Syllabus
Administrative Information
The syllabus information is seen below. This is a PDF copy of the syllabus.
Lecture Information
Lectures are Monday and Wednesday, 11:30 am - 12:45 pm, MSC W301
Staff and Office Hours
Office Hours will be decided after the first week of class
Catalog Information
3 credits. Mathematics and Quantitative Reasoning Credit. Math 315: Numerical Analysis or equivalent transfer credit as prerequisite. Not cross listed. Topics will be announced each semester when class is scheduled.
Prerequisites
Assumed knowledge of numerical analysis, specifically singular value decomposition, QR factorization, matrix terminology, linear system solves, numerical optimization, taught at the level of Math 315. Math 346/347 and/or Math 361/362 are recommended but not required. We will review numerical analysis, probability, and optimization needed for this class the first two weeks of the semester. Coding knowledge in MATLAB, or python is very beneficial, but not necessary.
Texts
Recommended Texts
- Tensor Decompositions for Data Science (TD), by Grey Ballard and Tamara G. Kolda
While this book is brand new, it is the premier text on tensor decompositions, truly one of a kind. This means the book might be expensive, so to be considerate of all's financial situations, the book can also be found here.
Course Work
Homework
You will have two homeworks per module and one homework at the beginning to set expectations of the material. There will be 7 total homework assignments. The assignments will be posted on and submitted through Canvas. The homework will be due on Wednesday at 11:30 am, which is the beginning of class, (except for holidays) and will be posted no later than three classes beforehand (Monday the week prior). The number of questions may vary week to week, but the assignments will not be very long. You will upload your written homework to Canvas in PDF format to grade.
The lowest two homework grades will be dropped. No makeup assignments will be given. If you have to miss an assignment, it will be one that is dropped.
Homework assignments will be graded on an individual basis. The instructor allows discussions with other students while solving the problems. The only requirement is that you acknowledge all contributors and sources used. Yes, this does include large language models such as ChatGPT. Identical solutions that are seen as Honors Code violations, will not be graded and will be reported to the Honor Council. The border between acceptable and unacceptable collaboration may be subtle. If you are uncertain whether a particular behavior is acceptable or not, please ask the instructor or teaching assistant as soon as possible.
Projects
There will be 2 module projects, which will be a combination of individual and small group projects. There will be a written and oral portion of each project. No project is dropped, and each are weighted equally, i.e. each project is 20% of your final course grade.
These projects allow us the flexibility to apply the mathematical topics from class in the broader context of environmentalism, sustainability, and green business.
There will be some class time dedicated to each project, but most work will have to be done outside of class time.
Exams
There will be one midterm exam given in class, on Nov. 23. You will be given the full class period (75 minutes) to take the midterm.
The final exam will be a final presentation to your Module 2 project. It will take place during finals week on Monday, Dec. 17, from 11:30 AM to 2:00 PM.
Conflicts with the final exam time slot must be reported through the Office for Undergraduate Education (OUE). You must notify the instructor at least two weeks before the exam date if you have a conflict, or have a valid excuse verified by the Office of Undergraduate Education (OUE).
Grading
Schedule
This schedule is tentative and subject to change.
| Week | Date | Topics | Homework |
|---|---|---|---|
| 1 | W 8-26 | Syllabus, Numerical Linear Algebra (NLA) review | |
| 2 | M 8-31 | NLA Review | |
| W 9-2 | Optimization, Probability Review | ||
| 3 | M 9-7 | Labor Day (no class) | |
| W 9-9 | Tensors, Slices, Fibers | HW0 Due | |
| 4 | M 9-14 | Mode unfoldings and examples | |
| W 9-16 | Vectorizations | ||
| 5 | M 9-21 | Matricization, Permutations | |
| W 9-23 | Tensor Matrix products | HW1 Due | |
| 6 | M 9-28 | Sparse Tensors and Multi-products | |
| W 9-30 | Tucker Decompositions | ||
| 7 | M 10-5 | Computing Tucker | |
| W 10-7 | Properties of Tucker | HW2 Due | |
| 8 | M 10-12 | Fall Break (no class) | |
| W 10-14 | Tensor Reconstruction | ||
| 9 | M 10-19 | Tucker Optimization | |
| W 10-21 | Tucker Optimization | HW3 Due | |
| 10 | M 10-26 | Tensor Train | |
| W 10-28 | Tensor Train | ||
| 11 | M 11-2 | Presentation 1: Tucker | |
| W 11-4 | Introduction to CP | HW4 Due | |
| 12 | M 11-9 | Extension of CP | |
| W 11-11 | Kruskal Tensors | ||
| 13 | M 11-16 | Properties and Operations on Kruskal | |
| W 11-18 | Midterm Review | HW5 Due | |
| 14 | M 11-23 | Midterm Exam | |
| W 11-25 | Thanksgiving Break (no class) | ||
| 15 | M 11-30 | CP Optimization Algorithms | |
| W 12-2 | CP Optimization Algorithms | ||
| 16 | M 12-7 | Catch-up | HW6 Due |
| Finals | T 12-17 | 11:30am - 02:00pm, MSC - N301 |