Course Schedule
Spring 2021
APC 199/MAT 199
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 problemset requirements. Students will learn by doing simple examples.
Schedule
APC 350/CEE 350/MAT 322
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):
Jiequn Han
C01
T Th
11:00 AM

12:20 PM
Schedule
COS 488/MAT 474
Introduction to Analytic Combinatorics
Analytic Combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the scientific analysis of algorithms in computer science and for the study of scientific models in many other disciplines. This course combines motivation for the study of the field with an introduction to underlying techniques, by covering as applications the analysis of numerous fundamental algorithms from computer science. The second half of the course introduces Analytic Combinatorics, starting from basic principles.
Instructor(s):
Robert Sedgewick
L01
M W
11:00 AM

12:20 PM
Schedule
MAE 305/MAT 391/EGR 305/CBE 305
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):
PierreThomas Brun
L01
01:00 AM

01:00 AM
P99
01:00 AM

01:00 AM
Schedule
MAE 306/MAT 392
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 timeseries data. The course synthesizes descriptive observations, mathematical theories, numerical methods, and engineering consequences.
Instructor(s):
Mikko Petteri Haataja
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
Schedule
MAT 100
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):
Takumi Murayama
L01
T Th
03:00 PM

04:20 PM
P01
W
07:30 PM

08:50 PM
Schedule
MAT 103
Calculus I
First semester of calculus. Topics include limits, continuity, the derivative, basic differentiation formulas and applications (curvesketching, optimization, related rates), definite and indefinite integrals, the fundamental theorem of calculus. The fall offering will emphasize applications to physics and engineering in preparation for MAT 104; the spring offering will emphasize applications to economics and life sciences, in preparation for MAT 175. In multisection calculus and linear algebra courses, students register for a time slot, not a particular section.
Instructor(s):
Tatiana Katarzyna Howard, Ana Menezes
C01
M W
01:30 PM

02:50 PM
C02
M W
08:00 PM

09:20 PM
Schedule
MAT 104
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. In multisection calculus and linear algebra courses, students register for a time slot, not a particular section. Students will be randomly allocated between available sections in their time slot prior to the beginning of classes.
Instructor(s):
Duncan Alexander McNicol Dauvergne, Eden Prywes, Maxime C.R Van De Moortel
C01
M W
08:30 AM

09:50 AM
C02
M W
10:00 AM

10:50 AM
C03
M W
11:00 AM

12:20 PM
C04
M W
01:30 PM

02:50 PM
C05
M W
07:30 PM

08:50 PM
Schedule
MAT 175
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. MAT 201/202 is strongly recommended for finance and math track economics. Students who complete 175 can continue in 202 if they wish.
Instructor(s):
Hannah Schwartz, Ian Michael Zemke, Boyu Zhang
C01
M W
08:30 AM

09:50 AM
C02
M W
10:00 AM

10:50 AM
C03
M W
11:00 AM

12:20 PM
C04
M W
01:30 PM

02:50 PM
C05
M W
07:30 PM

08:50 PM
Schedule
MAT 201
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):
Clark Wilmer Butler, Henry Theodore Horton, Sameer Subramanian Iyer, Chao Li
C01
M W
10:00 AM

10:50 AM
C02
M W
11:00 AM

12:20 PM
C03
M W
01:30 PM

02:50 PM
C04
M W
08:30 AM

09:50 AM
Schedule
MAT 202
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. MAT 201 and MAT 202 can be taken in either order, although most students take MAT 201 first.
Instructor(s):
David Boozer, Amitesh Datta, Shai Evra, Jennifer Michelle Johnson, Y. Baris Kartal, Casey Lynn Kelleher, Nicholas Fox Marshall, Mark Weaver McConnell, Joaquin Moraga, John Thomas Sheridan, Remy van Dobben de Bruyn
C01
M W
08:30 AM

09:50 AM
C02
M W
10:00 AM

10:50 AM
C03
M W
11:00 AM

12:20 PM
C04
M W
01:30 PM

02:50 PM
C05
M W
07:00 AM

08:20 AM
Schedule
MAT 204
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):
Amitesh Datta
C01
M W
08:30 AM

09:50 AM
C02
M W
10:00 AM

10:50 AM
C03
M W
11:00 AM

12:20 PM
C04
M W
01:30 PM

02:50 PM
C05
M W
07:00 AM

08:20 AM
C06
M W
07:40 AM

08:20 AM
C07
M W
03:00 PM

04:20 PM
Schedule
MAT 215
Single Variable Analysis with an Introduction to Proofs
An introduction to the mathematical discipline of analysis, to prepare for higherlevel course work in the department. Topics include rigorous epsilondelta treatment of limits, convergence, and uniform convergence of sequences and series. Continuity, uniform continuity, and differentiability of functions. The HeineBorel 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):
Alexandru D. Ionescu
C01
M W
11:00 AM

12:20 PM
C02
M W
01:30 PM

02:50 PM
Schedule
MAT 217
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 CayleyHamilton theorem, Jordan form, the spectral theorem for normal transformations, bilinear and quadratic forms.
Instructor(s):
Kenneth Brian Ascher, Andrew V Yarmola
L01
T Th
11:00 AM

12:20 PM
P01
F
11:00 AM

11:50 AM
Schedule
MAT 218
Multivariable Analysis and Linear Algebra II
Continuation of the rigorous introduction to analysis in MAT 216
Instructor(s):
Alan Chang
C01
T Th
11:00 AM

12:20 PM
C02
T Th
01:30 PM

02:50 PM
Schedule
MAT 325
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):
Yakov Mordechai ShlapentokhRothman
C01
T Th
11:00 AM

12:20 PM
C02
T Th
01:30 PM

02:50 PM
Schedule
MAT 330
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
L01
T Th
01:30 PM

02:50 PM
Schedule
MAT 346
Algebra II
This course is a continuation of MAT 345 and its introduction to representation theory. We will cover semisimple algebras, application to group theory, Artin's and Brauer's theorems characterizing representations over the complex numbers, rationality questions, and Brauer's theory of representations mod p. This will lead to one or more advanced topics in finite groups or Lie algebras.
Instructor(s):
Gabriele Di Cerbo
C01
M W
11:00 AM

12:20 PM
Schedule
MAT 355
Introduction to Differential Geometry
Introduction to geometry of surfaces. Surfaces in Euclidean space: first fundamental form, second fundamental form, geodesics, Gauss curvature, GaussBonnet Theorem. Minimal surfaces in the Euclidean space.
Instructor(s):
Fernando Codá Marques
L01
M W
03:00 PM

04:20 PM
Schedule
MAT 375/COS 342
Introduction to Graph Theory
The fundamental theorems and algorithms of graph theory. Topics include: connectivity, matchings, graph coloring, planarity, the fourcolor theorem, extremal problems, network flows, and related algorithms.
Instructor(s):
Maria Chudnovsky
C01
M W
11:00 AM

12:20 PM
Schedule
MAT 378
Theory of Games
Games in extensive form, pure and behavioral strategies; normal form, mixed strategies, equilibrium points; coalitions, characteristicfunction form, imputations, solution concepts; related topics and applications.
Instructor(s):
Jonathan Michael Fickenscher
C01
T Th
11:00 AM

12:20 PM
Schedule
MAT 385
Probability Theory
An introduction to probability theory. The course begins with the measure theoretic foundations of probability theory, expectation, distributions and limit theorems. Further topics include concentration of measure, Markov chains and martingales.
Instructor(s):
Allan M. Sly
C01
M W
01:30 PM

02:50 PM
Schedule
MAT 415
Analytic Number Theory
An introduction to classical results in analytic number theory, presenting fundamental theorems with detailed proofs and highlighting the tight connections between them. Topics covered might include: the prime number theorem, Dirichlet Lfunctions, zerofree regions, sieve methods, representation by quadratic forms, and Gauss sums.
Instructor(s):
Peter Clive Sarnak
C01
M W
01:30 PM

02:50 PM
Schedule
MAT 419
Topics in Number Theory: Algebraic Number Theory
Course on algebraic number theory. Topics covered include number fields and their integer rings, class groups, zeta and Lfunctions.
Instructor(s):
Christopher McLean Skinner
C01
T Th
11:00 AM

12:20 PM
Schedule
MAT 429
Topics in Analysis: Distribution Theory, PDE & Basic Inequalities of Analysis
Introduction to Geometric Partial Differential Equations. The course will review some basic topics in Elliptic theory and give a comprehensive introduction to linear and nonlinear wave equations with applications to relativistic filed theories including General Relativity.
Instructor(s):
Sergiu Klainerman
C01
T Th
11:00 AM

12:20 PM
Schedule
MAT 449
Topics in Algebra: Representation Theory
An introduction to representation theory of Lie groups and Lie algebras. The goal is to cover roughly the first half of Knapp's book.
Instructor(s):
ShouWu Zhang
C01
M W
11:00 AM

12:20 PM
Schedule
MAT 457
Algebraic Geometry
Introduction to affine and projective algebraic varieties over fields.
Instructor(s):
Chenyang Xu
C01
M W
01:30 PM

02:50 PM
Schedule
MAT 478
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
C01
T Th
01:30 PM

02:50 PM
Schedule
MAT 490/APC 490
Mathematical Introduction to Machine Learning
This course gives a mathematical introduction to machine learning. There are three major components in this course. (1) Machine learning models (kernel methods, shallow and deep neural network models) for both supervised and unsupervised learning problems. (2) Optimization algorithms (gradient descent, stochastic gradient descent, EM). (3) Mathematical analysis of these models and algorithms.
Instructor(s):
Weinan E
C01
T Th
09:30 AM

10:50 AM
Schedule
ORF 309/EGR 309/MAT 380
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):
Ramon van Handel
L01
01:00 AM

01:00 AM
P01
F
01:30 PM

02:20 PM
Schedule
PHY 403/MAT 493
Mathematical Methods of Physics
Mathematical methods and terminology which are essential for modern theoretical physics. These include some of the traditional techniques of mathematical analysis, but also more modern tools such as group theory, functional analysis, calculus of variations, nonlinear operator theory and differential geometry. Mathematical theories are not treated as ends in themselves; the goal is to show how mathematical tools are developed to solve physical problems.
Instructor(s):
Bogdan Andrei Bernevig
L01
01:00 AM

01:00 AM
P99
01:00 AM

01:00 AM
Schedule
C01
T Th
11:00 AM

12:20 PM