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

`MATH 1110`

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.

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`

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.

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 1310 ma1y be taken for credit.

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.

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.

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 1330`

`MATH 1340`

`MATH 1559`

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.

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 2559`

`MATH 2700`

`MATH 3000`

Introduces fundamental concepts/techniques of probability/the theory of randomness. Focuses on problem solving/understanding key theoretical ideas. Topics include sample spaces combinatorial analysis/discrete and continuous random variables/classical distributions/expectation/Chebyshev's inequality/independence/central limit theorem/conditional probability/generating functions. Prerequisite: MATH 1320. Recommended: knowledge of double integrals.

`MATH 3120`

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.

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/the construction of the Riemann integral. The focus of students' work will be on getting experience in constructing proofs and developing examples. Prerequisite: MATH 1320.

`MATH 3315`

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`

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.

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.

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

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 4080`

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

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`

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`

`MATH 4300`

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`

`MATH 4452`

`MATH 4559`

`MATH 4595`

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`

`MATH 4653`

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)

`MATH 4658`

`MATH 4660`

`MATH 4720`

`MATH 4750`

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, MATH 3351, MATH 3310, or higher level versions of these courses.

`MATH 4830`

`MATH 4840`

`MATH 4900`

`MATH 4901`

`MATH 4993`

`MATH 5010`

`MATH 5030`

`MATH 5100`

`MATH 5250`

`MATH 5305`

`MATH 5330`

`MATH 5559`

`MATH 5700`

`MATH 5720`

`MATH 5770`

`MATH 5855`

A rigorous program of supervised study designed to expose the student to a particular area of mathematics. Prerequisite: Instructor permission and graduate standing.

`MATH 6060`

`MATH 6120`

`MATH 6452`

`MATH 6453`

`MATH 6454`

`MATH 6559`

`MATH 6600`

`MATH 6630`

`MATH 6650`

`MATH 6660`

`MATH 6670`

`MATH 6700`

`MATH 6760`

`MATH 6800`

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 7010`

`MATH 7250`

`MATH 7305`

`MATH 7310`

Additional topics in measure theory. Banach and Hilbert spaces, and Fourier analysis. Prerequisite: MATH 7310, 7340, or equivalent.

Studies the fundamental theorems of analytic function theory.

`MATH 7360`

`MATH 7370`

`MATH 7410`

`MATH 7420`

`MATH 7450`

`MATH 7559`

`MATH 7600`

`MATH 7705`

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

`MATH 7752`

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

`MATH 7754`

`MATH 7755`

`MATH 7800`

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.

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`

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`

`MATH 8310`

`MATH 8320`

`MATH 8360`

`MATH 8380`

`MATH 8410`

`MATH 8450`

`MATH 8559`

`MATH 8600`

`MATH 8620`

`MATH 8630`

`MATH 8700`

`MATH 8710`

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

`MATH 8750`

`MATH 8850`

`MATH 8851`

Studies the foundations of representation and character theory of finite groups.

`MATH 8855`

`MATH 8880`

Thesis

For master's research, taken before a thesis director has been selected.

For master's thesis, taken under the supervision of a thesis director.

`MATH 9000`

`MATH 9010`

`MATH 9020`

Harmonic Analysis and PDEs seminar

Operator Theory Seminar

Probability Seminar

Galois-Grothendieck Seminar

`MATH 9450`

`MATH 9559`

Topology Seminar

Discusses subjects from geometry.

Algebra Seminar

Independent Research

`MATH 9998`

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.