UVa Course Catalog (Unofficial, Lou's List)
Catalog of Courses for Mathematics    
Class Schedules Index Course Catalogs Index Class Search Page
These pages present data mined from the University of Virginia's student information system (SIS). I hope that you will find them useful. — Lou Bloomfield, Department of Physics
Mathematics
MATH 1030Precalculus (3.00)
Studies computational skills, patterns of quantitative problem solving, and mathematical thought. Includes linear and quadratic equations, polynomials, inverse functions, logarithms, arithmetic and geometric sequences, trigonometric functions, and linear systems. (Does not satisfy the College natural science and mathematics requirement.) Prerequisite: High school algebra II and geometry.
MATH 1110Probability/Finite Mathematics (3.00)
Offered
Spring 2017
Studies finite probability theory including combinatorics, equiprobable models, conditional probability and Bayes' theorem, expectation and variance, and Markov chains.
MATH 1140Financial Mathematics (3.00)
Offered
Spring 2017
The study of the mathematics needed to understand and answer a variety of questions that arise in everyday financial dealings. The emphasis is on applications, including simple and compound interest, valuation of bonds, amortization, sinking funds, and rates of return on investments. A solid understanding of algebra is assumed.
MATH 1150The Shape of Space (3.00)
Provides an activity and project-based exploration of informal geometry in two and three dimensions. Emphasizes visualization skill, fundamental geometric concepts, and the analysis of shapes and patterns. Topics include concepts of measurement, geometric analysis, transformations, similarity, tessellations, flat and curved spaces, and topology.
MATH 1160Algebra, Number Systems, and Number Theory (3.00)
Offered
Spring 2017
Studies basic concepts, operations, and structures occurring in number systems, number theory, and algebra. Inquiry-based student investigations explore historical developments and conceptual transitions in the development of number and algebraic systems.
MATH 1190Applied Calculus I with Algebra (4.00)
Offered
Spring 2017
Topics include College Algebra; limits and continuity; differentiation and integration of algebraic and elementary transcendental functions; and applications to maximum-minimum problems, curve sketching and exponential growth.  Credit is not given for both Math 1210, 1190, and 1310.  Prerequisite: No previous exposure to Calculus.
MATH 1210Applied Calculus I (3.00)
Offered
Spring 2017
Topics include limits and continuity; differentiation and integration of algebraic and elementary transcendental functions; and applications to maximum-minimum problems, curve sketching and exponential growth. Credit is not given for both MATH 1210, 1212, and 1310.
MATH 1220Applied Calculus II (3.00)
Offered
Spring 2017
A second calculus course for business, biology, and social science students. Analyzes functions of several variables, their graphs, partial derivatives and optimization; multiple integrals. Reviews basic single variable calculus and introduces differential equations and infinite series. Credit is not given for both MATH 1220 and 1320. Prerequisite: MATH 1210 or equivalent.
MATH 1310Calculus I (4.00)
Offered
Spring 2017
Introduces calculus with emphasis on techniques and applications. Recommended for natural science majors and students planning additional work in mathematics. The differential and integral calculus for functions of a single variable is developed through the fundamental theorem of calculus. Credit is not given for both MATH 1210, 1212, and 1310. Prerequisite: Background in algebra, trigonometry, exponentials, logarithms, and analytic geometry.
MATH 1320Calculus II (4.00)
Offered
Spring 2017
Continuation of 1310. Applications of the integral, techniques of integration, infinite series, vectors. Credit is not given for both MATH 1220 and 1320. Prerequisite: MATH 1310 or equivalent, or instructor permission.
MATH 1330Calculus Workshop I (2.00)
Intensive calculus problem-solving workshop with topics drawn from MATH 1310. Prerequisite: Instructor permission; corequisite: MATH 1310.
MATH 1340Calculus Workshop II (2.00)
Intensive calculus problem-solving workshop with topics drawn from MATH 1320. Prerequisite: Instructor permission; corequisite: MATH 1320.
MATH 1559New Course in Mathematics (1.00 - 4.00)
This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 2310Calculus III (4.00)
Offered
Spring 2017
Studies functions of several variables including lines and planes in space, differentiation of functions of several variables, maxima and minima, multiple integration, line integrals, and volume. Prerequisite: MATH 1320 or its equivalent.
MATH 2315Advanced Calculus and Linear Algebra I (4.00)
Covers the material from Math 2310 (multivariable calculus) plus topics from complex numbers, set theory and linear algebra. Prepares students for taking advanced mathematics classes at an early stage.
MATH 2559New Course in Mathematics (1.00 - 4.00)
This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 2700Euclidean and Noneuclidean Geometry (3.00)
Examines assumptions and methods in the original text of Euclid's Elements. Covers selected geometric topics such as symmetries, spherical geometry, curvature, the dissection theory of area, constructable numbers, and the discovery of non-Euclidean geometry. Prerequisites: Some familiarity with calculus.
MATH 3000Transition to Higher Mathematics (4.00)
Covers basic concepts with an emphasis on writing mathematical proofs. Topics include logic, sets, functions and relations, equivalence relations and partitions, induction, and cardinality. Prerequisite: Math 1320; and students with a grade of B or better in Math 3310, 3354, or any 5000-level Math course are not eligible to enroll in Math 3000.
MATH 3100Introduction to Probability (3.00)
Offered
Spring 2017
Includes sample spaces, combinatorial analysis, discrete and continuous random variables, classical distributions, expectation, Chebyshev theorem, independence, central limit theorem, conditional probability, and generating functions. Prerequisite: MATH 1320. A knowledge of double integrals is recommended.
MATH 3120Introduction to Mathematical Statistics (3.00)
Includes sampling theory, point estimation, interval estimation, testing hypotheses (including the Neyman-Pearson lemma and likelihood ratio tests), and regression and correlation. Prerequisite: MATH 3100.
Course was offered Summer 2010
MATH 3250Ordinary Differential Equations (4.00)
Offered
Spring 2017
Introduces the methods, theory, and applications of differential equations. Includes first-order, second and higher-order linear equations, series solutions, linear systems of first-order differential equations, and the associated matrix theory. May include numerical methods, non-linear systems, boundary value problems, and additional applications. Prerequisite: MATH 1320 or its equivalent.
MATH 3255Ordinary Differential Equations (4.00)
Usually offered in the spring, this course covers the same material as MATH 3250 with some additional topics, including an introduction to Sturm-Liouville theory, Fourier series and boundary value problems, and their connection with partial differential equations. Physics majors should enroll in MATH 3255, although no knowledge of physics is assumed. Prerequisite: MATH 1320 or its equivalent.
MATH 3310Basic Real Analysis (3.00)
Offered
Spring 2017
Concentrates on proving the basic theorems of calculus, with due attention to the beginner with little or no experience in the techniques of proof. Includes limits, continuity, differentiability, the Bolzano-Weierstrass theorem, Taylor's theorem, integrability of continuous functions, and uniform convergence. Prerequisite: MATH 1320.
MATH 3315Advanced Calculus and Linear Algebra II (4.00)
Offered
Spring 2017
This course is a continuation of MATH 2315. Covers topics from linear algebra, differential equations and real analysis. Prepares students for taking advanced mathematical classes at an early stage. Prerequisite: MATH 2315
Course was offered Spring 2017, Spring 2016
MATH 3340Complex Variables with Applications (3.00)
Offered
Spring 2017
Topics include analytic functions, Cauchy formulas, power series, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: MATH 2310.
MATH 3350Applied Linear Algebra (3.00)
Offered
Spring 2017
Topics will include systems of linear equations, matrix operations and inverses, vector spaces and subspaces, determinants, eigenvalues and eigenvectors, matrix factorizations, inner products and orthogonality, and linear transformations. Emphasis will be on applications, with computer software integrated throughout the course. The target audience for MATH 3350 is non-math majors from disciplines that apply tools from linear algebra. Credit is not given for both MATH 3350 and 3351.
MATH 3351Elementary Linear Algebra (3.00)
Offered
Spring 2017
Includes matrices, elementary row operations, inverses, vector spaces and bases, inner products and Gram-Schmidt orthogonalization, orthogonal matrices, linear transformations and change of basis, eigenvalues, eigenvectors, and symmetric matrices. Credit is not given for both MATH 3350 and 3351. Prerequisite: MATH 1320.
MATH 3354Survey of Algebra (3.00)
Offered
Spring 2017
Surveys major topics of modern algebra: groups, rings, and fields. Presents applications to areas such as geometry and number theory; explores rational, real, and complex number systems, and the algebra of polynomials. Prerequisite: MATH 1320 or equivalent.
MATH 3559New Course in Mathematics (1.00 - 4.00)
This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 4040Discrete Mathematics (3.00)
Includes combinatorial principles, the binomial and multinomial theorems, partitions, discrete probability, algebraic structures, trees, graphs, symmetry groups, Polya's enumeration formula, linear recursions, generating functions and introduction to cryptography, time permitting. Prerequisite: MATH 3354 or instructor permission.
MATH 4080Operations Research (3.00)
Development of mathematical models and their solutions, including linear programming, the simplex algorithm, dual programming, parametric programming, integer programming, transportation models, assignment models, and network analysis. Prerequisite: MATH 1320 and 3351.
MATH 4110Introduction to Stochastic Processes (3.00)
Offered
Spring 2017
Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory. Prerequisite: MATH 3100 or APMA 3100; and a knowledge of matrix algebra
MATH 4140Mathematics of Derivative Securities (3.00)
Offered
Spring 2017
Topics include arbitrage arguments, valuation of futures, forwards and swaps, hedging, option-pricing theory, decision theory, and sensitivity analysis. Prerequisite: MATH 3100 or APMA 3100. Students should have a knowledge of matrix algebra.
Course was offered Spring 2017, Fall 2016, Spring 2016
MATH 4210Advanced Calculus with Applied Mathematics (3.00)
Offered
Spring 2017
Includes vector analysis, Green's, Stokes', divergence theorems, conservation of energy, and potential energy functions. Emphasizes physical interpretation, Sturm-Liouville problems and Fourier series, special functions, orthogonal polynomials, and Green's functions. Prerequisite: MATH 2310, 3250; 3351 recommended.
Course was offered Spring 2017, Fall 2016, Fall 2015
MATH 4220Partial Differential Equations and Applied Mathematics (3.00)
Offered
Spring 2017
Introduces partial differential equations, Fourier transforms. Includes separation of variables, boundary value problems, classification of partial differential equations in two variables, Laplace and Poisson equations, and heat and wave equations. Prerequisite: MATH 4210; 3351 recommended.
Course was offered Spring 2017, Spring 2016
MATH 4250Differential Equations and Dynamical Systems (3.00)
A second course in ordinary differential equations, from the dynamical systems point of view. Topics include: existence and uniqueness theorems; linear systems; qualitative study of equilibria and attractors; bifurcation theory; introduction to chaotic systems. Further topics as chosen by the instructor. Applications drawn from physics, biology, and engineering. Prerequisites: MATH 3351 or APMA 3080 and MATH 3310 or MATH 4310.
Course was offered Fall 2016
MATH 4300Elementary Numerical Analysis (3.00)
Includes Taylor's theorem, solution of nonlinear equations, interpolation and approximation by polynomials, numerical quadrature. May also cover numerical solutions of ordinary differential equations, Fourier series, or least-square approximation. Prerequisite: MATH 3250 and computer proficiency.
MATH 4310Introduction to Real Analysis (3.00)
The basic topology of Euclidean spaces; continuity, and differentiation of functions of a single variable; Riemann-Stieltjes integration; and convergence of sequences and series. Prerequisite: MATH 3310
Course was offered Fall 2016, Fall 2015
MATH 4452Algebraic Coding Theory (3.00)
Introduces algebraic techniques for communicating information in the presence of noise. Includes linear codes, bounds for codes, BCH codes and their decoding algorithms. May also include quadratic residue codes, Reed-Muller codes, algebraic geometry codes, and connections with groups, designs, and lattices. Prerequisite: MATH 3351 and 3354, or instructor permission.
MATH 4559New Course in Mathematics (1.00 - 4.00)
This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 4595Undergraduate Research Seminar (3.00)
Emphasizes direct contact with advanced mathematical ideas, communication of these ideas, the discovery of new results and connections among them, and the experience of mathematics as a collaborative venture among researchers at all levels. Students work collaboratively and individually on research projects, and present their results to the class. Prerequisite: Instructor permission.
MATH 4651Advanced Linear Algebra (3.00)
Review of topics from Math 3351 including vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth with emphasis on theoretical aspects. The course continues with more advanced topics including Jordan and rational canonical forms of matrices and introduction to bilinear forms. Additional topics such as modules and tensor products may be included. Prerequisite: MATH 3351
Course was offered Fall 2016, Fall 2015
MATH 4652Introduction to Abstract Algebra (3.00)
Offered
Spring 2017
Structural properties of basic algebraic systems such as groups, rings and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization and symmetric polynomials. Time permitting, such topics as group representations or algebras over a field may be included. Prerequisite: MATH 3351 or 5651
Course was offered Spring 2017, Spring 2016
MATH 4657Bilinear Forms and Group Representations (3.00)
This course will cover the representation theory of finite groups and other interactions between linear and abstract algebra. Topics include: bilinear and sesquilinear forms and inner product spaces; important classes of linear operators on inner product spaces; the notion of group representations; complete reducibility of complex representations of finite groups; character theory; some applications of representation theory. Prerequisite: MATH 3351 (or 4651) and MATH 3354 (or 4652)
Course was offered Fall 2015
MATH 4658Galois Theory (3.00)
Solutions of polynomials, algebraic field extensions, field automorphisms, and the fundamental theorem of Galois theory. Applications include the unsolvability of the quintic, as well as ruler and compass constructions. Prerequisite: MATH 3351 (or 4651) and MATH 4652
MATH 4660Algebraic Combinatorics (3.00)
Combinatorics of counting using basic tools from calculus, linear algebra, and occasionally group theory. Topics include: tableaux, symmetric polynomials, Catalan numbers, quantum binomial theorem, q-exponentials, partition and q-series identities. Bijective proofs will be emphasized when appropriate.
Course was offered Spring 2016
MATH 4720Introduction to Differential Geometry (3.00)
Offered
Spring 2017
Topics selected from the theory of curves and surfaces in Euclidean space and the theory of manifolds. Prerequisites: Math 2310 and Math 3351.
Course was offered Spring 2017
MATH 4750Introduction to Knot Theory (3.00)
Examines the knotting and linking of curves in space. Studies equivalence of knots via knot diagrams and Reidemeister moves in order to define certain invariants for distinguishing among knots. Also considers knots as boundaries of surfaces and via algebraic structures arising from knots. Prerequisite: MATH 3354 or instructor permission.
MATH 4770General Topology (3.00)
Topological spaces and continuous functions, connectedness, compactness, countability and separation axioms, and function spaces. Time permitting, more advanced examples of topological spaces, such as projective spaces, as well as an introduction to the fundamental group will be covered. Prerequisite: Math 2310 and Math 3351 with Math 3310 recommended.
MATH 4830Seminar (3.00)
Presentation of selected topics in mathematics. Prerequisite: MATH 5310; co-requisite: MATH 5652
MATH 4840Introduction to Mathematical Research (3.00)
Offered
Spring 2017
This course will introduce students to the techniques and methods of mathematical research. Students will independently work with mathematical literature on a topic assigned by the instructor and present their findings in various formats (presentation, paper etc.).
Course was offered Spring 2017, Spring 2016
MATH 4900Distinguished Major Thesis I (3.00)
This course provides a framework for the completion of a Distinguished Major Thesis, a treatise containing an exposition of a chosen mathematical topic. A faculty advisor guides the student through all phases of the process which culminates in an open presentation of the thesis to an audience including a faculty evaluation committee.
MATH 4901Distinguished Major Thesis II (3.00)
This is the second semester of a two semester sequence for the purpose of the completion of a Distinguished Major Thesis, a treatise containing an exposition of a chosen mathematical topic. A faculty advisor guides the student through all phases of the process which culminates in an open presentation of the thesis to an audience including a faculty evaluation committee. Prerequisite: MATH 4900
MATH 4993Independent Study (1.00 - 3.00)
Reading and study programs in areas of interest to individual students. For third- and fourth-years interested in topics not covered in regular courses. Students must obtain a faculty advisor to approve and direct the program.
MATH 5010The History of the Calculus (3.00)
Studies the evolution of the various mathematical ideas leading up to the development of calculus in the 17th century, and how those ideas were perfected and extended by succeeding generations of mathematicians. Emphasizes primary source materials. Prerequisite: MATH 2310 and 3351, or instructor permission.
Course was offered Fall 2015, Spring 2014
MATH 5030The History of Mathematics (3.00)
Offered
Spring 2017
Studies the development of mathematics from classical antiquity to the end of the 19th century, focusing on critical periods in the evolution of geometry, number theory, algebra, probability, and set theory. Emphasizes primary source materials. Prerequisite: MATH 2310 and 3351, or instructor permission.
MATH 5100Probability (3.00)
Offered
Spring 2017
Studies the development and analysis of probability models through the basic concepts of sample spaces, random variables, probability distributions, expectations, and conditional probability. Additional topics include distributions of transformed variables, moment generating functions, and the central limit theorem. Prerequisite: MATH 1320 or equivalent, and graduate standing. Credit cannot be received for both MATH 3100 and 5100.
MATH 5250Differential Equations and Dynamical Systems (3.00)
A second course in ordinary differential equations, from the dynamical systems point of view. Topics include: existence and uniqueness theorems; linear systems; qualitative study of equilibria and attractors; bifurcation theory; introduction to chaotic systems. Further topics as chosen by the instructor. Applications drawn from physics, biology, and engineering. Prerequisites:MATH 3351 and MATH 3310 or equivalent.
Course was offered Fall 2016
MATH 5305Proofs in Analysis (3.00)
This course reviews the proofs of the main theorems in analysis in preparation for the advanced graduate analysis courses. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.
MATH 5330Advanced Multivariate Calculus (3.00)
Offered
Spring 2017
Differential and Integral Calculus in Euclidean spaces; implicit and inverse function theorems, differential forms and Stokes' Theorem. Prerequisite: Calculus III (either MATH 2310 or MATH 2315) and one of MATH 5310 or MATH 5770.
MATH 5340Complex Variables with Applications (3.00)
Offered
Spring 2017
Analytic functions, Cauchy formulas, power series, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: graduate standing.
MATH 5559New Course in Mathematics (1.00 - 4.00)
This course provides the opportunity to offer a new topic in the subject of mathematics.
Course was offered Fall 2013
MATH 5653Number Theory (3.00)
Includes congruences, quadratic reciprocity, Diophantine equations, and number-theoretic functions, among others. Prerequisite: MATH 3354 or instructor permission.
MATH 5654Survey of Algebra (3.00)
Offered
Spring 2017
Surveys groups, rings, and fields, and presents applications to other areas of mathematics, such as geometry and number theory. Explores the rational, real, and complex number systems, and the algebra of polynomials. Prerequisite: MATH 1320 or equivalent and graduate standing.
MATH 5700Introduction to Geometry (3.00)
Offered
Spring 2017
Topics selected from analytic, affine, projective, hyperbolic, and non-Euclidean geometry. Prerequisite: MATH 2310, 3351, or instructor permission.
MATH 5720Introduction to Differential Geometry (3.00)
Topics selected from the theory of curves and surfaces in Euclidean space and the theory of manifolds. Prerequisite: MATH 2310 and 3351, or instructor permission.
MATH 5770General Topology (3.00)
Topological spaces and continuous functions, connectedness, compactness, countability and separation axioms, and function spaces. Time permitting, more advanced examples of topological spaces, such as projectives spaces, as well as an introduction to the fundamental group will be covered. Prerequisite: MATH 2310 and 3351, and 3310.
MATH 5855Proofs in Algebra (3.00)
This course reviews the proofs of the main theorems in algebra in preparation for the advanced graduate algebra courses.This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.
MATH 5896Supervised Study in Mathematics (3.00)
A rigorous program of supervised study designed to expose the student to a particular area of mathematics. Prerequisite: Instructor permission and graduate standing.
MATH 6060AFDA: Mathematical Modeling with Probability and Statistics (3.00)
Examines experimental design and probability and statistics through exploring, analyzing, and interpreting data sets. Explores the graphing calculator as a tool to display and analyze data obtained from sampling, observations, measurement, experiments, and internet sources.
Course was offered Spring 2010
MATH 6120Measurement and Data Analysis (3.00)
Measurement and Data Analysis
Course was offered Spring 2010
MATH 6452Functions and Algebra (3.00)
Functions and Algebra
MATH 6453Number Systems and Number Theory for K-8 Mathematics Specialists (3.00)
Number Systems and Number Theory for K-8 Mathematics Specialists
Course was offered Spring 2010
MATH 6454Rational Numbers and Proportional Reasoning (3.00)
Rational Numbers and Proportional Reasoning
MATH 6559New Course in Mathematics (1.00 - 4.00)
This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 6600Algebra for Middle School Specialists (3.00)
Algebra for Middle School Specialists
MATH 6630AAO Introductory College Algebra and Trigonometry (3.00)
AAO Introductory College Algebra and Trigonometry
Course was offered Spring 2010
MATH 6650AAO Calculus with Applications (3.00)
AAO Calculus with Applications
MATH 6660Euclidean Geometry (3.00)
Euclidean Geometry
Course was offered Spring 2012
MATH 6670AAO Probability and Statistics (3.00)
Explores introductory descriptive statistics, probability, and statistical inference. Develops conceptual understanding and procedural fluency in problem settings based on real data which investigate the use of visual methods from summarizing quantitative information, basic experimental design, sampling methods, and interpretation of statistical analysis.
MATH 6700Geometry and Measurement for K-8 Math Specialists (3.00)
Geometry and Measurement for K-8 Math Specialists
MATH 6760MM Data Analysis, Probability, and Statistics for Middle School Teachers (3.00)
Focuses on the representation of data for decision making and predictability based on data analysis as it relates to middle school mathematics and defined in the NCTM Professional Standards for School Mathematics and Virginia SOLS in Mathematics. Teachers deepen their understanding and use of the fundamental ideas in mathematics that underlie the probability and statistics strand.
MATH 6800Teaching Mathematics to Diverse Populations (3.00)
Teaching Mathematics to Diverse Populations
MATH 7000Seminar on College Teaching (1.00 - 3.00)
Discussion of issues related to the practice of teaching, pedagogical concerns in college level mathematics, and aspects of the responsibilities of a professional mathematician. Credits may not be used towards a Master's degree. Prerequisite: Graduate standing in mathematics.
MATH 7010Seminar on Research in Mathematics (1.00 - 3.00)
Offered
Spring 2017
This seminar discusses the issues related to research in Mathematics. There are speakers from the different areas of mathematics represented at the University of Virginia. Credit may not be used towards a Master's degree. Prerequisite: Graduate standing in mathematics.
MATH 7250Ordinary Differential Equations and Dynamical Systems (3.00)
Topics include well-posedness and stability of dynamical flows, attractors, invariant manifolds and their properties, and dissipative and Hamiltonian systems. Prerequisite: MATH 5310 and linear algebra, or the equivalent.
MATH 7305Problems in Analysis (3.00)
Applications of the theory presented in MATH 7310, 7320, and 7340 to specific examples in real and complex analysis. The course emphasizes problem-solving and preparation for the General Examination in Analysis. Problems are based on those from past General Exams. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.
MATH 7310Real Analysis and Linear Spaces I (3.00)
Offered
Spring 2017
Introduces measure and integration theory. Prerequisite: MATH 5310 or equivalent.
MATH 7320Real Analysis and Linear Spaces II (3.00)
Additional topics in measure theory. Banach and Hilbert spaces, and Fourier analysis. Prerequisite: MATH 7310, 7340, or equivalent.
Course was offered Spring 2011
MATH 7340Complex Analysis I (3.00)
Studies the fundamental theorems of analytic function theory.
MATH 7360Probability Theory I (3.00)
Offered
Spring 2017
Rigorous introduction to probability, using techniques of measure theory. Includes limit theorems, martingales, and stochastic processes. Prerequisite: 7310 or equivalent.
MATH 7370Probability Theory II (3.00)
Continuation of Probability Theory I. Elements of stochastic processes, including Brownian motion, continuous time martingales, and Markov processes.
MATH 7410Functional Analysis I (3.00)
Studies the basic principles of linear analysis, including spectral theory of compact and selfadjoint operators. Prerequisite: MATH 7340 and 7310, or equivalent.
MATH 7420Functional Analysis II (3.00)
Studies the spectral theory of unbounded operators, semigroups, and distribution theory. Prerequisite: MATH 7410 or equivalent.
Course was offered Spring 2013, Spring 2010
MATH 7450Introduction to Mathematical Physics (3.00)
An introduction to classical mechanics, with topics in statistical and quantum mechanics, as time permits. Prerequisite: MATH 5310.
Course was offered Spring 2014, Spring 2011
MATH 7559New Course in Mathematics (1.00 - 4.00)
This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 7600Homological Algebra (3.00)
Offered
Spring 2017
Examines categories, functors, abelian catqegories, limits and colimits, chain complexes, homology and cohomology, homological dimension, derived functors, Tor and Ext, group homology, Lie algebra homology, spectral sequences, and calculations. Prerequisite: MATH 5770.
Course was offered Spring 2017, Spring 2014, Spring 2011
MATH 7705Problems In Topology (3.00)
A continuation of the theory presented in MATH 5770 and 7800 intensively training students to apply the theory to proving theorems and solving problems in topology, especially in preparation for the General Examination in Topology. Problems are based on those from past General Exams. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.
MATH 7751Algebra I (3.00)
Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.
MATH 7752Algebra II (3.00)
Offered
Spring 2017
Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.
MATH 7753Algebra III (3.00)
Studies the Wedderburn theory, commutative algebra, and topics in advanced algebra. Prerequisite: MATH 7751, 7752, or equivalent.
MATH 7754Algebra IV (3.00)
Further topics in algebra.
MATH 7755Problems in Algebra (3.00)
A continuation of the theory presented in MATH 7751 and 7752 intensively training students to apply the theory to proving theorems in algebra, especially in preparation for the General Examination in Algebra. Problems are based on those from past General Exams. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.
MATH 7800Algebraic Topology I (3.00)
Offered
Spring 2017
Topics include the fundamental group, covering spaces, covering transformations, the universal covering spaces, graphs and subgroups of free groups, and the fundamental groups of surfaces. Additional topics will be from homology, including chain complexes, simplicial and singular homology, exact sequences and excision, cellular homology, and classical applications. Prerequisite: MATH 5352, 5770, or equivalent.
MATH 7810Algebraic Topology II (3.00)
Devoted to chomology theory: cohomology groups, the universal coefficient theorem, the Kunneth formula, cup products, the cohomology ring of manifolds, Poincare duality, and other topics if time permits. Prerequisite: MATH 7800.
MATH 7820Differential Topology (3.00)
Topics include smooth manifolds and functions, tangent bundles and vector fields, embeddings, immersions, transversality, regular values, critical points, degree of maps, differential forms, de Rham cohomology, and connections. Prerequisite: MATH 5310, 5770, or equivalent.
MATH 7830Fiber Bundles (3.00)
Offered
Spring 2017
Examines fiber bundles; induced bundles, principal bundles, classifying spaces, vector bundles, and characteristic classes, and introduces K-theory and Bott periodicity. Prerequisite: MATH 7800.
MATH 7840Homotopy Theory (3.00)
Definition of homotopy groups, homotopy theory of CW complexes, Huriewich theorem and Whitehead's theorem, Eilenberg-Maclane spaces, fibration and cofibration sequences, Postnikov towers, and obstruction theory. Prerequisite: MATH 7800.
Course was offered Fall 2013, Spring 2012, Spring 2011
MATH 8250Partial Differential Equations (3.00)
Theory of distributions. Sobolev spaces and their properties (trace and embedding theorems). Theory of elliptic equations. Time-dependent partial differential equations: parabolic and hyperbolic equations. Topics in nonlinear partial differential equations. Prerequisites: MATH 7410 and 7250.
MATH 8310Operator Theory I, II (3.00)
Topics in the theory of operators on a Hilbert space and related areas of function theory.
MATH 8320Operator Theory I, II (3.00)
Topics in the theory of operators on a Hilbert space and related areas of function theory.
Course was offered Fall 2014, Spring 2013
MATH 8360Stochastic Calculus and Differential Equations (3.00)
This course presents the basic theory of stochastic differential equations and provides examples of its applications. It is an essential topic for students preparing to do research in probability. Topics covered include a review of the relevant stochastic process and martingale theory; stochastic calculus including Ito's formula; existence and uniqueness for stochastic differential equations, strong Markov property; and applications. Prerequisite: MATH 7360 and 7370, or instructor permission.
Course was offered Fall 2013, Fall 2010
MATH 8380Random Matrices (3.00)
Discusses fundamental problems and results of the theory of random matrices, and their connections to tools of algebra and combinatorics: Wigner's semicircle law, free probability, Gaussian, circular, and beta ensembles of random matrices, bulk and edge asymptotics and universality, Dyson's Brownian motion, determinantal point processes, and discrete analogues of random matrix models. Prerequisite: MATH 7360 or instructor permission.
Course was offered Spring 2016
MATH 8410Harmonic Analysis (3.00)
This course studies real variable methods for singular integrals and related functional spaces.
Course was offered Spring 2016
MATH 8450Topics in Mathematical Physics (3.00)
Applies functional analysis to physical problems; scattering theory, statistical mechanics, and quantum field theory.
Course was offered Fall 2014
MATH 8559New Course in Mathematics (1.00 - 4.00)
This course provides the opportunity to offer a new topic in the subject of mathematics.
Course was offered Spring 2016, Fall 2014
MATH 8600Commutative Algebra (3.00)
The foundations of commutative algebra, algebraic number theory, or algebraic geometry.
Course was offered Spring 2015, Spring 2012
MATH 8620Algebraic Geometry (3.00)
Studies the foundations of algebraic geometry.
MATH 8630Algebraic Number Theory (3.00)
Theory of number fields and local fields, ramification theory, further topics as chosen by instructor.
Course was offered Spring 2016
MATH 8700Lie Groups (3.00)
Studies basic results concerning Lie groups, Lie algebras, and the correspondence between them.
Course was offered Fall 2015, Fall 2013
MATH 8710Lie Algebras (3.00)
Studies basic structure theory of Lie algebras.
Course was offered Fall 2016, Fall 2014, Fall 2010
MATH 8720Differential Geometry (3.00)
Studies differential geometry in the large; connections; Riemannian geometry; Gauss-Bonnet formula; and differential forms.
Course was offered Spring 2012, Spring 2011, Spring 2010
MATH 8750Topology of Manifolds (3.00)
Studies regular and critical values, gradient flow, handle decompositions, Morse theory, h-cobordism theorem, Dehn's lemma in dimension 3, and disk theorem in dimension 4. Prerequisite: Math 5770.
MATH 8850Topics in Algebraic Topology (3.00)
Offered
Spring 2017
Selected advanced topics in algebraic topology.
MATH 8851Group Theory (3.00)
Studies the basic structure theory of groups, especially finite groups.
MATH 8852Representation Theory (3.00)
Offered
Spring 2017
Studies the foundations of representation and character theory of finite groups.
MATH 8855Theory of Algebras (3.00)
Studies the basic structure theory of associative or nonassociative algebras.
Course was offered Fall 2011, Spring 2011, Spring 2010
MATH 8880Transformation Groups (3.00)
Studies groups of transformations operating on a space; properties of fixed-point sets, orbit spaces; and local and global invariants.
MATH 8995Thesis (3.00 - 12.00)
Offered
Spring 2017
Thesis
MATH 8998Non-Topical Research, Preparation for Research (1.00 - 12.00)
For master's research, taken before a thesis director has been selected.
MATH 8999Non-Topical Research (1.00 - 12.00)
For master's thesis, taken under the supervision of a thesis director.
MATH 9000Mathematics Colloquium (0.00)
Forum for invited speakers giving mathematical colloquium talks.
MATH 9010History of Mathematics Seminar (1.00 - 3.00)
Discusses subjects from the history of mathematics.
Course was offered Fall 2012, Fall 2011, Fall 2010
MATH 9020Graduate Seminar (0.00)
This is a meeting place for junior faculty members and graduate students to discuss mathematics and give talks reflecting the mathematical interests of the participants.
MATH 9250Harmonic Analysis and PDEs (3.00)
Offered
Spring 2017
Harmonic Analysis and PDEs seminar
MATH 9310Operator Theory Seminar (3.00)
Offered
Spring 2017
Operator Theory Seminar
MATH 9360Probability Seminar (3.00)
Offered
Spring 2017
Probability Seminar
MATH 9410Galois-Grothendieck Seminar (3.00)
Offered
Spring 2017
Galois-Grothendieck Seminar
MATH 9450Mathematical Physics Seminar (3.00)
Offered
Spring 2017
Mathematical Physics Seminar
MATH 9559New Course in Mathematics (1.00 - 4.00)
This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 9800Topology Seminar (3.00)
Offered
Spring 2017
Topology Seminar
MATH 9820Geometry Seminar (1.00 - 3.00)
Offered
Spring 2017
Discusses subjects from geometry.
MATH 9950Algebra Seminar (3.00)
Offered
Spring 2017
Algebra Seminar
MATH 9995Independent Research (3.00 - 9.00)
Offered
Spring 2017
Independent Research
MATH 9998Non-Topical Research, Preparation for Doctoral Research (1.00 - 12.00)
Offered
Spring 2017
For doctoral research, taken before a dissertation director has been selected.
MATH 9999Non-Topical Research (1.00 - 12.00)
Offered
Spring 2017
The Mathematics Colloquium is held weekly, the sessions being devoted to research activities of students and faculty members, and to reports by visiting mathematicians on current work of interest. For doctoral dissertation, taken under the supervision of a dissertation director.