Syllabus

Link to Syllabus PDF

Table of Contents

  1. Course Information
    1. Catalog Entry
      1. MAT 4353/MAT 6973 Mathematical Foundations of A.I.
    2. Prerequisites
    3. Credit Hours
    4. Course Modality
    5. Class Meetings Schedule
      1. Duration
      2. Campus
      3. Location
      4. Time(s)
  2. Learning Objectives
  3. About the Instructor
    1. About Me & My Teaching Philosophy
    2. Department
    3. Office Location
    4. Student Hours
    5. Preferred Method of Communication
  4. Course Materials
    1. Textbook (required)
    2. Reference Books
  5. Additional Course Information
  6. Assessments and Assignments
    1. Written assignments
    2. Midterm Oral/Class Presentations
    3. Final Presentations and Final Paper Due.
  7. Activities and Grading
    1. Weight of Course Activities
    2. Final Grade Ranks
    3. Notes
    4. Time Commitment Expectations
  8. Guidelines for the Use of Generative Artificial Intelligence
  9. Course Expectations and Policies
    1. Instructor-Initiated Drops
    2. Video and Audio Recording
    3. Syllabus Changes
  10. Course Schedule
  11. Department Policies & Resources
    1. Ombudsperson
  12. Essential Student Information

Course Information

Catalog Entry

MAT 4353/MAT 6973 Mathematical Foundations of A.I.

Vectors, matrices and tensors; discrete and continuous probability; random variables and expectation; elements of information theory; basic methods for probabilistic learning (maximum likelihood, Bayesian statistics); supervised and unsupervised learning algorithms; neural networks: feedforward, convolutional, recurrent/recursive; loss functions and gradient-based learning; optimization and regularization methods; algorithm implementations; testing on real-world datasets.

Prerequisites

MAT 2233 Linear Algebra, or MAT 2253 Applied Linear Algebra; STA3513 Probability and Statistics; MAT 2213 Calculus 3; CS 1063 Introduction to Computer Programming, or CS 1083 Programming I for Computer Scientists.

Credit Hours

3

Course Modality

Traditional in-person.

Class Meetings Schedule

Duration

01/21/2025–05/16/2025.

Campus

Main Campus.

Location

MH 3.02.32

Time(s)

MW 6:00–7:15 PM.

Learning Objectives

  • Describe a variety of machine learning tasks and explain their appropriate stochastic/probabilistic context.
  • Define and give examples of neural networks and architectures (feedforward, convolutional, recurrent), as well as their implementation as code libraries.
  • Explain the differences between supervised and unsupervised learning, and between generative and non-generative tasks.
  • Describe the backpropagation algorithm for differentiation of vector/tensor functions, and learn to use an autograd/autodiff library implementing it.
  • Describe the algorithm of stochastic gradient descent, and use an existing implementation to train specific neural networks.
  • Design and train neural networks with a specified architecture (feedforward or convolutional) to carry out classification tasks (e.g., MNIST digit database).
  • Communicate technical ideas clearly, precisely and concisely verbally and in writing.

About the Instructor

About Me & My Teaching Philosophy

I am Dr. Eduardo Dueñez, associate professor of mathematics. You can learn more about my academic trajectory and my teaching in my shortbio.

Department

Mathematics

Office Location

FLN 4.01.11

Student Hours

MW 5:00–6:00 PM

Preferred Method of Communication

Email to eduardo.duenez@utsa.edu

Course Materials

Textbook (required)

  • Ian Goodfellow, Yoshua Bengio and Aaron Courville. Deep Learning. MIT Press, 2016. ISBN-13: 978-0262035613.

Reference Books

Additional Course Information

  • Each student should be intimately familiar with the contents of any work submitted for grading, whether they are the sole author, or one of several. The instructor shall have the right to request adequate verbal explanation of methodology and content from any student, for any work they submit. Credit will not be awarded when such an explanation is requested but not satisfactorily provided. Excellence in technical communication both verbally and in writing is a central learning objective of this course.

    • Student Ombudsperson: Should you have a concern about this course that cannot be answered by the instructor, or which pertains to unjust or discriminatory treatment, please contact our third-party department representative, Ilse Rosales (Martinez) Cooper ilse.rosalesmartinez@utsa.edu, who can assist with an investigation and resolution of the matter.

Assessments and Assignments

Written assignments

Written assignments will be due every week or two. Submissions should be typeset using LaTeX or similar specialized software (TeXmacs, LyX). All submissions are to be handed in hardcopy by the specified deadline; no extensions.

Use of AI is allowed in translating content produced in some format—perhaps handwritten or hand-drawn—to LaTeX; however, AI is disallowed as a tool to generate/create the content proper (e.g., solutions, proofs or essays). Read the Guidelines for the Use of Generative Artificial Intelligence below for more details.

Midterm Oral/Class Presentations

Week of 3/16–3/20.

Final Presentations and Final Paper Due.

Monday 11 May, 5:00–6:50 PM.

Activities and Grading

Weight of Course Activities

  • Homework: 50%
  • Midterm presentation: 20%
  • Final presentation: 15%
  • Final paper: 15%

NOTE: Numerical grades of undergraduate students (enrolled in MAT 4953) will be multiplied by 1.25 when reporting midterm and final grades.

Final Grade Ranks

         
A: [90%, 100%] B+: [80%, 85%) C+: [69%, 72%) D: [50%, 60%) F: [0%, 50%)
A–: [85%, 90%) B: [76%, 80%) C: [65%, 69%)    
  B–: [72%, 76%) C–: [60%, 65%)    

Notes

  • The lowest (or missing) single grade among assignments will be dropped in computing the homework average.
  • There is no “make-up” provision to redo any for-credit course activities.
  • No extensions will be granted (barring specific circumstances dictated by University policy).

Time Commitment Expectations

MAT 4953/MAT 6973 is a cross-listed (upper-level undergraduate/master's) course. The expected average time commitment to this course (which varies week by week) is about 12 hours per week, but no less than 10 hours per week.

  • Attend class meetings (3 hours per week).
  • Class preparation and reading the assigned sections of the textbook (2–3 hours per week).
  • Solving homework and writing (3–4 hours per week).
  • Meet and discuss class material with your peer study group (1–2 hours per week).
  • Attend office hours (1–2 hours per week).

Guidelines for the Use of Generative Artificial Intelligence

Generative Artificial Intelligence (AI) is allowed in this course only as an aid in coding, and as an aid to writing (grammatical and stylistic aspects, spelling sentence structure, organization), but not to generate content proper. It remains the students' responsibility to properly acknowledge and credit all uses of AI. AI-aided search of information on the internet (e.g., Gemini summaries) is generally allowed. It remains the students' responsibility to verify and ensure the correctness and veracity of any information provided by AI, obtained from websites, or otherwise not directly authored by the students themselves. Any use of AI for purposes not explicitly allowed (e.g., uses to generate written content such as mathematical proofs) is deemed a violation of the Student Code of Conduct and is subject to applicable University sanctions.

Course Expectations and Policies

Instructor-Initiated Drops

This course uses instructor-initiated drops for students who exceed the absence and/or missed quiz limit. Up to the last withdrawal day from an individual course, students will be dropped for either exceeding three (3) missed graded activities or five (5) missed class meetings. Attending a class meeting is defined as being present for at least 90% of its duration. Students will receive at least one courtesy warning when approaching the absence/missed limit. Notification will be sent using ASAP to the student’s email address. A subsequent absence or missed assignment will result in being dropped from the course. Notification of being dropped will also be sent through ASAP to the student’s email address. This drop does not affect enrollment in other courses. Please consult the Dropping Courses website for further details on the process and appeals.

Video and Audio Recording

As the instructor of this course, I may record meetings and lessons. You are expected to follow appropriate University policies and maintain the security of passwords used to access recorded lectures. Recordings may not be published, reproduced, or shared with those not in the class. If the instructor or a UTSA office plans any other uses for the recordings, consent of the students identifiable in the recordings is required before such use unless an exception is allowed by law. For more information on your privacy and class recordings, review Student Privacy (FERPA) in Virtual Classrooms and Other Educational Recordings and the Guide to Secure Video Conferencing Tools.

Syllabus Changes

The syllabus is subject to change at the instructor’s discretion. Any changes/corrections to the course materials, assignment dates, or other updates will be communicated to the students ahead of time. You are responsible for checking Canvas for corrections or updates to the syllabus.

Course Schedule

Week Chapters Topics
1/20–1/23 — Syllabus and general overview.
1/26-1/30 1 Hands-on introduction to AI (experiments with code and datasets).
2/2-2/6 2 Review of linear algebra. Tensors. Introduction to NumPy.
2/9–2/13 3 Probability, random variables and information.
2/16–2/20 4 Review of vector calculus and Newton/Lagrange/KKT methods.
2/23–2/27 5.1–5.4 ML basics: Tasks, capacity, fitting, error, NFL, bias.
3/2–3/6 5.5–5.6 Max likelihood, Bayesian/MAP parameter estimation.
3/9–3/13 — Spring break.
3/16–3/20 — Midterm presentations.
3/23–3/27 5.7–5.11 (Un)supervised learning. SGD. Curse of dimensionality.
3/30–4/3 6.1 Feedforward networks. Implementation as Python libraries.
4/6–4/10 6.2–6.4 Hidden/output units. Loss functions. Architecture and universality.
4/13–4/17 6.5 Backpropagation and automatic differentiation.
4/20–4/24 9–10 Other architectures: convolutional and recurrent networks.
4/27–5/1 14 Generative networks: variational autoencoders and transformers.
5/4 — Library implementations. Experiments.
5/11   Final papers due. Final presentations.

Department Policies & Resources

Ombudsperson

The ombudsperson is an advocate who investigates complaints about a specific section or instructor and attempts to resolve them through mediation. Comments or complaints sent to this person will be brought to the attention of department leadership, who will follow up. If you have questions about the logistics of your class, please contact the instructor.

Contact Ilse Rosales Martinez at ilse.rosalesmartinez@utsa.edu.

Essential Student Information

  • Important: Bookmark and visit the Common Syllabus Information webpage to find important and valuable resources about counseling services, transitory/minor medical issues, supplemental instruction, tutoring services, academic success coaching, sexual harassment and sexual misconduct, campus safety and emergency preparedness, and the Roadrunner Creed.

  • For technical requirements, support, and resources, visit Academic Innovation’s Student Technical Support page.

  • UT San Antonio provides reasonable accommodations to students via Student Disability Services. For more details on eligibility, policies, and requirements, please visit www.utsa.edu/disability or call (210) 458-4157.

  • Your well-being is important. In addition to academic growth, life as a student can include many emotional experiences and opportunities. Being mindful of your own needs and available support can provide you with the tools to successfully navigate these experiences. Student support for well-being, including 24/7 mental health services, can be accessed from the Well-being at UT San Antonio site for students. If needed, we can schedule a meeting, and I can connect you to resources. You are not alone; I am available to help you find resources that might best meet your needs.

  • Student Assistance Services (SAS) is available to help you navigate academic and personal challenges. Campus Advocates in SAS are a central point of contact for students seeking clarity on university processes and policies. They also provide a direct connection to helpful resources and advocacy rooted in care. Campus Advocates offer confidential support and personalized guidance to help students succeed.

  • The Roadrunner Pantry is here to help UT San Antonio students stay healthy and focused by providing free access to groceries, toiletries, and other essentials. With locations at the Main and Downtown campuses, the pantry is organized like a small store and offers items such as canned goods, snacks, and hygiene products. Students with a valid UTSA ID can visit the pantry to pick up what they need. Our goal is to ensure every Roadrunner feels supported and has the resources to succeed. If you’re ever short on food or supplies, the Roadrunner Pantry is a welcoming space you can count on.

  • Students at UT San Antonio are responsible for ensuring their work is consistent with UT San Antonio’s standards for academic integrity. Students should review Section 203 of the UT San Antonio Student Code of Conduct for appropriate standards of academic integrity.

  • UT San Antonio provides numerous services for students from counseling to tutoring to a food pantry. Visit Student Affairs Programs and Services and Student Success for more information.

  • Visit the UT San Antonio Libraries and Museums site for access to journals, research tutorials, and tech gear you can borrow and to find your department’s librarian.

  • Enroll in the Roadrunner Success Playbook, an open-enrollment, self-paced, online hub in Canvas tailored to ensure you have the resources you need to excel at UT San Antonio.

  • Follow Digital Learning Netiquette standards for your online communication activities.