Math 20610: Linear Algebra

Fall 2025

Topics and schedule

Instructor: Jeffrey Diller (click for contact info, list of my papers, etc). Email is by far the best way to reach me.

Official Time and place: Monday, Wednesday, Friday 10:30-11:20 AM in DeBartolo 310.

Office hours: Tues 5-6 and Wed 7-8 in 125 Hayes-Healy 5-6 in my office.

Synopsis: Most mathematical situations, applied and theoretical, require more than just one variable (or dimension) to describe. To take an extreme example, a large language model like ChatGPT uses billions of variables. Linear algebra is a set of computational techniques and ideas that has been developed to help cope with high dimensional situations. It is IMHO as least as important and useful as Calculus. Like a lot of good mathematics, it reinforces our visual intution (geometry), which works well in two or three dimensional situations, with algebra so that we can think clearly and solve problems in any number of dimensions. The central concept of 'linearity' takes time to develop, but you should undestand it to mean something like 'best case scenario'.

Textbook: Linear Algebra with applications, 5^th edition by Otto Bretscher. I really really like this book.

Content: I hope to cover (most of) Chapters 1-3 and 5-7 of the textbook along with some of Chapter 4 and any of Chapter 8 that I can get to. Along the way, I'll try to point out the connections between linear algebra and other things, mathematical and otherwise. The ever-evolving schedule page linked at the top will give a detailed list of topics, readings, etc. Bretscher has a nice chapter by chapter sketch starting on page xi of the Preface.

Necessary/useful Background: Almost nothing beyond high school algebra is really needed for this class. However, I'd recommend a semester or two of Calculus to make sure your math muscles are well-developed and in particular that you're really used to working with functions.

Graded work:

• Homework: Assigned weekly on Fridays (no homework due during exam weeks), due the following Friday by classtime. Worth 15% of your grade. I'll drop your lowest score. Collaboration is a valuable mathematical skill, and I highly encourage you to discuss homework problems with each other. However, I expect you to write up your solutions yourself and in your own words.
• Quizzes: Weekly on Mondays Wednesdays (except for exam weeks and the first week of class), worth 15% of your grade. These will be short and focused on the previous few lectures. I might e.g. ask you to state some fact or definition, to answer a couple of true/false questions or to do a short computation. I'll drop your lowest score at the end of the semester.
• Midterms: in class October 6 and November 24, each worth 20% of your grade.
• Final exam: Tuesday Dec 16, 8-10 AM in DBRT 310 (our usual classroom), worth 30% of your grade. Comprehensive. If your final exam score is higher than one of your midterms, I'll count the lowest midterm for 10% of your grade and the final for 40%.

Any instance of cheating will be dealt with according to Notre Dame’s Academic Code of Honor.