Undergraduate courses

Please refer to SIS or Lou’s list for details about current instructors and current enrollment numbers.


MATH 1110    Probability/Finite Mathematics (3)
Offered Spring 2020
• (Offered Spring 2020)
Studies finite probability theory including combinatorics, equiprobable models, conditional probability and Bayes' theorem, expectation and variance, and Markov chains.
MATH 1140    Financial Mathematics (3)
Offered Spring 2020
• (Offered Spring 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.
MATH 1150    The Shape of Space (3)
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)
Offered Spring 2020
• (Offered Spring 2020)
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 1190    A Survey of Calculus I with Algebra (4)
Offered Spring 2020
• (Offered Spring 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.
MATH 1210    A survey of Calculus I (3)
Offered Spring 2020
• (Offered Spring 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.
MATH 1220    A Survey of Calculus II (3)
Offered Spring 2020
• (Offered Spring 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.
MATH 1310    Calculus I (4)
Offered Spring 2020
• (Offered Spring 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 Spring 2020
• (Offered Spring 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.
MATH 2310    Calculus III (4)
Offered Spring 2020
• (Offered Spring 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.
MATH 2315    Advanced Calculus and Linear Algebra I (4)
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.
MATH 3000    Transition to Higher Mathematics (4)
Offered Spring 2020
• (Offered Spring 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.
MATH 3100    Introduction to Probability (3)
Offered Spring 2020
• (Offered Spring 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
MATH 3250    Ordinary Differential Equations (4)
Offered Spring 2020
• (Offered Spring 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.
MATH 3310    Basic Real Analysis (3)
Offered Spring 2020
• (Offered Spring 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)
Offered Spring 2020
• (Offered Spring 2020)
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 Spring 2020
• (Offered Spring 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/Rouché's theorem. Applications include doing real integrals using complex methods and applications to fluid flow in two dimensions. Prerequisite: MATH 2310.
MATH 3350    Applied Linear Algebra (3)
Offered Spring 2020
• (Offered Spring 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.
MATH 3351    Elementary Linear Algebra (3)
Offered Spring 2020
• (Offered Spring 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.
MATH 3354    Survey of Algebra (3)
Offered Spring 2020
• (Offered Spring 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.
MATH 3559    New Course in Mathematics (1 - 4)
This course provides the opportunity to offer a new topic in the subject of mathematics.
MATH 4040    Discrete Mathematics (3)
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 Spring 2020
• (Offered Spring 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
MATH 4140    Mathematics of Derivative Securities (3)
Offered Spring 2020
• (Offered Spring 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.
MATH 4210    Mathematics for Physics (3)
Offered Spring 2020
• (Offered Spring 2020)
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)
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)
Offered Spring 2020
• (Offered Spring 2020)
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)
Offered Spring 2020
• (Offered Spring 2020)
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 4310    Introduction to Real Analysis (3)
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)
Offered Spring 2020
• (Offered Spring 2020)
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)
Offered Spring 2020
• (Offered Spring 2020)
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 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 Spring 2020
• (Offered Spring 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
MATH 4652    Introduction to Abstract Algebra (3)
Offered Spring 2020
• (Offered Spring 2020)
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.
MATH 4720    Introduction to Differential Geometry (3)
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.
MATH 4770    General Topology (3)
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)
Offered Spring 2020
• (Offered Spring 2020)
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)
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)
Offered Spring 2020
• (Offered Spring 2020)
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 Spring 2020
• (Offered Spring 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.

Undergraduate program

Information Contacts Academic life Awards Collaborative learning, tutoring, and graders Research opportunities and support Competitions Summer programs at UVA Where graduates go Directed reading program  AWM@UVa  Undergraduate Math Club 

Policies (FAQ) Degree requirements and declaration Math placement Transfer of credit Double counting for SEAS 4+1 (or 3+1) BA/MA Program Distinguished Major Program (DMP) Miscellaneous forms

Course descriptions