Course Schedule
Fall 2018
COS 487/MAT 407
Theory of Computation
Introduction to computability and complexity theory. Topics will include models of computation such as automata, and Turing machines; decidability and decidability; computational complexity; P, NP, and NP completeness; others.
Instructor(s):
Zeev Dvir
Schedule
EGR 191/MAT 191/PHY 191
An Integrated Introduction to Engineering, Mathematics, Physics
Taken concurrently with EGR/MAT/PHY 192, this course offers an integrated presentation of the material from PHY 103 (General Physics: Mechanics and Thermodynamics) and MAT 201 (Multivariable Calculus) with an emphasis on applications to engineering. Physics topics include: mechanics with applications to fluid mechanics; wave phenomena; and thermodynamics.
Instructor(s):
James D. Olsen
L01
T Th
01:30 PM

02:50 PM
P01
M
07:30 PM

08:20 PM
P02
T
07:30 PM

08:20 PM
Schedule
EGR 192/MAT 192/PHY 192/APC 192
An Integrated Introduction to Engineering, Mathematics, Physics
Taken concurrently with EGR/MAT/PHY 191, this course offers an integrated presentation of the material from PHY 103 (General Physics: Mechanics and Thermodynamics) and MAT 201 (Multivariable Calculus) with an emphasis on applications to engineering. Math topics include: vector calculus; partial derivatives and matrices; line integrals; simple differential equations; surface and volume integrals; and Green's, Stokes', and divergence theorems.
Instructor(s):
Otis Chodosh
L01
M
11:00 AM

11:50 AM
P01
M W F
09:00 AM

09:50 AM
P02
M W F
10:00 AM

10:50 AM
P03
M W F
10:00 AM

10:50 AM
B01
T
01:30 PM

04:20 PM
B02
W
01:30 PM

04:20 PM
B03
M
01:30 PM

04:20 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 standard problems in this field.
Instructor(s):
Howard A. Stone
L01
W
11:00 AM

11:50 AM
P01
T Th
09:00 AM

09:50 AM
P02
T Th
10:00 AM

10:50 AM
Schedule
MAT 100
Calculus Foundations
An intensive and rigorous treatment of algebra and trigonometry as preparation for further courses in calculus or statistics. Topics include functions and their graphs, equations involving polynomial and rational functions, exponentials, logarithms and trigonometry.
Instructor(s):
Tatiana Katarzyna Howard, Jennifer Michelle Johnson
L01
M W F
11:00 AM

11:50 AM
P01
T
02:30 PM

03:20 PM
P02
T
03:30 PM

04:20 PM
P03
T
07:30 PM

08:20 PM
P04
W
01:30 PM

02:20 PM
P05
W
07:30 PM

08:20 PM
P06
Th
02:30 PM

03:20 PM
P07
Th
03:30 PM

04:20 PM
P08
Th
07:30 PM

08:20 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.
Instructor(s):
Jonathan Michael Fickenscher
C01
M W F
10:00 AM

10:50 AM
Schedule
MAT 104
Calculus II
Continuation of MAT103. 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):
Jonathan Hanselman
C01
M W F
09:00 AM

09:50 AM
C02
M W F
10:00 AM

10:50 AM
C03
M W F
11:00 AM

11:50 AM
C04
M W F
12:30 PM

01:20 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.
Instructor(s):
Jennifer Michelle Johnson
C01
M W F
09:00 AM

09:50 AM
C02
M W F
10:00 AM

10:50 AM
C03
M W F
11:00 AM

11:50 AM
C04
M W F
12:30 PM

01:20 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):
Gabriele Di Cerbo
C01
M W F
10:00 AM

10:50 AM
C02
M W F
11:00 AM

11:50 AM
C03
M W F
12:30 PM

01:20 PM
Schedule
MAT 202
Linear Algebra with Applications
Companion course to MAT201. 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):
Oanh Thi Hoang Nguyen
C01
M W F
09:00 AM

09:50 AM
C02
M W F
10:00 AM

10:50 AM
C03
M W F
11:00 AM

11:50 AM
C04
M W F
12:30 PM

01:20 PM
Schedule
MAT 203
Advanced Vector Calculus
Vector spaces, limits, derivatives of vectorvalued functions, Taylor's formula, Lagrange multipliers, double and triple integrals, change of coordinates, surface and line integrals, generalizations of the fundamental theorem of calculus to higher dimensions. More abstract than 201 but more concrete than 218. Recommended for prospective physics majors and others with a strong interest in applied mathematics.
Instructor(s):
Tetiana Shcherbyna
C01
M W F
09:00 AM

09:50 AM
C02
M W F
10:00 AM

10:50 AM
C02A
M W F
10:00 AM

10:50 AM
C03
M W F
11:00 AM

11:50 AM
C04
M W F
12:30 PM

01:20 PM
C04A
M W F
12:30 PM

01:20 PM
Schedule
MAT 214
Numbers, Equations, and Proofs
An introduction to classical number theory, to prepare for higherlevel courses in the department. Topics include Pythagorean triples and sums of squares, unique factorization, Chinese remainder theorem, arithmetic of Gaussian integers, finite fields and cryptography, arithmetic functions and quadratic reciprocity. There will be a topic, chosen by the instructor, from more advanced or more applied number theory: possibilities include padic numbers, cryptography, and Fermat's Last Theorem. This course is suitable both for students preparing to enter the Mathematics Department and for nonmajors interested in exposure to higher mathematics.
L01
M W F
11:00 AM

11:50 AM
L02
M W F
12:30 PM

01:20 PM
P01
Th
07:30 PM

08:20 PM
P02
Th
03:30 PM

04:20 PM
Schedule
MAT 215
Honors Analysis (Single Variable)
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):
Charles Louis Fefferman, Javier GómezSerrano
C01
T Th
11:00 AM

12:20 PM
Schedule
MAT 216
Accelerated Honors Analysis I
Rigorous theoretical introduction to the foundations of analysis in one and several variables: basic set theory, vector spaces, metric and topological spaces, continuous and differential mapping between ndimensional real vector spaces. Normally followed by MAT218.
Instructor(s):
Robert Clifford Gunning
C01
T Th
11:00 AM

12:20 PM
C02
T Th
01:30 PM

02:50 PM
Schedule
MAT 320
Introduction to Real Analysis
Introduction to real analysis, including the theory of Lebesgue measure and integration on the line and ndimensional space, and the theory of Fourier series and Hilbert spaces.
C01
T Th
03:00 PM

04:20 PM
Schedule
MAT 321/APC 321
Numerical Methods
Introduction to numerical methods with emphasis on algorithms, applications and numerical analysis. Topics covered include solution of nonlinear equations; numerical differentiation, integration, and interpolation; direct and iterative methods for solving linear systems; computation of eigenvectors and eigenvalues; and approximation theory. Lectures include mathematical proofs where they provide insight and are supplemented with numerical demos using MATLAB.
Instructor(s):
Nicolas Boumal
C01
T Th
11:00 AM

12:20 PM
Schedule
MAT 335
Analysis II: Complex Analysis
Study of functions of a complex variable, with emphasis on interrelations with other parts of mathematics. Cauchy's theorems, singularities, contour integration, power series, infinite products. The gamma and zeta functions and the prime number theorem. Elliptic functions, theta functions, Jacobi's triple product and combinatorics. This course is the second semester of a foursemester sequence, but may be taken independently of the other semesters.
Instructor(s):
Assaf Naor
L01
T Th
01:30 PM

02:50 PM
L01
F
01:30 PM

02:20 PM
Schedule
MAT 340
Applied Algebra
An applied algebra course that integrates the basics of theory and modern applications for students in MAT, APC, PHY, CBE, COS, ELE. This course is intended for students who have taken a semester of linear algebra and who have an interest in a course that treats the structures, properties and application of groups, rings, and fields. Applications and algorithmic aspects of algebra will be emphasized throughout.
Instructor(s):
Mark Weaver McConnell
L01
T Th
01:30 PM

02:50 PM
L01
F
01:30 PM

02:20 PM
Schedule
MAT 345
Algebra I
This course will be devoted to Galois theory, developing the necessary group theory, including the Sylow theorems, and algebra from scratch.
L01
T Th
03:00 PM

04:20 PM
Schedule
MAT 350
Differential Manifolds
Fundamentals of multivariable analysis and calculus on manifolds. Topics to be covered include: differentiation and integration in multiple dimensions; smooth manifolds; vector fields and differential forms; stokes' theorem; de Rham cohomology; Frobenius' theorem on integrability of plane fields. This course will serve as a preparation for advanced courses in differential geometry and topology.
Instructor(s):
Paul ChienPing Yang
C01
T Th
03:00 PM

04:20 PM
Schedule
MAT 365
Topology
Introduction to pointset topology, the fundamental group, covering spaces, methods of calculation and applications.
Instructor(s):
Zoltán Szabó
C01
T Th
11:00 AM

12:20 PM
Schedule
MAT 377/APC 377
Combinatorial Mathematics
Introduction to combinatorics, a fundamental mathematical discipline as well as an essential component of many mathematical areas. While in the past many of the basic combinatorial results were at first obtained by ingenuity and detailed reasoning, modern theory has grown out of this early stage and often relies on deep, welldeveloped tools. Topics include Ramsey Theory, Turan Theorem and Extremal Graph Theory, Probabilistic Argument, Algebraic Methods and Spectral Techniques. Showcases the gems of modern combinatorics.
Instructor(s):
Noga Mordechai Alon
C01
M W
01:30 PM

02:50 PM
Schedule
MAT 419
Topics in 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 SwinnertonDyer conjeture.
C01
T Th
11:00 AM

12:20 PM
Schedule
MAT 425
Analysis III: Integration Theory and Hilbert Spaces
The theory of Lebesgue integration in ndimensional 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 foursemester sequence, but may be taken independently of the other semesters.
Instructor(s):
Mihalis Dafermos
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):
Sophie Marguerite Morel
C01
T Th
01:30 PM

02:50 PM
Schedule
MAT 477
Advanced Graph Theory
Advanced course in Graph Theory. Further study of graph coloring, graph minors, perfect graphs, graph matching theory. Topics covered include: stable matching theorem, list coloring, chiboundedness, excluded minors and average degree, Hadwiger's conjecture, the weak perfect graph theorem, operations on perfect graphs, and other topics as time permits.
Instructor(s):
Maria Chudnovsky
C01
M W
11:00 AM

12:20 PM
Schedule
MAT 490/APC 390
Mathematical Introduction to Machine Learning
This course gives a mathematical introduction to machine learning. It is not about proving theorems in machine learning, but rather a unified understanding of the models and algorithms used in machine learning. It begins with a simple introduction to supervised and unsupervised learning, including regression, classification, density estimation, clustering, and dimension reduction. Simple models such as linear regression, support vector machines, and kmeans will be introduced, followed by focus on deep learning.
L01
T Th
11:00 AM

12:20 PM
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):
Mykhaylo Shkolnikov
C01
M W
11:00 AM

12:20 PM
Schedule
L01
M W F
11:00 AM

11:50 AM
P01
M
07:30 PM

08:20 PM
P02
T
07:30 PM

08:20 PM
P03
M
03:30 PM

04:20 PM
P04
T
03:30 PM

04:20 PM
P05
M
03:30 PM

04:20 PM
P06
T
03:30 PM

04:20 PM