Spring 2025

APC 199/MAT 199(link is external) Math Alive Mathematics has profoundly changed our world, from the way we communicate with each other and listen to music, to banking and computers. This course is designed for those without college mathematics who want to understand the mathematical concepts behind important modern applications. The course consists of individual modules, each focusing on a particular application (e.g. compression, animation and using statistics to explain, or hide, facts). The emphasis is on ideas, not on sophisticated mathematical techniques, but there will be substantial problem-set requirements. Students will learn by doing simple examples. Instructor(s): Sheng Xu
Schedule
C01 T Th 11:00 AM - 12:20 PM
APC 350/MAT 322(link is external) Introduction to Differential Equations This course will introduce the basic theory, models and techniques for ordinary and partial differential equations. Emphasis will be placed on the connection with other disciplines of science and engineering. We will try to strike a balance between the theoretical (e.g. existence and uniqueness issues, qualitative properties) and the more practical issues such as analytical and numerical approximations. Instructor(s): Hans Emil Oscar Mickelin
Schedule
L01 T Th 01:30 PM - 02:50 PM
MAE 305/MAT 391/EGR 305/CBE 305(link is external) Mathematics in Engineering I A treatment of the theory and applications of ordinary differential equations with an introduction to partial differential equations. The objective is to provide the student with an ability to solve problems in this field. Instructor(s): Ehud Yariv
Schedule
L01 M W F 11:00 AM - 11:50 AM
P01 W 01:30 PM - 02:20 PM
P02 Th 02:30 PM - 03:20 PM
P03 Th 07:30 PM - 08:20 PM
MAE 306/MAT 392(link is external) Mathematics in Engineering II This course covers a range of fundamental mathematical techniques and methods that can be employed to solve problems in contemporary engineering and the applied sciences. Topics include algebraic equations, numerical integration, analytical and numerical solution of ordinary and partial differential equations, harmonic functions and conformal maps, and time-series data. The course synthesizes descriptive observations, mathematical theories, numerical methods, and engineering consequences. Instructor(s): Mikko Petteri Haataja
Schedule
L01 T Th 03:00 PM - 04:20 PM
P01 W 07:30 PM - 08:20 PM
MAT 100(link is external) Calculus Foundations Introduction to limits and derivatives as preparation for further courses in calculus. Fundamental functions (polynomials, rational functions, exponential, logarithmic, trigonometric) and their graphs will be also reviewed. Other topics include tangent and normal lines, linearization, computing area and rates of change. The emphasis will be on learning to think independently and creatively in the mathematical setting. Instructor(s): Tatiana Katarzyna Howard
Schedule
C01 M W 08:30 AM - 09:50 AM
P01 F 09:00 AM - 09:50 AM
P99 01:00 AM - 01:00 AM
MAT 103(link is external) Calculus I First semester of calculus. Topics include limits, continuity, the derivative, basic differentiation formulas and applications (curve-sketching, optimization, related rates), definite and indefinite integrals, the fundamental theorem of calculus. Instructor(s): Tatiana Katarzyna Howard, Mark Weaver McConnell, Stan Palasek, Sahana Vasudevan
Schedule
C01 M W 08:30 AM - 09:50 AM
C02 M W 11:00 AM - 12:20 PM
C02A M W 11:00 AM - 12:20 PM
C02B M W 11:00 AM - 12:20 PM
C03 M W 01:30 PM - 02:50 PM
P01 F 09:00 AM - 09:50 AM
P02 F 10:00 AM - 10:50 AM
P03 F 11:00 AM - 11:50 AM
P03A F 11:00 AM - 11:50 AM
P03B F 11:00 AM - 11:50 AM
P03C F 11:00 AM - 11:50 AM
P04 F 12:30 PM - 01:20 PM
P05 F 01:30 PM - 02:20 PM
P99 01:00 AM - 01:00 AM
MAT 104(link is external) Calculus II Continuation of MAT 103. Topics include techniques of integration, arclength, area, volume, convergence of series and improper integrals, L'Hopital's rule, power series and Taylor's theorem, introduction to differential equations and complex numbers. Instructor(s): Fraser Malcolm Watt Binns, Hongyi Liu, Liyang Yang
Schedule
C01 M W 08:30 AM - 09:50 AM
C02 M W 11:00 AM - 12:20 PM
C02A M W 11:00 AM - 12:20 PM
C03 M W 01:30 PM - 02:50 PM
P01 F 09:00 AM - 09:50 AM
P02 F 10:00 AM - 10:50 AM
P03 F 11:00 AM - 11:50 AM
P03A F 11:00 AM - 11:50 AM
P04 F 12:30 PM - 01:20 PM
P05 F 01:30 PM - 02:20 PM
P99 01:00 AM - 01:00 AM
MAT 175(link is external) Mathematics for Economics/Life Sciences Survey of topics from multivariable calculus as preparation for future course work in economics or life sciences. Topics include basic techniques of integration, average value, vectors, partial derivatives, gradient, optimization of multivariable functions, and constrained optimization with Lagrange multipliers. Instructor(s): Tatyana Chmutova
Schedule
C01 M W 08:30 AM - 09:50 AM
C02 M W 11:00 AM - 12:20 PM
C02A M W 11:00 AM - 12:20 PM
C03 M W 01:30 PM - 02:50 PM
P01 F 10:00 AM - 10:50 AM
P02 F 11:00 AM - 11:50 AM
P02A F 11:00 AM - 11:50 AM
P03 F 12:30 PM - 01:20 PM
P04 F 01:30 PM - 02:20 PM
P99 01:00 AM - 01:00 AM
MAT 201(link is external) Multivariable Calculus Vectors in the plane and in space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields and Stokes's theorem. Instructor(s): Dmitry Krachun, Jennifer Li, Semon Rezchikov, Ravi Shankar
Schedule
C01 M W 08:30 AM - 09:50 AM
C02 M W 11:00 AM - 12:20 PM
C02A M W 11:00 AM - 12:20 PM
C02B M W 11:00 AM - 12:20 PM
C03 M W 01:30 PM - 02:50 PM
P01 F 09:00 AM - 09:50 AM
P02 F 10:00 AM - 10:50 AM
P03 F 11:00 AM - 11:50 AM
P03A F 11:00 AM - 11:50 AM
P04 F 12:30 PM - 01:20 PM
P05 F 01:30 PM - 02:20 PM
P99 01:00 AM - 01:00 AM
MAT 202(link is external) Linear Algebra with Applications Companion course to MAT 201. Matrices, linear transformations, linear independence and dimension, bases and coordinates, determinants, orthogonal projection, least squares, eigenvectors and their applications to quadratic forms and dynamical systems. Instructor(s): Bjoern Bringmann, Tangli Ge, Tongmu He, Jennifer Michelle Johnson, Kimoi Kemboi, Ana Menezes, Lue Pan, John Thomas Sheridan, David Villalobos, Bogdan Zavyalov
Schedule
C01 M W 08:30 AM - 09:50 AM
C01A M W 08:30 AM - 09:50 AM
C02 M W 11:00 AM - 12:20 PM
C02A M W 11:00 AM - 12:20 PM
C02B M W 11:00 AM - 12:20 PM
C02C M W 11:00 AM - 12:20 PM
C02D M W 11:00 AM - 12:20 PM
C02E M W 11:00 AM - 12:20 PM
C02F M W 11:00 AM - 12:20 PM
C02G M W 11:00 AM - 12:20 PM
C03 M W 01:30 PM - 02:50 PM
C03A M W 01:30 PM - 02:50 PM
C04 M W 03:00 PM - 04:20 PM
C04A M W 03:00 PM - 04:20 PM
P01 F 09:00 AM - 09:50 AM
P01A F 09:00 AM - 09:50 AM
P02 F 10:00 AM - 10:50 AM
P02A F 10:00 AM - 10:50 AM
P03 F 11:00 AM - 11:50 AM
P03A F 11:00 AM - 11:50 AM
P03B F 11:00 AM - 11:50 AM
P03C F 11:00 AM - 11:50 AM
P03D F 11:00 AM - 11:50 AM
P03E F 11:00 AM - 11:50 AM
P04 F 12:30 PM - 01:20 PM
P04A F 12:30 PM - 01:20 PM
P04B F 12:30 PM - 01:20 PM
P04C F 12:30 PM - 01:20 PM
P05 F 01:30 PM - 02:20 PM
P05A F 01:30 PM - 02:20 PM
P99 01:00 AM - 01:00 AM
MAT 204(link is external) Advanced Linear Algebra with Applications Companion course to MAT203. Linear systems of equations, linear independence and dimension, linear transforms, determinants, (real and complex) eigenvectors and eigenvalues, orthogonality, spectral theorem, singular value decomposition, Jordan forms, other topics as time permits. More abstract than MAT202 but more concrete than MAT217. Recommended for prospective physics majors and others with a strong interest in applied mathematics. Prerequisite: MAT104 or MAT215 or equivalent. Instructor(s): Marc Aurèle Tiberius Gilles
Schedule
C01 M W 11:00 AM - 12:20 PM
P01 F 11:00 AM - 11:50 AM
P02 F 01:30 PM - 02:20 PM
MAT 215(link is external) Single Variable Analysis with an Introduction to Proofs An introduction to the mathematical discipline of analysis, to prepare for higher-level course work in the department. Topics include rigorous epsilon-delta treatment of limits, convergence, and uniform convergence of sequences and series. Continuity, uniform continuity, and differentiability of functions. The Heine-Borel Theorem. The Riemann integral, conditions for integrability of functions and term by term differentiation and integration of series of functions, Taylor's Theorem. Instructor(s): Jonathan Hanselman
Schedule
L01 T Th 11:00 AM - 12:20 PM
P01 F 11:00 AM - 11:50 AM
MAT 217(link is external) Honors Linear Algebra A rigorous course in linear algebra with an emphasis on proof rather than applications. Topics include vector spaces, linear transformations, inner product spaces, determinants, eigenvalues, the Cayley-Hamilton theorem, Jordan form, the spectral theorem for normal transformations, bilinear and quadratic forms. Instructor(s): Louis Esser, Justin Lacini, Andrew O'Desky, Jakub Witaszek
Schedule
C01 T Th 11:00 AM - 12:20 PM
C02 T Th 01:30 PM - 02:50 PM
C02A T Th 01:30 PM - 02:50 PM
P01 F 11:00 AM - 11:50 AM
P01A F 11:00 AM - 11:50 AM
P02 F 01:30 PM - 02:20 PM
P02A F 01:30 PM - 02:20 PM
MAT 218(link is external) Multivariable Analysis and Linear Algebra II Continuation of the rigorous introduction to analysis in MAT 216 Instructor(s): Joshua Xu Wang
Schedule
C01 T Th 01:30 PM - 02:50 PM
MAT 325(link is external) Analysis I: Fourier Series and Partial Differential Equations Basic facts about Fourier Series, Fourier Transformations, and applications to the classical partial differential equations will be covered. Also Finite Fourier Series, Dirichlet Characters, and applications to properties of primes. Instructor(s): Alexandru D. Ionescu
Schedule
L01 T Th 01:30 PM - 02:50 PM
MAT 330(link is external) Complex Analysis with Applications The theory of functions of one complex variable, covering analyticity, contour integration, residues, power series expansions, and conformal mapping. The goal in the course is to give adequate treatment of the basic theory and also demonstrate the use of complex analysis as a tool for solving problems. Instructor(s): Michael Aizenman
Schedule
C01 M W 11:00 AM - 12:20 PM
MAT 346(link is external) Algebra II Local Fields and the Galois theory of Local Fields. Instructor(s): Nicholas Michael Katz
Schedule
L01 T Th 03:00 PM - 04:20 PM
MAT 355(link is external) Introduction to Differential Geometry Introduction to geometry of surfaces. Surfaces in Euclidean space: first fundamental form, second fundamental form, geodesics, Gauss curvature, Gauss-Bonnet Theorem. Minimal surfaces in the Euclidean space. Instructor(s): Paul Chien-Ping Yang
Schedule
C01 M W 01:30 PM - 02:50 PM
MAT 375/COS 342(link is external) Introduction to Graph Theory The fundamental theorems and algorithms of graph theory. Topics include: connectivity, matchings, graph coloring, planarity, the four-color theorem, extremal problems, network flows, and related algorithms. Instructor(s): Paul Seymour
Schedule
C01 T Th 11:00 AM - 12:20 PM
MAT 378(link is external) Theory of Games Games in extensive form, pure and behavioral strategies; normal form, mixed strategies, equilibrium points; coalitions, characteristic-function form, imputations, solution concepts; related topics and applications. Instructor(s): Jonathan Michael Fickenscher
Schedule
C01 M W 03:00 PM - 04:20 PM
MAT 419(link is external) Topics in Geometry and Number Theory: Arithmetic of Elliptic Curves The study of the arithmetic of elliptic curves is an extremely rich area of mathematics, incorporating ideas from complex analysis, algebraic geometry, group and Galois theory, and of course number theory. Many fundamental problems in number theory, such as Fermat's Last Theorem and the congruent number problem, lead naturally to the study of elliptic curves. The purpose of this course is to explore some of the basic ideas in this area, including the group law on elliptic curves, the structure of this group over various fields, and the Birch and Swinnerton-Dyer conjeture. Instructor(s): Will Sawin
Schedule
C01 M W 01:30 PM - 02:50 PM
MAT 425(link is external) Analysis III: Integration Theory and Hilbert Spaces The theory of Lebesgue integration in n-dimensional space. Differentiation theory. Hilbert space theory and applications to Fourier Transforms, and partial differential equations. Introduction to fractals. This course is the third semester of a four-semester sequence, but may be taken independently of the other semesters. Instructor(s): Jacob Shapiro
Schedule
C01 T Th 01:30 PM - 02:50 PM
MAT 457(link is external) Algebraic Geometry Introduction to affine and projective algebraic varieties over fields. Instructor(s): Bhargav Bharat Bhatt
Schedule
C01 T Th 01:30 PM - 02:50 PM
MAT 478(link is external) Topics In Combinatorics: Extremal Combinatorics This course will cover topics in Extremal Combinatorics including ones motivated by questions in other areas like Computer Science, Information Theory, Number Theory and Geometry. The subjects that will be covered include Graph powers, the Shannon capacity and the Witsenhausen rate of graphs, Szemeredi's Regularity Lemma and its applications in graph property testing and in the study of sets with no 3 term arithmetic progressions, the Combinatorial Nullstellensatz and its applications, the capset problem, Containers and list coloring, and related topics as time permits. Instructor(s): Noga Mordechai Alon
Schedule
C01 T Th 09:30 AM - 10:50 AM
MAT 90(link is external) Structure Theorems and Algorithms No description available Instructor(s): Maria Chudnovsky
Schedule
S01 01:00 AM - 01:00 AM
MAT 91(link is external) Topics in Geometry: Convexities No description available Instructor(s): Assaf Naor
Schedule
S01 01:00 AM - 01:00 AM
MAT 92(link is external) Birational Geometry via Toric Varieties No description available Instructor(s): Louis Esser
Schedule
S01 01:00 AM - 01:00 AM
MAT 93(link is external) Automorphic Forms and Representations No description available Instructor(s): Lue Pan
Schedule
S01 01:00 AM - 01:00 AM
MAT 94(link is external) Characteristic Classes and Applications No description available Instructor(s): Zoltán Szabó
Schedule
S01 01:00 AM - 01:00 AM
MAT 95(link is external) Random Matrix Theory II No description available Instructor(s): Jacob Shapiro
Schedule
S01 01:00 AM - 01:00 AM
MAT 983(link is external) Senior Departmental Exam
Schedule
S99 01:00 AM - 01:00 AM
MAT 984(link is external) Senior Thesis
Schedule
S99 01:00 AM - 01:00 AM
ORF 309/EGR 309/MAT 380(link is external) Probability and Stochastic Systems An introduction to probability and its applications. Topics include: basic principles of probability; Lifetimes and reliability, Poisson processes; random walks; Brownian motion; branching processes; Markov chains. Instructor(s): Ioannis Akrotirianakis
Schedule
L01 M W F 09:00 AM - 09:50 AM
P01 M 03:30 PM - 04:20 PM
P02 M 07:30 PM - 08:20 PM
P03 T 03:30 PM - 04:20 PM
P04 T 07:30 PM - 08:20 PM