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 1110 | Probability/Finite Mathematics (3) |

Studies finite probability theory including combinatorics, equiprobable models, conditional probability and Bayes' theorem, expectation and variance, and Markov chains. Course was offered Spring 2020, Spring 2019, Spring 2018, Spring 2017, Spring 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 | |

MATH 1140 | Financial Mathematics (3) |

Offered Fall 2020 | 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. Course was offered Summer 2020, Spring 2020, Fall 2019, Summer 2019, Spring 2019, Fall 2018, Summer 2018, Spring 2018, Fall 2017, Summer 2017, Spring 2017, Fall 2016, Summer 2016, Spring 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Summer 2014, Spring 2014, Fall 2013, Summer 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |

MATH 1150 | The Shape of Space (3) |

Offered Fall 2020 | 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 1160 | Algebra, Number Systems, and Number Theory (3) |

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. Course was offered Spring 2020, Spring 2019, Spring 2018, Spring 2017, Spring 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 | |

MATH 1190 | A Survey of Calculus I with Algebra (4) |

Offered Fall 2020 | A first calculus course for business/biology/social-science students. Topics include college algebra/limits and continuity/differentiation and integration of algebraic and elementary transcendental functions/applications to related-rates & optimization problems as well as to curve sketching & exponential growth. At most one of MATH 1190, MATH 1210, and 1310 may be taken for credit. Prerequisite: No previous exposure to Calculus. Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013 |

MATH 1210 | A survey of Calculus I (3) |

Offered Fall 2020 | A first calculus course for business/biology/social-science students. Topics include limits and continuity/differentiation & integration of algebraic & elementary transcendental functions/applications to related-rates & optimization problems as well as to curve sketching & exponential growth. At most one of MATH 1190, MATH 1210, and MATH 1310 may be taken for credit. Course was offered Summer 2020, Spring 2020, Fall 2019, Summer 2019, Spring 2019, Fall 2018, Summer 2018, Spring 2018, Fall 2017, Summer 2017, Spring 2017, Fall 2016, Summer 2016, Spring 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Summer 2014, Spring 2014, Fall 2013, Summer 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |

MATH 1220 | A Survey of Calculus II (3) |

Offered Fall 2020 | A second calculus course for business/biology/and social-science students. Topics include differential equations/infinite series/analysis of functions of several variables/analysis of probability density functions of continuous random variables. The course begins with a review of basic single-variable calculus. Prerequisite: MATH 1210 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit. Course was offered Summer 2020, Spring 2020, Fall 2019, Summer 2019, Spring 2019, Fall 2018, Summer 2018, Spring 2018, Fall 2017, Summer 2017, Spring 2017, Fall 2016, Summer 2016, Spring 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Summer 2014, Spring 2014, Fall 2013, Summer 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |

MATH 1310 | Calculus I (4) |

Offered Fall 2020 | A first calculus course for natural-science majors/students planning further work in mathematics/students intending to pursue graduate work in applied social sciences. Introduces differential & integral calculus for single-variable functions, emphasizing techniques/applications & major theorems, like the fundamental theorem of calculus. Prerequisite: Background in algebra/trigonometry/exponentials/logarithms/analytic geometry. |

MATH 1320 | Calculus II (4) |

Offered Fall 2020 | A second calculus course for natural-science majors, students planning additional work in mathematics, and students intending to pursue graduate work in the applied social sciences. Topics include applications of the integral, techniques of integration, differential equations, infinite series, parametric equations, and polar coordinates.
Prerequisite: MATH 1310 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit. |

MATH 1559 | New Course in Mathematics (1 - 4) |

This course provides the opportunity to offer a new topic in the subject of mathematics. Course was offered January 2020 | |

MATH 2310 | Calculus III (4) |

Offered Fall 2020 | A continuation of Calc I and II, this course is about functions of several variables. Topics include finding maxima and minima of functions of several variables/surfaces and curves in three-dimensional space/integration over these surfaces and curves. Additional topics: conservative vector fields/Stokes' and the divergence theorems/how these concepts relate to real world applications. Prerequisite: MATH 1320 or the equivalent. Course was offered Summer 2020, Spring 2020, Fall 2019, Summer 2019, Spring 2019, Fall 2018, Summer 2018, Spring 2018, Fall 2017, Summer 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Summer 2014, Spring 2014, Fall 2013, Summer 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |

MATH 2315 | Advanced Calculus and Linear Algebra I (4) |

Offered Fall 2020 | 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. Credit is not given for both Math 2310 and Math 2315. |

MATH 2559 | New Course in Mathematics (1 - 4) |

This course provides the opportunity to offer a new topic in the subject of mathematics. | |

MATH 2700 | Euclidean and Non-Euclidean Geometry (3) |

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, constructible numbers, and the discovery of non-Euclidean geometry. Prerequisite: Some familiarity with calculus. Course was offered January 2020, January 2019, January 2018, January 2017, January 2016, January 2015, January 2014, January 2013, January 2012, January 2011, January 2010 | |

MATH 3000 | Transition to Higher Mathematics (4) |

Offered Fall 2020 | 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. Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2016, Spring 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 |

MATH 3100 | Introduction to Probability (3) |

Offered Fall 2020 | Introduces fundamental ideas of probability, the theory of randomness. Focuses on problem solving and understanding key theoretical ideas. Topics include sample spaces, counting, random variables, classical distributions, expectation, Chebyshev's inequality, independence, central limit theorem, conditional probability, generating functions, joint distributions. Prerequisite: MATH 1320 or equivalent. Strongly recommended: MATH 2310 Course was offered Summer 2020, Spring 2020, Fall 2019, Summer 2019, Spring 2019, Fall 2018, Summer 2018, Spring 2018, Fall 2017, Summer 2017, Spring 2017, Fall 2016, Summer 2016, Spring 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Summer 2014, Spring 2014, Fall 2013, Summer 2013, Spring 2013, Fall 2012, Summer 2012, Fall 2011, Summer 2011, Fall 2010, Summer 2010, Fall 2009 |

MATH 3250 | Ordinary Differential Equations (4) |

Offered Fall 2020 | 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. Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 3310 | Basic Real Analysis (3) |

Offered Fall 2020 | A rigorous development of the properties of the real numbers and the ideas of calculus including theorems on limits, continuity, differentiability, convergence of infinite series, and the construction of the Riemann integral. Students without prior experience constructing rigorous proofs are encouraged to take Math 3000 before or concurrently with Math 3310. Prerequisite: MATH 1320. |

MATH 3315 | Advanced Calculus and Linear Algebra II (4) |

This course is a continuation of MATH 2315. Covers topics from linear algebra/differential equations/real analysis. Success in this course and MATH 2315 (grades of B- or higher) exempts the student from the math major requirement of taking MATH 3351 and MATH 3250. Students are encouraged to take more advanced courses in these areas. Prerequisite: MATH 2315. | |

MATH 3340 | Complex Variables with Applications (3) |

Offered Fall 2020 | Covers functions of a complex variable that are complex differentiable and the unusual and useful properties of such functions. Some topics: Cauchy's integral formula/power series/the residue theorem/RouchÃ©'s theorem. Applications include doing real integrals using complex methods and applications to fluid flow in two dimensions. Prerequisite: MATH 2310. Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 |

MATH 3350 | Applied Linear Algebra (3) |

Offered Fall 2020 | 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. Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Spring 2017, Spring 2016, Spring 2015, Spring 2014 |

MATH 3351 | Elementary Linear Algebra (3) |

Offered Fall 2020 | 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. Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 3354 | Survey of Algebra (3) |

Offered Fall 2020 | 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. Students without prior experience constructing rigorous proofs are encouraged to take Math 3000 before or concurrently with Math 3354. Prerequisite: MATH 1320. Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 3559 | New Course in Mathematics (1 - 4) |

This course provides the opportunity to offer a new topic in the subject of mathematics. Course was offered Fall 2017 | |

MATH 4040 | Discrete Mathematics (3) |

Offered Fall 2020 | 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 4110 | Introduction to Stochastic Processes (3) |

Offered Fall 2020 | 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 Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015 |

MATH 4140 | Mathematics of Derivative Securities (3) |

Offered Fall 2020 | This class introduces students to the mathematics used in pricing derivative securities. Topics include a review of the relevant probability theory of conditional expectation and martingales/the elements of financial markets and derivatives/pricing contingent claims in the binomial & the finite market model/(time permitting) the Black-Scholes model. Prerequisites: MATH 3100 or APMA 3100. Students should have a knowledge of matrix algebra. Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016 |

MATH 4210 | Mathematics for Physics (3) |

This course covers linear algebra/complex analysis/vector differential & integral calculus. Thus it is a compressed version of MATH 3351 & MATH 3340 and a review of some of the material in MATH 2310. Emphasis is on the physical interpretation. [This course does not count as a Mathematics elective for Mathematics majors if both MATH 3351 and MATH 3340 are to be counted.] Prerequisite: MATH 2310 or MATH 2315 or APMA 2120 | |

MATH 4220 | Partial Differential Equations and Applied Mathematics (3) |

Offered Fall 2020 | This course is a beginning course in partial differential equations/Fourier analysis/special functions (such as spherical harmonics and Bessel functions). The discussion of partial differential equations will include the Laplace and Poisson equations and the heat and wave equations. Prerequisites: MATH 3250 and either MATH 3351 or MATH 4210. |

MATH 4250 | Differential Equations and Dynamical Systems (3) |

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. | |

MATH 4300 | Elementary Numerical Analysis (3) |

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. Course was offered Spring 2020, Spring 2019 | |

MATH 4310 | Introduction to Real Analysis (3) |

Offered Fall 2020 | This course covers the basic topology of metric spaces/continuity and differentiation of functions of a single variable/Riemann-Stieltjes integration/convergence of sequences and series. Prerequisite: MATH 3310 or permission of instructor. |

MATH 4330 | Calculus on Manifolds (3) |

Differential and integral calculus in Euclidean spaces. Implicit and inverse function theorems, differential forms and Stokes' theorem.
Prerequisites: MATH 2310 or MATH 2315; MATH 3351 or MATH 4651 or APMA 3080; and MATH 3310 or MATH 4310 | |

MATH 4452 | Algebraic Coding Theory (3) |

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. Course was offered Spring 2020 | |

MATH 4559 | New Course in Mathematics (1 - 4) |

This course provides the opportunity to offer a new topic in the subject of mathematics. | |

MATH 4651 | Advanced Linear Algebra (3) |

Offered Fall 2020 | 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 Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Fall 2016, Fall 2015 |

MATH 4652 | Introduction to Abstract Algebra (3) |

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. Prerequisites: MATH 3351 or 4651 and MATH 3354 or permission of the instructor. | |

MATH 4658 | Galois Theory (3) |

This course studies the symmetries of solutions of polynomials. Topics include algebraic field extensions/field automorphisms/the fundamental theorem of Galois theory. Applications include the unsolvability of the quintic, as well as ruler & compass constructions. Prerequisites: MATH 3351 (or 4651) and MATH 4652. | |

MATH 4660 | Algebraic Combinatorics (3) |

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 2019, Spring 2016 | |

MATH 4720 | Introduction to Differential Geometry (3) |

Offered Fall 2020 | Geometric study of curves/surfaces/their higher-dimensional analogues. Topics vary and may include curvature/vector fields and the Euler characteristic/the Frenet theory of curves in 3-space/geodesics/the Gauss-Bonnet theorem/and/or an introduction to Riemannian geometry on manifolds. Prerequisites: MATH 2310 and MATH 3351 or instructor permission. |

MATH 4750 | Introduction to Knot Theory (3) |

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. Prerequisites: MATH 2310 and MATH 3351 and MATH 3354 or instructor permission. Course was offered Spring 2018 | |

MATH 4770 | General Topology (3) |

Offered Fall 2020 | Topics include abstract topological spaces & continuous functions/connectedness/compactness/countability/separation axioms. Rigorous proofs emphasized. Covers myriad examples, i.e., function spaces/projective spaces/quotient spaces/Cantor sets/compactifications. May include intro to aspects of algebraic topology, i.e., the fundamental group. Prerequisites: MATH 2310 or 2315 or APMA 2120 and MATH 3315 or MATH 3351 or MATH 4651 or APMA 3080 |

MATH 4840 | Introduction to Mathematical Research (3) |

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.). | |

MATH 4900 | Distinguished Major Thesis (3) |

Offered Fall 2020 | 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 a student through the beginning phases of the process of research and writing. Prerequisite: Acceptance into the Distinguished Major Program. |

MATH 4901 | Distinguished Major Thesis (3) |

This is the second semester of a two semester sequence for the purpose of the completion of a Distinguished Major Thesis. A faculty member 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 4993 | Independent Study (1 - 3) |

Offered Fall 2020 | 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. Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Summer 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Summer 2010, Spring 2010, Fall 2009 |

MATH 5010 | The History of the Calculus (3) |

Offered Fall 2020 | 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. |

MATH 5030 | The History of Mathematics (3) |

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 5250 | Differential Equations and Dynamical Systems (3) |

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 5305 | Proofs in Analysis (3) |

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. Course was offered Summer 2020, Summer 2019, Summer 2017, Summer 2016, Summer 2013, Summer 2012, Summer 2011, Summer 2010 | |

MATH 5559 | New Course in Mathematics (1 - 4) |

This course provides the opportunity to offer a new topic in the subject of mathematics. Course was offered Fall 2013 | |

MATH 5653 | Number Theory (3) |

Offered Fall 2020 | The study of the integers and related number systems. Includes polynomial congruences, rings of congruence classes and their groups of units, quadratic reciprocity, diophantine equations, and number-theoretic functions. Additional topics such as the distribution of prime numbers may be included. Prerequisite: MATH 3354. Course was offered Fall 2019, Fall 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 |

MATH 5657 | Bilinear Forms and Group Representations (3) |

Covers the representation theory of finite groups/other interactions between linear & abstract algebra. Topics include: bilinear & sesquilinear forms & inner product spaces/important classes of linear operators on inner product spaces/the notion of group representation/complete reducibility of complex representations of finite groups/character theory/some applications of representation theory. Prerequisite: MATH 3351 or 4651/MATH 3354 or 4652. Course was offered Fall 2019 | |

MATH 5700 | Introduction to Geometry (3) |

Topics selected from analytic, affine, projective, hyperbolic, and non-Euclidean geometry. Prerequisite: MATH 2310, 3351, or instructor permission. Course was offered Spring 2020, Spring 2019, Spring 2018, Spring 2017, Spring 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 | |

MATH 5720 | Introduction to Differential Geometry (3) |

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 5770 | General Topology (3) |

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 5855 | Proofs in Algebra (3) |

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. Course was offered Summer 2017, Summer 2016, Summer 2014, Summer 2013, Summer 2012, Summer 2011, Summer 2010 | |

MATH 5896 | Supervised Study in Mathematics (3) |

A rigorous program of supervised study designed to expose the student to a particular area of mathematics. Prerequisite: Instructor permission and graduate standing. Course was offered Fall 2016, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 | |

MATH 6060 | AFDA: Mathematical Modeling with Probability and Statistics (3) |

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 6120 | Measurement and Data Analysis (3) |

Measurement and Data Analysis Course was offered Spring 2010 | |

MATH 6452 | Functions and Algebra (3) |

Functions and Algebra | |

MATH 6453 | Number Systems and Number Theory for K-8 Mathematics Specialists (3) |

Number Systems and Number Theory for K-8 Mathematics Specialists Course was offered Spring 2010 | |

MATH 6454 | Rational Numbers and Proportional Reasoning (3) |

Rational Numbers and Proportional Reasoning | |

MATH 6559 | New Course in Mathematics (1 - 4) |

This course provides the opportunity to offer a new topic in the subject of mathematics. | |

MATH 6600 | Algebra for Middle School Specialists (3) |

Algebra for Middle School Specialists | |

MATH 6630 | AAO Introductory College Algebra and Trigonometry (3) |

AAO Introductory College Algebra and Trigonometry Course was offered Spring 2010 | |

MATH 6650 | AAO Calculus with Applications (3) |

AAO Calculus with Applications | |

MATH 6660 | Euclidean Geometry (3) |

Euclidean Geometry Course was offered Spring 2012 | |

MATH 6670 | AAO Probability and Statistics (3) |

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 6700 | Geometry and Measurement for K-8 Math Specialists (3) |

Geometry and Measurement for K-8 Math Specialists | |

MATH 6760 | MM Data Analysis, Probability, and Statistics for Middle School Teachers (3) |

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 6800 | Teaching Mathematics to Diverse Populations (3) |

Teaching Mathematics to Diverse Populations | |

MATH 7000 | Seminar on College Teaching (1 - 3) |

Offered Fall 2020 | 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'sÂ degree. Prerequisite: Graduate standing in mathematics. |

MATH 7010 | Seminar on Research in Mathematics (1 - 3) |

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 7250 | Ordinary Differential Equations and Dynamical Systems (3) |

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 7305 | Problems in Analysis (3) |

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. Course was offered Summer 2020, Summer 2019, Summer 2018, Summer 2017, Summer 2015, Summer 2014, Summer 2013, Summer 2012, Summer 2011, Summer 2010 | |

MATH 7310 | Real Analysis and Linear Spaces I (3) |

Introduces measure and integration theory. Prerequisite: MATH 5310 or equivalent. Course was offered Spring 2020, Spring 2019, Spring 2018, Spring 2017, Spring 2016, Spring 2015, Spring 2014, Fall 2012, Fall 2011, Fall 2010, Fall 2009 | |

MATH 7320 | Real Analysis and Linear Spaces II (3) |

Additional topics in measure theory. Banach and Hilbert spaces, and Fourier analysis. Prerequisite: MATH 7310, 7340, or equivalent. Course was offered Fall 2017, Spring 2011 | |

MATH 7340 | Complex Analysis I (3) |

Offered Fall 2020 | Studies the fundamental theorems of analytic function theory. Course was offered Fall 2019, Fall 2018, Fall 2017, Fall 2016, Fall 2015, Fall 2014, Fall 2013, Spring 2013, Spring 2012, Spring 2011, Spring 2010 |

MATH 7360 | Probability Theory I (3) |

Rigorous introduction to probability, using techniques of measure theory. Includes limit theorems, martingales, and stochastic processes. Prerequisite: 7310 or equivalent. | |

MATH 7370 | Probability Theory II (3) |

Continuation of Probability Theory I. Elements of stochastic processes, including Brownian motion, continuous time martingales, and Markov processes. Course was offered Spring 2019, Spring 2017, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 | |

MATH 7410 | Functional Analysis I (3) |

Studies the basic principles of linear analysis, including spectral theory of compact and selfadjoint operators. Prerequisite: MATH 7340 and 7310, or equivalent. Course was offered Spring 2020, Spring 2019, Fall 2016, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010, Fall 2009 | |

MATH 7420 | Functional Analysis II (3) |

Studies the spectral theory of unbounded operators, semigroups, and distribution theory. Prerequisite: MATH 7410 or equivalent. Course was offered Spring 2013, Spring 2010 | |

MATH 7450 | Introduction to Mathematical Physics (3) |

An introduction to classical mechanics, with topics in statistical and quantum mechanics, as time permits. Prerequisite: MATH 5310. | |

MATH 7559 | New Course in Mathematics (1 - 4) |

Offered Fall 2020 | This course provides the opportunity to offer a new topic in the subject of mathematics. |

MATH 7600 | Homological Algebra (3) |

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. | |

MATH 7705 | Problems In Topology (3) |

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. Course was offered Summer 2020, Summer 2019, Summer 2018, Summer 2017, Summer 2016, Summer 2015, Summer 2014, Summer 2013, Summer 2012, Summer 2011 | |

MATH 7751 | Algebra I (3) |

Offered Fall 2020 | Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent. |

MATH 7752 | Algebra II (3) |

Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent. | |

MATH 7753 | Algebra III (3) |

Studies the Wedderburn theory, commutative algebra, and topics in advanced algebra. Prerequisite: MATH 7751, 7752, or equivalent. | |

MATH 7754 | Algebra IV (3) |

Offered Fall 2020 | Further topics in algebra. Course was offered Spring 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, Spring 2011, Spring 2010 |

MATH 7755 | Problems in Algebra (3) |

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. Course was offered Summer 2020, Summer 2019, Summer 2018, Summer 2017, Summer 2016, Summer 2015, Summer 2014, Summer 2013, Summer 2012, Summer 2011, Summer 2010 | |

MATH 7800 | Algebraic Topology I (3) |

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 7810 | Algebraic Topology II (3) |

Offered Fall 2020 | 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 7820 | Differential Topology (3) |

Offered Fall 2020 | 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 7830 | Fiber Bundles (3) |

Examines fiber bundles; induced bundles, principal bundles, classifying spaces, vector bundles, and characteristic classes, and introduces K-theory and Bott periodicity. Prerequisite: MATH 7800. Course was offered Spring 2020, Spring 2019, Spring 2018, Spring 2017, Spring 2015, Spring 2013, Fall 2011, Spring 2010 | |

MATH 7840 | Homotopy Theory (3) |

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. | |

MATH 8250 | Partial Differential Equations (3) |

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. Course was offered Fall 2018, Fall 2016, Fall 2014, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Fall 2010, Spring 2010, Fall 2009 | |

MATH 8310 | Operator Theory I, II (3) |

Topics in the theory of operators on a Hilbert space and related areas of function theory. | |

MATH 8320 | Operator Theory I, II (3) |

Topics in the theory of operators on a Hilbert space and related areas of function theory. Course was offered Fall 2014, Spring 2013 | |

MATH 8360 | Stochastic Calculus and Differential Equations (3) |

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. | |

MATH 8380 | Random Matrices (3) |

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 Fall 2019, Spring 2016 | |

MATH 8410 | Harmonic Analysis (3) |

This course studies real variable methods for singular integrals and related functional spaces. Course was offered Spring 2016 | |

MATH 8450 | Topics in Mathematical Physics (3) |

Applies functional analysis to physical problems; scattering theory, statistical mechanics, and quantum field theory. Course was offered Fall 2014 | |

MATH 8510 | Topics in Number Theory (3) |

Studies selected topics in algebraic or analytic number theory Course was offered Fall 2019 | |

MATH 8559 | New Course in Mathematics (1 - 4) |

Offered Fall 2020 | This course provides the opportunity to offer a new topic in the subject of mathematics. |

MATH 8600 | Commutative Algebra (3) |

The foundations of commutative algebra, algebraic number theory, or algebraic geometry. | |

MATH 8620 | Algebraic Geometry (3) |

Offered Fall 2020 | Studies the foundations of algebraic geometry. |

MATH 8630 | Algebraic Number Theory (3) |

Theory of number fields and local fields, ramification theory, further topics as chosen by instructor. Course was offered Spring 2020, Spring 2016 | |

MATH 8700 | Lie Groups (3) |

Studies basic results concerning Lie groups, Lie algebras, and the correspondence between them. | |

MATH 8710 | Lie Algebras (3) |

Offered Fall 2020 | Studies basic structure theory of Lie algebras. |

MATH 8720 | Differential Geometry (3) |

Studies differential geometry in the large; connections; Riemannian geometry; Gauss-Bonnet formula; and differential forms. | |

MATH 8750 | Topology of Manifolds (3) |

Offered Fall 2020 | 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. Course was offered Fall 2019, Spring 2019, Fall 2018, Spring 2018, Spring 2016, Spring 2015, Fall 2013, Spring 2012, Fall 2009 |

MATH 8850 | Topics in Algebraic Topology (3) |

Selected advanced topics in algebraic topology. Course was offered Spring 2020, Spring 2019, Fall 2018, Spring 2017, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Spring 2013, Spring 2012, Fall 2011, Fall 2010 | |

MATH 8851 | Group Theory (3) |

Offered Fall 2020 | Studies the basic structure theory of groups, especially finite groups. Course was offered Spring 2020, Spring 2018, Fall 2016, Spring 2016, Spring 2015, Spring 2014, Spring 2013, Fall 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 8852 | Representation Theory (3) |

Studies the foundations of representation and character theory of finite groups. Course was offered Fall 2019, Fall 2018, Fall 2017, Spring 2017, Fall 2015, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Spring 2010 | |

MATH 8853 | Algebraic Combinatorics (3) |

Covers methods of abstract algebra that can be applied to various combinatorial problems and combinatorial methods to approach problems in representation theory, algebraic geometry, and homological algebra. Course was offered Spring 2020, Spring 2018 | |

MATH 8855 | Theory of Algebras (3) |

Studies the basic structure theory of associative or nonassociative algebras. | |

MATH 8880 | Transformation Groups (3) |

Studies groups of transformations operating on a space; properties of fixed-point sets, orbit spaces; and local and global invariants. | |

MATH 8995 | Thesis (3 - 12) |

Thesis Course was offered Spring 2018, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 | |

MATH 8998 | Non-Topical Research, Preparation for Research (1 - 12) |

Offered Fall 2020 | For master's research, taken before a thesis director has been selected. Course was offered Fall 2019, Fall 2018, Fall 2017, Fall 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 8999 | Non-Topical Research (1 - 12) |

Offered Fall 2020 | For master's thesis, taken under the supervision of a thesis director. Course was offered Fall 2019, Fall 2018, Fall 2017, Fall 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 9010 | History of Mathematics Seminar (1 - 3) |

Discusses subjects from the history of mathematics. | |

MATH 9250 | Harmonic Analysis and PDEs (3) |

Offered Fall 2020 | Harmonic Analysis and PDEs seminar |

MATH 9310 | Operator Theory Seminar (3) |

Offered Fall 2020 | Operator Theory Seminar |

MATH 9360 | Probability Seminar (3) |

Offered Fall 2020 | Probability Seminar Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 9410 | Galois-Grothendieck Seminar (3) |

Offered Fall 2020 | Galois-Grothendieck Seminar Course was offered Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 9450 | Mathematical Physics Seminar (3) |

Mathematical Physics Seminar Course was offered Spring 2018, Spring 2017, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 | |

MATH 9559 | New Course in Mathematics (1 - 4) |

This course provides the opportunity to offer a new topic in the subject of mathematics. | |

MATH 9800 | Topology Seminar (3) |

Topology Seminar | |

MATH 9820 | Geometry Seminar (1 - 3) |

Offered Fall 2020 | Discusses subjects from geometry. |

MATH 9950 | Algebra Seminar (3) |

Offered Fall 2020 | Algebra Seminar |

MATH 9995 | Independent Research (3 - 9) |

Offered Fall 2020 | Independent Research Course was offered Summer 2020, Spring 2020, Fall 2019, Summer 2019, Spring 2019, Fall 2018, Summer 2018, Spring 2018, Fall 2017, Summer 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 9998 | Non-Topical Research, Preparation for Doctoral Research (1 - 12) |

Offered Fall 2020 | For doctoral research, taken before a dissertation director has been selected. Course was offered Summer 2020, Spring 2020, Fall 2019, Summer 2019, Spring 2019, Fall 2018, Summer 2018, Spring 2018, Fall 2017, Summer 2017, Spring 2017, Fall 2016, Summer 2016, Spring 2016, Fall 2015, Summer 2015, Spring 2015, Fall 2014, Summer 2014, Spring 2014, Fall 2013, Summer 2013, Spring 2013, Fall 2012, Summer 2012, Spring 2012, Fall 2011, Summer 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009 |

MATH 9999 | Non-Topical Research (1 - 12) |

Offered Fall 2020 | 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. |