• MTH 110: Introduction to Statistics

  An introductory statistics course, with topics such as data analysis, probability, confidence intervals, hypothesis testing, and basic statistical modeling.

• Math 1271: Calculus I and II

  First-year calculus, covering derivatives, applications of differentiation, integration, techniques of integration, sequences, and series.

• Math 2243: Differential Equations and Linear Algebra

  A combined introduction to differential equations and linear algebra, including core topics such as matrices, eigenvalues, systems of differential equations, and phase plane methods.

• Math 4242: Applied Linear Algebra

  An upper-level linear algebra course emphasizing theory, computation, and applications of vector spaces, linear transformations, eigenvalues, and matrix methods.

• MTH 311: Introduction to Probability Theory

  An introduction to probability, including random variables, distributions, expectation, conditioning, and foundational theoretical ideas.

• Machine Learning with Python

  A mathematically focused machine learning course with class notes, exercises, worked solutions, and Python starter scripts covering optimization, regression, classification, PCA, clustering, regularization, kernels, neural networks, decision trees, random forests, and gradient boosting.

Dynamical Systems

Study materials on qualitative dynamics, phase portraits, equilibria, stability, and the behavior of nonlinear systems.

• Dynamical Systems notes (PDF)
• Dynamical Systems flash cards (PDF)

Celestial Mechanics

Notes on orbital motion and classical celestial mechanics, including mathematical methods used to study two-body and related dynamical problems.

• Celestial orbital mechanics notes (PDF)
• Celestial orbital mechanics flash cards (PDF)

Probability

Supplementary notes focused on probability theory, with emphasis on random walks, Markov chains, martingales, in preparation for oral examination topics.

• Probability notes on random walks, Markov chains, and martingales (PDF)
• Probability flash cards on random walks, Markov chains, and martingales (PDF)
• Possible probability oral exam questions and answers (PDF)

Advanced Calculus I (MATH 4603)

Archived notes from a course in analysis, based on Edward D. Gaughan’s Introduction to Analysis, with attention to rigorous foundations and proof-based reasoning.

• Class notes from Fall 2014 (Scott Adams); text: Introduction to Analysis, 5th edition, by Edward D. Gaughan

Classical Mechanics

Notes based on Leonard Susskind’s Stanford lectures on classical mechanics, intended as a mathematical companion to the lecture series.

• Class notes for Leonard Susskind’s Stanford lectures on classical mechanics (PDF)