Math 405 -- Linear Algebra

Course guide:

Text: Sheldon Axler, Linear Algebra Done Right: Fourth Edition, Springer-Verlag, 2024.

Content:

This is a course in linear algebra, with few mathematical prerequisites (mainly a familiarity with abstract mathematical reasoning). Our main goal is to study vector spaces, linear transformations and their invariants, inner product spaces and the spectral theorem, together with some important applications. There will be many proofs done in class, and you will also need to prove results on your own in the homework and provide (simpler) proofs on exams. I plan to cover most of the textbook, and include some additional topics, time permitting.

Homework:

The best and only way to learn mathematics is to do mathematics! Your weekly homework assignments are therefore the most important part of this course. Homework will be assigned on Thursday and is due in class on the Thursday of the following week. I urge you to hand in all of your assignments on time - however my policy is to allow up to TWO late homework assignments per student, which should be turned in at most two weeks after their due date. Any further late assignments will not be graded. You may discuss the problems with others if you wish, but whatever you turn in should be written up on your own. The extra credit problems are optional - they can improve your grade, but you do not need to solve them to do well in the course. People looking for a challenge are encouraged to attempt them! Our homework grader is TBA, and her email is TBA. She has office hours on TBA. Please contact her with any questions you may have about the homework grading and solutions to the problems.

Exams:

We will have three exams during the course, two midterms and a final exam. The two midterms will be held in class from 9:30 - 10:45, on Thursday, October 10 and Thursday, November 14. The final exam has been scheduled for Thursday, December 12, 10:30 - 12:30. Make-up exams will only be given for compelling and documented reasons.

Grading Policy:

The course grade will be determined by adding your two midterm test scores (20%+20%) to your final exam score (30%) and your homework total (30%). Participating in class and working on extra credit problems is encouraged and will help to improve your grade.

READ THIS:

University of Maryland course related policies. This includes a discussion of academic integrity, the honor pledge, and accomodations for students with disabilities. If you have a documented disability and wish to discuss academic accommodations with me, please contact me as soon as possible.

Electronic devices:

No electronic devices are required for this course, and they will not be allowed in class during exams.

Office Hours:

I will be available at these times specifically to help you: Tuesdays from 11:00 - 12:00 in my office (Kirwan Hall 4419) and Wednesdays from 10:00 - 11:00 (on Zoom). Feel free to come by my office and talk at any time, either by chance or by appointment.

Resources:

The testbank archive of past exams has examples of tests from past years, and is a good source of problems. A complete set of videos for Math 401, Applied Linear Algebra, is provided courtesy of professor Jeffrey Adams. Although these are at a lower level than our course, they are a useful supplement to it.