Course Schedule
Spring 2019
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., digital music, sending secure emails, 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.
Instructor(s):
Adam Wade Marcus
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 433/MAT 473
Cryptography
An introduction to the theory and practice of modern cryptography, with an emphasis on the fundamental ideas. Topics covered include private key and public key encryption schemes, digital signatures, pseudorandom generators and functions, chosen ciphertext security, and some advanced topics.
Instructor(s):
Mark Landry Zhandry
L01
M W
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
01:30 PM

02:50 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):
Stanislav Yefimovic Shvartsman
C01
M W
03:00 PM

04:20 PM
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, vectors and tensors, numerical integration, analytical and numerical solution of ordinary and partial differential equations, timeseries data and the Fourier transform, and calculus of variations. 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
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):
Tatiana Katarzyna Howard, Ana Menezes
L01
T Th
03:00 PM

04:20 PM
P01
W
07:30 PM

08:50 PM
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 Michael Fickenscher, Tetiana Shcherbyna, Boyu Zhang
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 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):
Chiara Damiolini, 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
C03A
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 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):
Theodore Dimitrios Drivas, Henry Theodore Horton, Chao Li
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):
Clark Wilmer Butler, Mark Weaver McConnell, Rafael Montezuma Pinheiro Cabral, Remy van Dobben de Bruyn
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
C03A
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 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):
Andrew V Yarmola
C01
M W F
09:00 AM

09:50 AM
C01A
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
C02B
M W F
10:00 AM

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

11:50 AM
C03A
M W F
11:00 AM

11:50 AM
C03B
M W F
11:00 AM

11:50 AM
C03C
M W F
11:00 AM

11:50 AM
C03D
M W F
11:00 AM

11:50 AM
C03E
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
C04B
M W F
12:30 PM

01:20 PM
C04C
M W F
12:30 PM

01:20 PM
Schedule
MAT 215
Honors Analysis (Single Variable)
An introduction to the mathematicsal 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 Rieman integral, conditions for integrability of functions and term by term differentiation and integration of series of functions, Taylor's Theorem.
Instructor(s):
Stephen Edward McKeown
L01
M W F
12:30 PM

01:20 PM
P01
Th
03:30 PM

04:20 PM
P02
Th
07:30 PM

08:20 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):
Yunqing Tang, Ian Michael Zemke
C01
T Th
11:00 AM

12:20 PM
Schedule
MAT 218
Accelerated Honors Analysis II
Continuation of the rigorous introduction to analysis in MAT216
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 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
C02
T Th
03:00 PM

04:20 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):
Javier GómezSerrano
L01
T Th
01:30 PM

02:50 PM
P01
F
01:30 PM

02:20 PM
Schedule
MAT 346
Algebra II
Local Fields and the Galois theory of Local Fields.
Instructor(s):
ShouWu Zhang
C01
M W
01:30 PM

02:50 PM
Schedule
MAT 355
Introduction to Differential Geometry
Introduction to geometry of surfaces. Surfaces in Euclidean space, second fundamental form, minimal surfaces, geodescis, Gauss curvature, GaussBonnet formula. Then differential forms and the higherdimensional GaussBonnet, as time permits.
Instructor(s):
Otis Chodosh
L01
M W
01:30 PM

02:50 PM
L01A
F
01:30 PM

02:20 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):
Paul Douglas Seymour
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 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):
Francesc Castella
C01
M W
03:00 PM

04:20 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 447
Commutative Algebra
This course will cover the standard material in a first course on commutative algebra. Topics include: ideals in and modules over commutative rings, localization, primary decomposition, integral dependence, Noetherian rings and chain conditions, discrete valuation rings and Dedekind domains, completion; and dimension theory.
Instructor(s):
Hansheng Diao
C01
T Th
11:00 AM

12:20 PM
Schedule
MAT 468
Topics in Knot Theory, Modern Knot Invariantiants & Applications
Knot theory involves the study of smoothly embedded circles in threedimensional space. There ar lots of different techniques to study knots: combinatorial invariants, algebraic topology, hyperbolic geometry, Khovanov homology and mathematical gauge theory. This course will cover some of the modern techniques and recent developments in the field.
Instructor(s):
Zoltán Szabó
L01
T Th
01:30 PM

02:50 PM
P99
01:00 AM

01:00 AM
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
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
C01
T Th
09:30 AM

10:50 AM
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
M W F
09:00 AM

09:50 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
Schedule
C01
T Th
11:00 AM

12:20 PM