888 TOpics in Mathematical Data Science: Algebraic Foundations of Data
***** LEC 001 MWF 1:20 PM - 2:10 PM, B211 Van Vleck Hall
***** LEC 001 MWF 1:20 PM - 2:10 PM, B211 Van Vleck Hall
This course will dive into the fundamental tools (algorithms and theorems) for data through an algebraic lens. We will see how notions from algebra provide a foundation for many aspects of data science.
A list of covered topics will be updated with learning outcomes lecture by lecture --- these are subject to change according to time constraints and the pace of the course.
Course Material
Lectures: As this is a topics course, we will not follow a textbook from cover to cover. Instead, book chapters and articles will be listed as supplementary references for the lecture material. There will be time for in-class discussion about homework (usually on Wednesdays).
Learning outcomes: The development of a common language amongst the class to communicate ideas from data science across wide ranging disciplines such as statistics, engineering, and the sciences. Learning outcomes for each lecture will be found in the topics list.
Participation will account for 40% of the course grade.
About every three weeks there will be a participation survey.
Here is a Canvas link to the first one.
Final projects will account for 40% of the course grade. I am open to people working in a group of two, but a collaboration agreement form needs to be filled out.
Homework will account for 20% of the course grade (depending if we have a grader). It is graded on completion. The grader is greatly encouraged to provide feedback.
For the final project you are tasked with designing a minisymposium that has a connection to the topics in this course (other related topics require instructor approval). The components of the final project are below (subject to minor changes). The peer review components have strict deadlines. I can do extensions for the other components, but a request needs to be made through Canvas before the deadline (submit the request instead of the work).
5 points. Acknowledgement: this is a confirmation that you know about the project and an opportunity to express concerns and ask questions, e.g. if it is okay to work with a partner. (Sept 12)
5 points. Title and first draft of the minisymposium abstract (3 - 12 sentences, due Sept 27)
Here is a website of a minisymposium organized by Thomas Yahl with an abstract after the organizers' names.
A long list of minisymposium for SIAM AG23 and SIAM MDS2024 is provided (by clicking on a link you will be taken to a page with a list of speakers and minisumposium abstract).
5 points. Speaker details: List of four to six speakers, their websites (if available), titles of their talks (this can be the title of the relevant article), and pdfs of the article(s) you want the speaker to cover (due Oct 9 )
5 points. Obtaining feedback of your current progress (Due between Oct 10 and Oct 23)
Obtain feedback from a student in the class or other math/stat/engineering graduate students who attend the University of Wisconsin --- Madison.
You only have to submit the name of the peer and how you got the feedback (was it over Zoom, email, or in-person).
A student in the class can provide feedback to at most two other classmates.
I am open minded on how you obtain the feedback. Here are two ideas to be concrete.
Idea 1: Send a peer your minisymposium materials (title, abstract, and speaker details) and ask (1) if they can identify the target audience for your minisymposium, (2) do they think the target audience would come to the session based on the minisymposium materials, and (3) if they have comments/suggestions for additional speakers or replacements.
Idea 2: Send a peer your minisymposium title and abstract to have a conversation about who the speakers are and why you chose them.
10 points. Revised title, abstract and speaker information (Update according to peer feedback, due Oct 26)
5 points. No more than 500 words explaining your choice of speakers and their work --- think of this as justifying travel support for these speakers to a funding agency (due Oct 26)
5 points. A logo and less than 250 words explaining the logo: a logo is some type of graphic here are examples from MXM (due Nov 3)
5 points. Second time obtaining feedback on your current progress (Due between Nov 10 and Nov 24th)
(a) Obtain feedback from a different UW Madison graduate student (math/stat/engineering) and submit the name of the person who gave feedback and how it was obtained.
(b) For 5-10 minutes, chat with your favorite generative AI (the university provides access to Copilot) about your minisymposium. Submit the chats, and what you disagree with.
10 points. Reflection: State some open problems and new directions that would be discussed at the minisymposium. This may also involve the student working out some preliminary examples to put these into context. (A bulleted list is acceptable, but a 1-2 page summary with some examples or key ideas is preferred) (Due by Dec 7).
Code can be included in the 1-2 page summary
If you use a generative AI, then, in an appendix, you must (1) include the logs and (2) specify what disagreed with.
10 points. Deliverable (Presentation/Slides+Notes/Recording/Write-up): The default option is a voice-over recording with slides, but other options are okay with instructor approval. An in class presentation may be possible if time permits. (Due by Dec 7).
Presentations/recordings can be 15 -25 minutes long
Here are some types of presentations if you are looking for defaults:
Focus on one result of a speaker
Focus on a broad problem and how the session pulls together people in this context
Give an introduction to the themes of your symposium
If you use a generative AI then in an appendix you must include the logs and specify what disagreed with.
Homework is graded based on completion. Full credit (4pts) will be awarded if the student turns in a good-faith attempt for a first draft on time and submits a revised final version; otherwise, at most two points will be awarded for turning in a first draft and/or final version.
Note: Submissions should be able to be understood without reference to the problem statement --- meaning you should include a copy of the question (e.g. writing it out or screenshots embedded into a latex file) in your submission or structure your write-ups to communicate this information. The grader has been instructed to provide feedback on the first problem in each submitted assignment, and you may have the questions in any order for your submission. Some class time will also be devoted for small group discussions about the homework.
Homework #1 has a first draft/attempt due Wednesday Sept 10 before class; final version has a flexible deadline of Friday Sept 12. Select four problems from this list.
VMLS Chapter 12 (page 239): 10.39, 10.40, 12.4, 12.8, 12.10, 12.13(a,b), 12.13(c), 12.15, 12.16.
Homework #2 has a first draft/attempt due Wednesday Sept 17 before class; final version has a flexible deadline of Friday Sept 19. Select seven problems from this list.
Homework #3 has a first draft/attempt due Wednesday Sept 24 before class; final version has a flexible deadline of Friday Sept 26. Select six problems from this list.
ALA Chapter 8: 8.5.23, 8.5.28, 8.5.30; 8.5.32(i,iv), 8.5.43, 8.5.45; 8.6.4, 8.6.22, 8.6.23(a); 8.7.12, 8.7.19, 8.7.24.
Homework #4 has a first draft/attempt due Wednesday Oct 1 before class; final version has a flexible deadline of Friday Oct 3. Select six problems from this list.
ALA Chapter 8: 8.7.25, 8.7.30, 8.7.31, 8.7.35(b), 8.8.7; 8.8.9(b,c), 8.8.9(d,g), 8.8.10, 8.8.11, 8.8.12,
and MGU: 3.11; 3.12.
Remarks/Corrections from the grader:
For problem 4.13: In that problem UT denotes a matrix group, it is closed in GLn but not in the space of all matrices (since you want the diagonals to be non-zero). So the problem is correctly stated.
For problem 7.3: The problem should be to prove that the given cone is not a smooth manifold. The given space is homeomorphic to R^2, therefore it's a topological manifold but not a smooth one!
Homework #5 has a first draft/attempt due Wednesday Oct 8 before class; final version has a flexible deadline of Friday Oct 10. Select five problems from this list.
MGU: 3.13(c), 3.14; 4.12, 4.20, 5.1, 5.2, 5.6, 5.10, 6.1, 6.3, 6.4, 6.5.
Homework #6 has a first draft/attempt due Wednesday Oct 15 before class; final version has a flexible deadline of Friday Oct 17. Select five problems from this list.
MGU: 6.9, 7.1, 7.3, 7.4, 7.7, 7.12, 7.13, 7.16, 7.17 and TBD
No more required homework will be assigned, but optional questions will be posted.
Many of the topics in this course are related to the long program Algebraic statistics and our changing world at IMSI (Chicago) Fall 2023 as well as the program on Metric Algebraic Geometry at ICERM in Spring 2027.