Math 405, Fall 2025

Office Hours: 

Kirwan 4408, Tuesdays 1:30PM to 2:15AM. Thursdays: 2:30PM to 3:15PM. Wednesday 2PM to 3PM. If there are any circumstances that prevent me from coming in person, I will send everyone a zoom link. If you'd like to meet me on zoom instead because you absolutely can't make it in person, just email me and we can set up a zoom call.

Syllabus and Policies for Math 405 Fall 2025:

0: Textbook: The textbook we will be using for this class is: Linear Algebra, An Introductory Approach by Charles Curtis, ISBN 0-387-90992-3,3-540900002-3. This is published by Springer in the Undergraduates Texts in Mathematics. Note this is different from an older book by the same author, with the same title, published by Allyn and Bacon.

1: Homework: The course will have assigned HW assignments (see HW section on https://sites.google.com/view/srivatsavke/umd-math-405-fall-2025?authuser=0 for more details) These will be graded for completion, and only one problem will graded carefully each assignment. I highly recommend to do these carefully and honestly, as a significant portion of the exams will be based on these. If you would like more feedback on how you presented a problem, please come to office hours and I would be very happy to offer my full feedback.  

2: Exams: There will be two midterm exams and will account for 40% of the final grade. The first midterm will be in class on Tuesday October 7th. The second midterm will be in class on Thursday November 6. The final exam will account for the remaining 50% of the grade and will be held on Monday, December 15, 10:30am - 12:30pm. 

3. Lectures: As per university policy, there will be no attendance requirement, however, I highly encourage everyone to attend lectures, and this will be a source of getting insights into what type of questions I like to ask on exams. I will not record lectures, and not post lecture notes because in my experience, this leads to an extremely low attendance rate. Use the opportunity to make friends with other students, and work on homework problems together.

4. Appeals: After each in-class exam the students have one week from when the exam is returned to appeal aspects of the grading. A written email to the instructor, with the specific details of an appeal (I do not entertain blanket regrade requests) is required. Appeals for the final exam will typically not be entertained. 

5. Integrity: On exams students must write out the following pledge by hand and sign it: "I pledge on my honor that I have not given or received any unauthorized assistance on this examination". I of course hope that you believe in the merit of this philosophy and sincerely follow it. 

6. Makeup policy: Makeups for in-class exams will only be given in the case of a documented absence due to illness, religious observances, participation in a University activity at the request of University authorities or other compelling circumstances. The makeup exam may be a written exam or an oral exam, but as per university policy, it has to happen in a timely manner, preferably within a week of the missed exam. 

7: Accommodations: ADS Students who require require special examination conditions must register with the Office of Accessibility and Disability Services (ADS) in Shoemaker Hall. Documentation must be provided to the instructor. Proper forms must be filled in and provided to the instructor before every exam. 

Homework assignments for Math 405 Fall 2025:

1. Due on Thursday September 11th 11:59PM: Section 4: 4(a,b,c and e only) 5,6,7,8. Additional problem: Prove that the set {1,x,x^2, ... ,x^n, ... } is a basis for the vector space of all polynomials in one variable x over the reals.

2. Due on Thursday September 18th 11:59PM. Section 5: 1, 2, 4, 5. Also prove rigorously using induction that every system of linear equations over the reals, which has more variables than equations, has a non zero solution tuple. Section 7: 1,2,3,4,5. 

Content covered in class: 

1. Week 1, till September 4th: Definitions of field, vector space, spanning sets, linear independence, and examples. 

2. Week 2: bases, some facts about finite dimensional vector spaces.