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Introduction to algebraic topology emphasizing geometric aspects: two-dimensional manifolds, fundamental group, covering spaces, simplicial homology, Euler-Poincare formula, and homotopy classes.

Offering recorded · Spring 2027 · Sources

Differential Geometry covers the theory of curves and surfaces using differential methods in n-dimensional real space, including manifolds, Riemannian metrics, curvature, and geodesics.

Offering recorded · Spring 2027 · Sources

Number theory covering fundamentals and modern applications like modular arithmetic, quadratic reciprocity, Diophantine equations, and the circle method.

Offering recorded · Spring 2027 · Sources

Introduction to data-driven dynamical systems covering mathematical theory, numerical algorithms, and coding for stochastic modeling and prediction.

Offering recorded · Spring 2027 · Sources

Complex Analysis covers elementary functions of a complex variable, conformal mapping, complex integrals, and the calculus of residues.

Offering recorded · Spring 2027 · Sources

Introduction to Measure and Integration covering the Lebesgue integral, abstract measure, differentiation, and spaces of integrable functions.

Offering recorded · Spring 2027 · Sources

Senior Honors Thesis is individual study for honors math majors writing a thesis in mathematics.

Offering recorded · Spring 2027 · Sources

Senior Honors Thesis is an individual study course for honors math majors to write a thesis in mathematics.

Offering recorded · Spring 2027 · Sources

Undergraduate Thesis is an individual study course for students writing a thesis in mathematics.

Offering recorded · Spring 2027 · Sources

Directed Study involves projects arranged with a faculty member, focusing on proving or disproving mathematical statements using various argument techniques.

Offering recorded · Spring 2027 · Sources

DIRECTED STUDY involves directed study projects as arranged with a faculty member.

Offering recorded · Spring 2027 · Sources

Methods of Applied Mathematics covers derivation and solutions for canonical PDEs, including conservation laws, Fourier analysis, Green's functions, asymptotics, and perturbation methods.

Offering recorded · Spring 2027 · Sources

A systematic study of randomized linear algebra solvers covering mathematical backgrounds, algorithms like randomized SVD and matrix completion, and their implementation and application.

Offering recorded · Spring 2027 · Sources

Covers linear elliptic, parabolic, and hyperbolic equations, calculus of variations, and nonlinear initial value problems in Partial Differential Equations.

Offering recorded · Spring 2027 · Sources

A graduate course covering the basic theory of functions of one complex variable, from Cauchy formulas and residues through conformal mappings and the nonhomogeneous d-bar equation.

Offering recorded · Spring 2027 · Sources

A second course in real analysis covering Banach spaces, Fourier transforms, distribution theory, and applications.

Offering recorded · Spring 2027 · Sources

Abstract Algebra continuation covering commutative rings and fields, including ring-theoretic and field-theoretic topics such as Galois theory and the Hilbert Nullstellensatz.

Offering recorded · Spring 2027 · Sources

Graduate course covering Lie algebras and matrix groups, including tangent spaces, exponentials, classification theorems, representations, root systems, and Dynkin diagrams.

Offering recorded · Spring 2027 · Sources

Continuation ofMATH 751. Cohomology, Universal Coefficient Theorem, Kunneth Formula, cup and cap products, applications to manifolds, orientability, Poincare Duality. Differential forms, integration and Stokes Theorem, De Rham Theorem. Calculations, further duality theorems, Euler class, Lefschetz Fixed-Point Theorem.

Offering recorded · Spring 2027 · Sources

Introduction to ergodic theory and dynamics covering fundamental theorems, classical examples of one and two dimensional dynamics, and applications to group actions.

Offering recorded · Spring 2027 · Sources

Graduate differential geometry course covering the metric properties of Riemannian manifolds, including geodesics, comparison theorems, and Hodge-de Rham theory.

Offering recorded · Spring 2027 · Sources

Computability Theory covers Turing degrees, strong reducibilities, the arithmetic hierarchy, index sets, simple sets, forcing arguments, injury methods, and key theorems including Friedberg-Muchnik and Sacks results.

Offering recorded · Spring 2027 · Sources

Independent work on a Master's thesis in mathematics under faculty supervision.

Offering recorded · Spring 2027 · Sources

Advanced Topics in Real Analysis covers topics in partial differential equations and real analysis.

Offering recorded · Spring 2027 · Sources

An introduction to Fourier analysis in Euclidean spaces, covering related topics such as singular and oscillatory integrals and trigonometric series.

Offering recorded · Spring 2027 · Sources

An advanced graduate topic course in number theory where topics vary by offering, targeting students in number theory, representation theory, and algebraic geometry.

Offering recorded · Spring 2027 · Sources

Advanced Topics in Foundations covers advanced topics from all areas of mathematical logic.

Offering recorded · Spring 2027 · Sources

Seminar in Analysis covering selected topics in Analysis.

Offering recorded · Spring 2027 · Sources

A graduate seminar covering selected topics in Algebra.

Offering recorded · Spring 2027 · Sources

Seminar in Topology covering selected topics in Topology.

Offering recorded · Spring 2027 · Sources