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.
Probability and Statistics (Math 230 level).
Introduction of Probability and Analysis will be helpful.

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:

[Weeks 1] Linear algebra for AI

[Weeks 2–3] Differentiation and Optimization (for training neural networks).
Matrix calculus, chain rule, gradient descent, stochastic gradient descent, and adaptive gradient methods.

[Weeks 4–5] Probability and Information Theory (for understanding large language models).
Conditional probability, likelihood, entropy, cross-entropy, KL divergence, and softmax.

[Week 6-7] High-Dimensional Probability and Geometry (for understanding high-dimensional representations).
Random vectors, covariance, Gaussian examples, concentration, and high-dimensional inner products.

[Week 8-9] Stochastic Kernels and Averaging Operators (for understanding attention algorithms).
Stochastic matrices, row-stochastic operators, weighted averaging, and data-dependent kernels.

[Week 10] Markov Processes and Sampling.
Markov chains, transition kernels, stationary distributions, detailed balance, and Markov chain Monte Carlo.

[Week 11-12] Stochastic Dynamics and Generative Modeling.
Gaussian noise, denoising, score functions, and Langevin-type dynamics.

[Week 13 (optional)] Spike neural networks. Reservoir computing. Biology computing.

Midterm: October 27st, 3:30–5:00 pm.
Final: December 22th, 3:30–5:00 pm.

No late homeworks will be accepted without an approved excuse.

-Letter grades will be assigned purely based on each student’s performance, not on relative comparison.
-The course will be taught in English.
-Linear algebra for AI is a critical topic. PCA, SVD, and Low-rank approximation must be taught in this course. However, these topics will be covered in Comput. Linear Algebra and its App (Math 402). Hence, we will briefly cover these topics this semester and focus on others.