. Linear algebra is also the core mathematical tool, in addition to statistics, in data science and artificial intelligence.

We will work through the first 8 chapters of Axler's book. The first test will cover Chapters 1-3 on vector spaces and linear maps. The second test will cover Chapters 5 and 8 on linear operators (which are linear transformations from a space to itself), eigenvectors, and eigenspaces. The final weeks of the semester will cover Chapters 6 and 7 on inner product spaces and orthogonality. The final test will be cumulative, with particular emphasis on the inner product material.

Primary Topics

Vector Spaces and linear maps.
Eigenvalues, eigenvectors, eigenspaces and Jordan form.
Inner product spaces, spectral theorem, singular value decomposition.

Prerequisites

Math 254 Introduction to Linear Algebra (or similar course
M at 245 Discrete Mathematics (or similar proof oriented course).

Format

Class time will mix lecture with problem solving. See the schedule for specific topics and sections of the book to be covered each day. Read ahead: you may not understand some of the material, but, it will help you absorb the materila during class. formulate questions that you have, and be prepared to discuss this in class.

Learning Outcomes

It is standard these days to have learning outcomes for every course; rather than simply listing the topics covered. My approach to this is as follows. In every math course that I teach, I want students to advance in the skills listed below (adapted from the Degree Learning Outcomes for the SDSU math major as presented on the department website). In this course we do this work in the context of linear algebra.

[Foundational knowledge.] State major definitions, axioms, and theorems and use examples to illustrate.
[Use logical reasoning.] Read a proof and explain the logic and derivations. Write a mathematical proof using an appropriate method.
[Use algebraic tools and methods.] Derive answers, apply algorithms, and compute, both by hand and using mathematics software.
[Explore mathematical ideas independently.] Have confidence to read challenging material that is beyond that explored in a textbook or class.
[Communicate mathematical ideas effectively.] Make progress toward the mathematicians goal: writing that gets to the essence of the matter and is brief, clear, and polished.
[Nurture the learning of others.] Work with others in a way that is collegial, inclusive and empowering. Contribute, but seek understanding of other perspectives.