We focus on how machine learning or data science build upon the mathematics.
To this end, we cover the basic but fundamental mathematics; linear algebra,
probability/statistics, and optimization. We apply these mathematics to some
basic but central machine learning problems. It is hoped that students will
have a firm understanding of the mathematics for artificial intelligence and get ready to
solve practical problems arising from machine learning.

Calculus and Linear Algebra will be helpful.
Basic Programming may be required for homework.

Some materials for textbook 2: https://math.mit.edu/~gs/learningfromdata/
Simon J. D. Prince (2025), Understanding Deep Learning, https://udlbook.github.io/udlbook/
Yann LeCun. (1988) A Theoretical Framework from Back-Propagation.
Ben Recht. (2016) Mechanics of Lagrangians.
Aurélien Géron (2022) Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems

It covers the following materials:
[Week 1] Motivation: Introduction of simple AI models. Which (how) mathematical theory contributes to those models?
[Week 1] Intro and basic overview of neural networks and linear algebra.
[Weeks 2-5, textbook 2] Linear Algebra and Matrix decompositions.
[Week 6 and 7, textbooks 1 and 2] Optimization, gradient descent, and ADAM.
[Week 8 and 9, textbooks 1 and 2] Probability and statistics.
[Week 10 and 11] Others: Diffusion models and Bayesian.
[Week 12] Applications.

Midterm: October 21st, 3:30-5:00 pm.
Final: December 16th, 3:30-5:00 pm.

No late homeworks will be accepted without an approved excuse.

Messages for those who take this course remotely during military service & off-campus students (off-campus students have to be confirmed by me for virtual participation in this course).
1. Every lecture will be recorded and uploaded to PLMS.

2. Midterm and final exams will be live take-home exams: At the appointed time, I will send the exam problems to each student, who must then submit their solutions within 2 hours. To prevent cheating (e.g., using AI to solve problems), each exam will be designed to test understanding rather than testing calculations or formula use. Solutions are expected to follow a clear and logically consistent flow. When math problems are solved using generative models such as ChatGPT, the results often contain correct calculations but logically flawed reasoning. If your solutions show correct computations but lack logical rigor, I will assume you used a generative model. In such cases, a significant deduction will be applied.

3. Letter grades will be assigned purely based on each student’s performance, not on relative comparison.

4. Grades for military students will be evaluated separately from those of regular students.