Course Schedule

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 problem-set requirements. Students will learn by doing simple examples. Instructor(s): Sheng Xu APC 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): Hans Emil Oscar Mickelin 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): Ehud Yariv 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 time-series data. The course synthesizes descriptive observations, mathematical theories, numerical methods, and engineering consequences. Instructor(s): Mikko Petteri Haataja 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): Tatiana Katarzyna Howard MAT 103 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 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. Instructor(s): Fraser Malcolm Watt Binns, Hongyi Liu, Liyang Yang 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): Tatyana Chmutova 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): Dmitry Krachun, Jennifer Li, Semon Rezchikov, Ravi Shankar 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. Instructor(s): Bjoern Bringmann, Tangli Ge, Tongmu He, Jennifer Michelle Johnson, Kimoi Kemboi, Ana Menezes, Lue Pan, John Thomas Sheridan, David Villalobos, Bogdan Zavyalov 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): Marc Aurèle Tiberius Gilles MAT 215 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 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 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 MAT 218 Multivariable Analysis and Linear Algebra II Continuation of the rigorous introduction to analysis in MAT 216 Instructor(s): Joshua Xu Wang 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): Alexandru D. Ionescu 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 MAT 346 Algebra II Local Fields and the Galois theory of Local Fields. Instructor(s): Nicholas Michael Katz MAT 355 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 MAT 375/COS 342 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 MAT 378 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 MAT 419 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 MAT 425 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 MAT 457 Algebraic Geometry Introduction to affine and projective algebraic varieties over fields. Instructor(s): Bhargav Bharat Bhatt 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 MAT 90 Structure Theorems and Algorithms No description available Instructor(s): Maria Chudnovsky MAT 91 Topics in Geometry: Convexities No description available Instructor(s): Assaf Naor MAT 92 Birational Geometry via Toric Varieties No description available Instructor(s): Louis Esser MAT 93 Automorphic Forms and Representations No description available Instructor(s): Lue Pan MAT 94 Characteristic Classes and Applications No description available Instructor(s): Zoltán Szabó MAT 95 Random Matrix Theory II No description available Instructor(s): Jacob Shapiro MAT 983 Senior Departmental Exam MAT 984 Senior Thesis 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): Ioannis Akrotirianakis