Mathematical Foundations of Machine Learning

Course materials for MATH 4990V and MATH 5990V, Fall 2026.

Course Offering

Fall 2026 · MWF 8:35–9:25 AM · CHPN 425 · University of Arkansas

Course Description

This is an introductory course to machine learning (ML), taught from a mathematical and computational point of view. We study how learning algorithms represent data, fit models, evaluate predictions, and manage uncertainty.

The course develops each method from two viewpoints at once: the mathematics of the model and the engineering of training it. Students should be able both to derive and justify a method and to run and diagnose its training process. We begin with Python, Git, and standard data tools, then develop classical machine learning — linear and logistic regression, regularization, nearest neighbors, clustering, dimensionality reduction, support vector machines, trees, and ensembles — before connecting those foundations to neural networks and modern deep learning in PyTorch, extending through convolutional and recurrent networks to variational autoencoders and generative models.

Lecture Notes

These are the written notes for the course. They are the primary reference; slides are a companion to lecture.

Part I — Classical Machine Learning

  1. Introduction, Workflow, and Starting Linear Regression
  2. Linear Regression, Least Squares, and a First Look at Networks
  3. Gradient Descent, Convergence, PyTorch Tensors, and Activation Functions
  4. Logistic Regression and Classification Metrics
  5. Regularization, Cross-Validation, and Model Evaluation
  6. KNN, Kernel Functions, and k-Means Clustering
  7. PCA, t-SNE, and a Probability Review
  8. Support Vector Machines and Kernels
  9. Decision Trees (CART)
  10. Random Forests, Bagging, and Boosting

Part II — Neural Networks and Modern ML

  1. Neural Networks and Backpropagation
  2. PyTorch Modules, Optimizers, and Training Dynamics
  3. Convolutional Neural Networks
  4. Recurrent Neural Networks
  5. Variational Autoencoders
  6. Generative Models: GANs, Diffusion, and Autoregressive Models

Lecture numbers refer to topics, not calendar weeks — the first five topics are covered in a compressed order early in the term, and most topics span two or three class meetings.

Assessment

Homework 35% · Weekly labs 15% · Blackboard notes 10% · Quizzes 5% · Exams 35%. There is no final project; the neural-network and generative-model material in the final third of the course is assessed through homework. Exams test the mathematics (derivations, objective functions, optimization, margins and kernels, backpropagation); quizzes test the training process (data splits, feature scaling, learning-rate behavior, over/underfitting diagnosis, metric choice).

Course Materials

Datasets, lab specifications, and homework assignments are distributed through the UARK GitLab repository, which enrolled students fork and push their work to. Access requires a UARK account and either an on-campus connection or the VPN. Students in the course will receive the repository link directly.

If you are not part of the UARK community but are interested in the course, the lecture notes above are freely available — please email me at jiahuic@uark.edu with any questions.

Archive

Materials from the earlier offering of this course are available here.