Mathematics

Program Offerings

Offering type
A.B.

Most first-year students and sophomores interested in science, engineering or finance take courses from the standard calculus and linear algebra sequence 103-104-201-202, which emphasizes concrete computations over more theoretical considerations. Note that 201 and 202 can be taken in either order.

Students who are not prepared to begin with 103 may take 100, an introduction to calculus with pre-calculus review. 

Prospective economics majors can minimally fulfill their mathematics prerequisites with (100)-103-175. Note that 175 covers selected topics from 201, with biology and economics applications in mind. It is recommended that prospective math-track economics/finance majors take the standard sequence 103-104-201-202 instead of 175.

More mathematically inclined students, especially prospective physics majors, may opt to replace 201-202 with 203-204, for greater emphasis on theory and more challenging computational problems.

Prospective mathematics majors must take at least one course introducing formal mathematical argument and rigorous proofs. The recommended first-year sequence for prospective majors is 215-217-300. Prospective majors who already have substantial experience with university-level proof-based analysis courses may consider the accelerated sequence 216-218 instead. Other possible sequences for prospective majors include 210-215-217-300 or 214-204-203 and 203-204-215, although the latter two are relatively rare. Note that 203 and 204 can be taken in either order. Some of our successful majors became interested in mathematics as a major after taking courses at the 100 level. As an alternative to 104, and as a lead-in to MAT215, students may opt to take 210 in the fall, followed by 215 in the spring. Such students should consult with the junior adviser or the associate director of undergraduate studies as soon as possible to plan a course of study.

Placement Guidelines

Students who need placement advice about 214, 215, or 216 should consult the Department of Mathematics home page (the "Undergraduate" tab has a section on placement) or contact Professor McConnell, the junior adviser.

Students with little or no background in calculus, but with strong pre-calculus skills, should take 103. Alternatively, 100 offers intensive pre-calculus review, along with an introduction to the main ideas of calculus, as preparation for 103. To succeed in 104 or 175, a background in differential calculus at the level of a 5 on the BC Advanced Placement Examination is advised. Students with a stronger calculus preparation in differential and integral calculus, as well as infinite series, may opt to start in 201. Students who possess, in addition, a particularly strong interest in mathematics as well as a SAT mathematics score of at least 750 may opt for 203 or 210 or 214 or 215 or 216 instead.

The placement workshops for incoming students at orientation are designed to help students consider all these issues in order to make a good initial self-placement in the mathematics curriculum, which can then be adjusted during drop/add if necessary.

Goals for Student Learning

Mathematics is a discipline inseparable from scientific and philosophical inquiry. The rigorous and logical thinking that characterizes mathematics is an essential tool for theory-building of any kind because its clarity and precision expose hidden assumptions, inner inconsistencies and deep structural similarities in problems that seem unrelated on the surface. Our courses cover a wide variety of well-established mathematical knowledge that is actively under development by today’s mathematicians and that offers fundamental tools for scientists and engineers of all kinds.

Students begin their work in the department with a thorough training in rigorous logical reasoning and mathematical proofs in the context of analysis and linear algebra. Next, they complete a survey of the main areas of modern mathematics by completing core courses in real and complex analysis, in algebra and in geometry/topology or discrete mathematics. Then students are free to take courses exploring a wide variety of topics in both pure and applied mathematics to acquire a good general knowledge of the main areas of current mathematical work.

In the independent work, students learn how to move beyond the classical knowledge found in textbooks to explore contemporary research literature through collaboration with their peers and with active researchers in mathematics or applied fields. Through this collaboration, students:

  • Learn how to join a scholarly discussion in progress to orient themselves in a rapidly developing area of research.
  • Build on their broad general knowledge of mathematics and logical reasoning skills in order to develop a working knowledge of a significant area of contemporary mathematics via the research literature.
  • Learn to identify interesting problems they want to investigate and develop their own ideas about how to carry out those investigations.
  • Learn to come up with a complete argument of their own, adapting and expanding ideas and techniques from various sources, as needed.
  • Develop mastery of rigorous logical thinking by constructing complete and correct arguments.
  • Develop mastery of clear mathematical exposition in a manner that allows and invites dialog with other scholars in the intended audience, where important definitions and theorems are clearly explained and contributions of other scholars are properly acknowledged.

The program produces critical and creative thinkers with a broad general knowledge of contemporary mathematics and with the analytic and expository skills needed for collaborative problem-solving in any quantitative setting.

Advanced Placement

Incoming first-year students who report a score of 5 on the BC Advanced Placement Examination (or a 7 on the IC [higher level] math examination, or an A on the British A-level math exam) will receive one unit of advanced placement credit for MAT103. For more information, please consult the website of the Office of the Dean of the College.

One unit of advanced placement credit is provisionally granted when a student enrolls in MAT 104 or 175 in the fall term of their first year. Two units of advanced placement credit are provisionally granted when a student enrolls in MAT 201, 203, 215 or 216 in the fall term of their first year. Provisional credit will be converted to advanced placement credit upon successful completion of the relevant course.

Prerequisites

To major in mathematics, students need a strong foundation in linear algebra and analysis, in both one and several variables, as well as experience in understanding and writing rigorous mathematical proofs. Generally, prospective majors with a very strong background in calculus are strongly recommended to start in 215, followed by 217 and 300. Prospective majors with extensive prior experience with calculus and rigorous proofs can start in 216, followed by 218. Students with an interest in rigorous proofs may start in 210 or 214 and then continue to the 215-217-300 sequence.

Students who are undecided, or students who are initially planning to major in a different quantitative discipline, may opt instead to begin their calculus and linear algebra work in the 203-204 or the 103-104-201-202 sequences, where proofs are not an emphasis. From these sequences, prospective mathematics majors should consult with the junior adviser or the associate director of undergraduate studies early on, in order to plan a program that includes as much of the 215-217-300 sequence as possible.

Most majors begin taking courses at the 300 level by the second semester of sophomore year, in preparation for their junior independent work. The junior adviser meets with students individually to help them plan a course of study. A student’s path through the upper-division courses will naturally depend on their long-term goals and prior experience.

Further information for prospective majors is available on the department home page.

Program of Study

Students must complete four core requirements:

  • one course in real analysis (e.g., 300 or 320 or 325 or 425 or 385)
  • one course in complex analysis (e.g., 330 or 335)
  • one course in algebra (e.g., 340 or 345)
  • one course in geometry or topology (e.g., 355 or 365 or 560)

It is recommended that students complete some of these core requirements by the end of their sophomore year. Completing these core courses early allows for more options for junior and senior independent work.

Note: One course in discrete mathematics (e.g., 375, 377, or 378) can replace the geometry/topology core requirement, if desired.

In addition to the four core requirements, students must complete an additional four courses at the 300 level or higher, up to three of which may be cognate courses outside the mathematics department, with permission from the junior or senior advisers or the director of undergraduate studies. No more than two of the eight courses may be reading courses.

The departmental grade (the average grade of the eight departmental courses) together with grades and reports on independent work is the basis on which honors and prizes are awarded upon graduation.

Students should refer to Course Offerings to determine which courses are offered in a given term. Programs of study in various fields of pure mathematics and applied mathematics are available. Appropriate plans of study may be arranged for students interested in specialized related fields such as physics, the biological sciences, finance and computer science, for example. For students interested in these areas, a coherent program containing up to three courses in a cognate field may be approved.

Independent Work

All departmental students engage in independent work, supervised by a member of the department chosen in consultation with a departmental adviser. The junior year independent work generally consists of participating actively in a junior seminar in both the fall and spring semesters. Alternatively, a student may opt to replace one junior seminar with supervised reading in a special subject and then writing a paper based on that reading. The independent work in the senior year centers on writing a senior thesis. A substantial percentage of our majors work with faculty in other departments on their senior project.

Senior Departmental Examination

Each senior takes an oral examination based on the senior thesis and the broader subfield to which it contributes. A departmental committee conducts the examination in May.

Faculty

  • Chair

    • Igor Rodnianski
  • Associate Chair

    • János Kollár
  • Director of Undergraduate Studies

    • Jennifer M. Johnson (associate)
    • János Kollár
  • Director of Graduate Studies

    • Lue Pan (associate)
    • Chenyang Xu
  • Professor

    • Michael Aizenman
    • Noga M. Alon
    • Manjul Bhargava
    • Sun-Yung A. Chang
    • Maria Chudnovsky
    • Fernando Codá Marques
    • Peter Constantin
    • Mihalis Dafermos
    • Zeev Dvir
    • Charles L. Fefferman
    • David Gabai
    • June E. Huh
    • Alexandru D. Ionescu
    • Nicholas M. Katz
    • Sergiu Klainerman
    • János Kollár
    • Emmy Murphy
    • Assaf Naor
    • Peter Steven Ozsváth
    • John V. Pardon
    • Igor Rodnianski
    • Peter C. Sarnak
    • Paul Seymour
    • Amit Singer
    • Christopher M. Skinner
    • Allan M. Sly
    • Zoltán Szabó
    • Chenyang Xu
    • Paul C. Yang
    • Shou-Wu Zhang
  • Assistant Professor

    • Matija Bucic
    • Jonathan Hanselman
    • Casey L. Kelleher
    • Ana Menezes
    • Evita Nestoridi
    • Lue Pan
    • Jacob Shapiro
    • Jakub Witaszek
    • Ian Zemke
    • Ruobing Zhang
  • Associated Faculty

    • John P. Burgess, Philosophy
    • René A. Carmona, Oper Res and Financial Eng
    • Bernard Chazelle, Computer Science
    • Hans P. Halvorson, Philosophy
    • William A. Massey, Oper Res and Financial Eng
    • Frans Pretorius, Physics
    • Robert E. Tarjan, Computer Science
    • Robert J. Vanderbei, Oper Res and Financial Eng
    • Ramon van Handel, Oper Res and Financial Eng
  • Instructor

    • Louis Esser
    • Tangli Ge
    • Lili He
    • Dmitry Krachun
    • Jennifer Li
    • Hongyi Liu
    • Anubhav Mukherjee
    • Jean Pierre Mutanguha
    • Semon Rezchikov
    • Ravi Shankar
    • Artane Siad
    • Liyang Yang
    • Mingjia Zhang
  • University Lecturer

    • Jennifer M. Johnson
  • Senior Lecturer

    • Jonathan M. Fickenscher
    • Mark W. McConnell
  • Lecturer

    • Fraser M. Binns
    • David Boozer
    • Tatyana Chmutova
    • Giorgio Cipolloni
    • Federico Glaudo
    • Xiaoyu He
    • Tatiana K. Howard
    • Dominique Kemp
    • Justin Lacini
    • Samuel Mundy
    • Andrew O'Desky
    • Samuel Pérez-Ayala
    • John T. Sheridan
    • David Villalobos
    • Ruiyi Yang
  • Visiting Professor

    • Bhargav B. Bhatt
  • Visiting Lecturer with Rank of Professor

    • Camillo De Lellis
    • Helmut H. Hofer
    • Akshay Venkatesh

For a full list of faculty members and fellows please visit the department or program website.

Courses

MAT 100 - Calculus Foundations Fall/Spring QCR

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. Staff

MAT 102 - Survey of Calculus Not offered this year QCR

One semester survey of the major concepts and computational techniques of calculus including limits, derivatives and integrals. Emphasis on basic examples and applications of calculus including approximation, differential equations, rates of change and error estimation for students who will take no further calculus. Prerequisites: MAT100 or equivalent. Restrictions: Cannot receive course credit for both MAT103 and MAT102. Provides adequate preparation for MAT175. Three classes. Staff

MAT 103 - Calculus I Fall/Spring QCR

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. Prerequisite: MAT100 or equivalent. Staff

MAT 104 - Calculus II Fall/Spring QCR

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. Prerequisite: MAT103 or equivalent. Staff

MAT 175 - Mathematics for Economics/Life Sciences Fall/Spring QCR

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. Students preparing for math track econometrics and finance courses need MAT201/202 instead. Students who complete 175 can continue in 202 if they wish. Staff

MAT 191 - An Integrated Introduction to Engineering, Mathematics, Physics (also EGR 191/PHY 191) Not offered this year SEL

MAT 192 - An Integrated Introduction to Engineering, Mathematics, Physics (also APC 192/EGR 192/PHY 192) Not offered this year QCR

MAT 199 - Math Alive (also APC 199) Spring QCR

MAT 201 - Multivariable Calculus Fall/Spring QCR

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. Prerequisite: 104 or equivalent. Staff

MAT 202 - Linear Algebra with Applications Fall/Spring QCR

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. Prerequisite: MAT103 or equivalent. Staff

MAT 203 - Advanced Vector Calculus Fall QCR

Vector spaces, limits, derivatives of vector-valued 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 216/218. Recommended for prospective physics majors and others with a strong interest in applied mathematics. Prerequisite: MAT104 or equivalent. D. Gabai

MAT 204 - Advanced Linear Algebra with Applications Spring QCR

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 equivalent. Staff

MAT 214 - Numbers, Equations, and Proofs Fall QCR

An introduction to classical number theory to prepare for higher-level 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 from more advanced or more applied number theory such as p-adic numbers, cryptography, and Fermat's Last Theorem. This course is suitable both for students preparing to enter the mathematics department and for non-majors interested in exposure to higher mathematics. Staff

MAT 215 - Single Variable Analysis with an Introduction to Proofs Fall/Spring QCR

An introduction to the mathematical discipline of analysis, to prepare for higher-level course work in the department. Topics include the 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. Staff

MAT 217 - Honors Linear Algebra Spring QCR

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. Staff

MAT 218 - Multivariable Analysis and Linear Algebra II Spring QCR

Continuation of Multivariable Analysis and Linear Algebra I (MAT 216) from the fall. A rigorous course in analysis with an emphasis on proof rather than applications. Topics include metric spaces, completeness, compactness, total derivatives, partial derivatives, inverse function theorem, implicit function theorem, Riemann integrals in several variables, Fubini. See the department website for details: http://www.math.princeton.edu. Staff

MAT 300 - Multivariable Analysis I Fall QCR

Continuation of Single Variable Analysis (MAT215) and Honors Linear Algebra (MAT217) needed to prepare for further work in differential geometry, analysis and topology. Calculus on manifolds: Introduces the concept of differentiable manifold, develops the notions of vector fields and differential forms, Stokes' theorem and the de Rham complex. The basic existence theorem in ODEs is used to prove the Frobenius theorem on integrability of plane fields. The intent is to provide the preparation for the courses in differential geometry and topology. Staff

MAT 305 - Mathematical Logic Not offered this year QCR

A development of logic from the mathematical viewpoint, including propositional and predicate calculus, consequence and deduction, truth and satisfaction, the Goedel completeness and incompleteness theorems. Applications to model theory, recursion theory, and set theory as time permits. Some underclass background in logic or in mathematics is recommended. Staff

MAT 306 - Set Theory (also PHI 323) Fall QCR

MAT 320 - Introduction to Real Analysis Fall QCR

Introduction to real analysis, including the theory of Lebesgue measure and integration on the line and n-dimensional space and the theory of Fourier series. Prerequisite: MAT201 and MAT202 or equivalent. Staff

MAT 323 - Topics in Mathematical Modeling (also APC 323) Not offered this year QCR

Draws problems from the sciences and engineering for which mathematical models have been developed and analyzed to describe, understand and predict natural and man-made phenomena. Emphasizes model building strategies, analytical and computational methods, and how scientific problems motivate new mathematics. This interdisciplinary course in collaboration with Molecular Biology, Psychology and the Program in Neuroscience is directed toward upper class undergraduate students and first-year graduate students with knowledge of linear algebra and differential equations. Staff

MAT 325 - Analysis I: Fourier Series and Partial Differential Equations Spring QCR

Basic facts about Fourier Series, Fourier Transformations, and applications to the classical partial differential equations will be covered. Also Fast Fourier Transforms, Finite Fourier Series, Dirichlet Characters, and applications to properties of primes. Prerequisites: 215, 218, or permission of instructor. Staff

MAT 330 - Complex Analysis with Applications Spring QCR

The theory of functions of one complex variable, covering power series expansions, residues, contour integration, and conformal mapping. Although the theory will be given adequate treatment, the emphasis of this course is the use of complex analysis as a tool for solving problems. Prerequisite: MAT201 and MAT202 or equivalent. Staff

MAT 335 - Analysis II: Complex Analysis Fall QCR

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. An overall view of Special Functions via the hypergeometric series. This course is the second semester of a four-semester sequence, but may be taken independently of the other semesters. Staff

MAT 345 - Algebra I Fall QCR

This course will cover the basics of symmetry and group theory, with applications. Topics include the fundamental theorem of finitely generated abelian groups, Sylow theorems, group actions, and the representation theory of finite groups, rings and modules. Staff

MAT 346 - Algebra II Spring QCR

Continuation of MAT345. Further develop knowledge of algebraic structures by exploring examples that connect to higher mathematics. Staff

MAT 355 - Introduction to Differential Geometry Spring QCR

Introduction to geometry of surfaces. Surfaces in Euclidean space, second fundamental form, minimal surfaces, geodesics, Gauss curvature, Gauss-Gonnet formula, uniformization of surfaces, elementary notions of contact geometry. Prerequisite: MAT218 or MAT300, or MAT203 or equivalent. F. Codá Marques

MAT 365 - Topology Fall QCR

Introduction to point-set topology, the fundamental group, covering spaces, methods of calculation and applications. Prerequisite: MAT202 or 204 or 218 or equivalent. Z. Szabó

MAT 375 - Introduction to Graph Theory (also COS 342) Spring QCR

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. Prerequisite: MAT202 or 204 or 217 or equivalent. P. Seymour

MAT 377 - Combinatorial Mathematics (also APC 377) Fall QCR

Combinatorics is the study of enumeration and structure of discrete objects. These structures are widespread throughout mathematics, including geometry, topology and algebra, as well as computer science, physics and optimization. This course will give an introduction to modern techniques in the field, and how they relate to objects such as polytopes, permutations and hyperplane arrangements. N. Alon

MAT 378 - Theory of Games Spring QCR

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. Prerequisite: MAT202 or 204 or 217 or equivalent. MAT215 or equivalent is recommended. Staff

MAT 380 - Probability and Stochastic Systems (also EGR 309/ORF 309) Fall/Spring

MAT 385 - Probability Theory Fall QCR

Sequence of independent trials, applications to number theory and analysis, Monte Carlo method. Markov chains, ergodic theorem for Markov chains. Entropy and McMillan theorem. Random walks, recurrence and non-recurrence; connection with the linear difference equations. Strong laws of large numbers, random series and products. Weak convergence of probability measures, weak Helly theorems, Fourier transforms of distributions. Limit theorems of probability theory. Prerequisite: MAT203 or 218 or equivalent. A. Sly

MAT 391 - Mathematics in Engineering I (also CBE 305/EGR 305/MAE 305) Fall/Spring QCR

MAT 392 - Mathematics in Engineering II (also MAE 306) Spring

MAT 393 - Mathematical Programming Not offered this year QCR

Linear programs, duality, Dantzig's simplex method; theory of dual linear systems; matrix games, von Neumann's minimax theorem, simplex solution; algorithms for assignment, transport, flow; brief introduction to nonlinear programming. Staff

MAT 407 - Theory of Computation (also COS 487) Fall

MAT 419 - Topics in Number Theory Fall/Spring QCR

Topics introducing various aspects of number theory, including analytic and algebraic number theory, L-functions, and modular forms. See Course Offerings listing for topic details. Prerequisites: MAT 215, 345, 346 or equivalent. Staff

MAT 425 - Analysis III: Integration Theory and Hilbert Spaces Spring QCR

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. Prerequisites: MAT215 or 218 or equivalent. Staff

MAT 427 - Ordinary Differential Equations Not offered this year QCR

Introduction to the study of ordinary differential equations; explicit solutions, general properties of solutions, and applications. Topics include explicit solutions of some non-linear equations in two variables by separation of variables and integrating factors, explicit solution of simultaneous linear equations with constant coefficients, explicit solution of some linear equations with variable forcing term by Laplace transform methods, geometric methods (description of the phase portrait), and the fundamental existence and uniqueness theorem. Staff

MAT 429 - Topics in Analysis Not offered this year QCR

Introduction to incompressible fluid dynamics. The course will give an introduction to the mathematical theory of the Euler equations, the fundamental partial differential equation arising in the study of incompressible fluids. We will discuss several topics in analysis that emerge in the study of these equations: Lebesgue and Sobolev spaces, distribution theory, elliptic PDEs, singular integrals, and Fourier analysis. Content varies from year to year. See Course Offerings listing for topic details. Staff

MAT 449 - Topics in Algebra Fall QCR

Topics in algebra selected from areas such as representation theory of finite groups and the theory of Lie algebras. Prerequisite: MAT 345 or MAT 346. Staff

MAT 459 - Topics in Geometry Not offered this year QCR

Elements of smooth manifold theory, tensors, and differential forms, Riemannian metrics, connection and curvature; selected applications to Hodge theory, curvature in topology and general relativity. Staff

MAT 473 - Cryptography (also COS 433) Not offered this year

MAT 474 - Introduction to Analytic Combinatorics (also COS 488) Not offered this year

MAT 478 - Topics In Combinatorics Spring QCR

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. N. Alon

MAT 486 - Random Processes Spring QCR

Wiener measure. Stochastic differential equations. Markov diffusion processes. Linear theory of stationary processes. Ergodicity, mixing, central limit theorem for stationary processes. If time permits, the theory of products of random matrices and PDE with random coefficients will be discussed. Prerequisite: MAT385. A. Sly

MAT 493 - Mathematical Methods of Physics (also PHY 403) Not offered this year QCR