Applied Linear Algebra
MTH 415-001
| Instructor: | Mark Iwen |
| Time and Place: | Lectures are MWF 1:50 pm - 2:40 pm in Wells Hall A318 |
| E-mail: | markiwen@math.msu.edu |
| Office: | D220 WH |
| Office Hours: | Monday 2:45 pm -- 3:45 pm, Wednesday 2:45 pm -- 3:45 pm, and Thursday 9 am -- 10 am |
This course will cover the mathematical topics necessary to, e.g., begin understanding general feedforward neural network structures, including convolutional neural networks. The course will cover finite dimensional inner product spaces, norms and related inequalities, unitary matrices and their properties, discrete Fourier transform matrices, convolutions and the Fast Fourier Transform (FFT) algorithm, the Singular Value Decomposition (SVD), least squares regression, and tools used in linear inverse problems such as Tikhonov regularization.
Course website for MTH 415-001:
http://math.msu.edu/~markiwen/Teaching/MTH415/MTH415_F25.html
The course website is mandatory reading for the course. On it you will find the course schedule, the syllabus, and supplementary reading. Homework assignments will be posted on the schedule.
Textbook:
The class will utilize free course notes created by the instructor. The current course notes will be linked to on the course schedule.
Homework:
Homework assignments will be given most weeks and will constitute 50% of your final grade. The homework questions will be assigned on the web with their due dates. Posting of new assignments will be announced in class. You must submit your homework solutions during the class period on the due date unless prior permission has been granted to submit otherwise. Late homework assignments will never be graded. The lowest two homework scores will be dropped when computing your average homework grade. Homework solutions must be original copies in the student's own handwriting/compiled LaTeX. No other submissions will be graded. Solutions must be clear and neatly written to receive credit. A subset of the homework problems will be graded on each assignment.
Midterm Exam:
There will be a midterm exam in class on Friday, October 17, 2025. It will constitute 20% of your final grade.
Final Exam:
There will be a final exam on TBD, in Wells Hall A318. It will constitute 30% of your final grade.
Grading:
Your final course percentage will be determined by averaging your homework, midterm exam, and final exam percentages with the following weights: Homework (50%), Midterm Exam (20%), and the Final Exam (30%). The result of this weighted average will then be rounded to the nearest integer.
Your final grade (e.g., 3.5, 4.0, etc.) will be assigned according to a class ranking. That is, the weighted averages calculated as above for all the students in the class will be rank ordered. Finally, threshold scores (e.g., a score above which a 4.0 is earned) will be determined, thereby establishing each student's final grade in the class. The threshold scores for each grade will never be higher than those indicated in following table.
| 90% -- 100% | A | 4.0 |
| 85% -- 89% | A-/B+ | 3.5 |
| 80% -- 84% | B | 3.0 |
| 75% -- 79% | B-/C+ | 2.5 |
| 70% -- 74% | C | 2.0 |
| 65% -- 69% | C-/D+ | 1.5 |
| 60% -- 64% | D | 1.0 |
| 0% -- 59% | F | 0.0 |
Incomplete grades will be given only in unusual cases of illness or other personal emergency, which causes the student to miss a significant amount of the course. This grade cannot be given for any other reason.
Academic Integrity:
You are encouraged to work with your peers on solving homework assignments. However, all submitted homework solutions must be written up individually in your own words. Submitting another student's written work (or AI generated solutions) as your own work will be considered plagiarism.