MTH 800-001: Quantitative Foundations for Machine Learning
| Instructor: | Mark Iwen |
| Time and Place: | MWF 9:20 am -- 10:10 am in A120 WH |
| E-mail: | markiwen@math.msu.edu |
| Physical Office: | D220 WH |
| Office Hours: | Monday 1:30 pm -- 2:30 pm, Tuesday 9 am -- 10 am, and Wednesday 1:30 pm -- 2:30 pm |
This course will cover the mathematical topics necessary to begin understanding general feedforward neural networks including, e.g., convolutional neural networks. The course will begin by discussing 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), and least squares regression. The course will then continue to discuss topics in optimization needed to begin understanding neural network training including, e.g., convex functions and sets, gradients, gradient descent, convergence results, stopping conditions, learning rates, and supporting theory from the optimization literature. Neural network and machine learning examples and connections will be made often to motivate the value of the mathematical theory discussed throughout the course.
Course website for MTH800-001:
http://math.msu.edu/~markiwen/Teaching/MTH800/MTH800_F24.html
The course website has the syllabus and required reading. Any papers covered in class will also be posted there and/or on the course D2L page.
Textbook:
There is no official textbook. Instead we will utilize material from other pdf sources provided by the instructor on D2L.
Homework:
Homework assignments will be given most weeks and will constitute 70% of your final grade. They will be assigned and submitted on D2L. Posting of new assignments will be announced in class. 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.
Students are encouraged to work with their peers on homework assignments. Math is a collaborative discipline and two or three minds are often better than one. However, your final homework solutions must be written up individually in your own words and then kept to help you study for the final exam. The solutions will be useless to you if you don't understand how they work. And, you need to understand how to solve the problems yourself or you will struggle on the final exam!
Final Exam:
There will be a final exam on Thursday 12/12, 7:45 am -- 9:45 am, in Wells Hall A120. It will constitute 30% of your final grade, and will consist of selected homework assignments. If you have done the homework and can repeat your solutions (with minor variations) you should do well on the final exam.
Asynchronous Lecture Dates:
There will be two asynchronous lectures during the semester on Monday 11/25 and Wednesday 11/27 (the two classes before Thanksgiving). A link to the video lectures for each of those classes will be posted to the course D2L page at least a day in advance.
Grading:
Your final course percentage will be determined by averaging your homework and final exam percentages with the following weights: Homework (70%) and the Final Exam (30%). The result of this weighted average will then be rounded to the nearest integer. This final percentage will then be used to determine your course grade.
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 as your own will be considered plagiarism.