Math 20610: Linear Algebra
Spring, 2026

Instructor: Juan Migliore
Office: HAYE 236
Phone: 631-7345

Email: migliore.1@nd.edu Email is by far the best way to reach me.

Office hours:
Monday, 2:00-3:00
Thursday, 2:00-3:00
Or by appointment.

Time and place of class: MWF 12:50-1:40 in DBRT 209.
Textbook: Linear Algebra with applications, 5^th edition by Otto Bretscher.

Important Links.

• Topics and schedule. This includes the weekly homework assignments. Be sure to check regularly, as these assignments will be updated as the semester progresses.

• Here are the lecture notes for the Spring 2026 semester (pdf format). After every class I'll post that day's lecture later the same day.

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'.

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.

Course content.

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: Your course grade will be based on your total score out of 500 possible points, allocated as follows:

• Homework: There will be regularly assigned homework, collected weekly on Fridays by class time. It will be scaled so that at the end it is worth a total of 100 points. The assignments can be found in the second link above. Pay attention to the due dates listed in the homework schedule. No homework scores will be dropped, so make sure you get started early on the next week's homework. 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.

  The homework assignments will be updated regularly on the schedule page .

• Quizzes: Weekly on Wednesdays (except for exam weeks, spring break, the week after Easter, and the first and last weeks of class), worth 50 points, total. 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 quiz score at the end of the semester. If you miss a quiz, that will be the score that's dropped.
• Midterm Examinations: There will be two in-class midterm exams, worth 100 points each. They will take place in class on
  • Wednesday, February 25, 2026, and

  • Wednesday, April 22, 2026
  
  
• Final exam: This will be worth 150 points. It will take place on Tuesday, May 5 , 10:30-12:30. Location TBA. Please keep this in mind when making travel plans.

Practice Exams and completed exams: Practice exams will be put in this spot a week or two before each exam.

Exam 1

• Here is the practice exam for Exam 1.
• Here are the solutions to Practice Exam 1.
• Here is the actual Exam 1.
• Here are the solutions to the actual Exam 1.

Exam 2

• Here is the practice exam for Exam 2.
• Here are the solutions to Practice Exam 2.
• Here is the actual Exam 2.
• Here are the solutions to the actual Exam 2.

Final Exam

• Here is the practice final exam.
• Here are the solutions to Practice final exam.

Homework and Reading: The homework problems will be assigned on a lecture-to-lecture basis, and will be collected weekly on TBA. You should attempt the problems the day that they are assigned, so as to be able to ask me in class about any difficulties you encounter. (I generally won't do a homework problem for you in class, but may discuss a similar problem.) Similarly, there will be regularly assigned reading for most class periods, and you should come to class prepared to ask questions about any of it you did not understand. I encourage you to collaborate with each other on homework problems and in understanding the required reading. However, I would like everyone to submit their own assignments, written by themselves. See below about copying homework.

Honor Code: Notre Dame students are expected to abide by Academic Code of Honor Pledge: "As a member of the Notre Dame community, I will not participate in or tolerate academic dishonesty." Both the homework and the exams are conducted under the honor code. Examinations are closed book and are to be done completely by yourself with no assistance from others. Although collaboration on homework is permitted (and encouraged), directly copying the work of other students would constitute a violation of the honor code. Similarly, if you have access to any solutions to the homework problems that were written by someone else, a direct copying of such solutions is a violation of the honor code. However, you are allowed to consult such a source if you get stuck, since I would rather that you get help than that you give up entirely; but direct copying from such a source is again an honor code violation.

Support for Student Mental Health at Notre Dame: Care and Wellness Consultants provide support and resources to students who are experiencing stressful or difficult situations that may be interfering with academic progress. Through Care and Wellness Consultants, students can be referred to The University Counseling Center (for cost-free and confidential psychological and psychiatric services from licensed professionals), University Health Services (which provides primary care, psychiatric services, case management, and a pharmacy), and The McDonald Center for Student Well Being (for problems with sleep, stress, and substance use). Visit the Center for Student Support and Care webpage.