A rigorous treatment of fundamental concepts in analysis, with emphasis on careful reasoning and proofs. Topics covered include the completeness and order properties of real numbers; limits and continuity; conditions for integrability and differentiability; infinite sequences and series of functions. Basic notions of the topology of the real line are also introduced.

A modern treatment of calculus of functions of several real variables. Topics include: Euclidean spaces, differentiation, integration and manifolds leading to the classical theorems of Green and Stokes.

Complex functions, limit, continuity, analytic functions, power series, contour integration, Laurent expansion, singularities and residues.

A rigorous treatment of fundamental concepts in algebra, with emphasis on careful reasoning and proofs. Topics covered include equivalence relations, binary operations. Integers: divisibility, factorization, integers modulo n, elementary group theory, subgroups, cyclic groups, permutation groups, quotient groups. Homomorphisms and isomorphisms. Introductory topics in ring theory as time permits.

A continuation of MTH-431. Includes the study of polynomial rings, ideals, field extensions and Galois Theory.

An introduction to point-set topology, including a study of metric spaces, topological spaces, countability and separation axioms, compactness, connectedness, product spaces.

A study of selected topics from Euclidean and non-Euclidean geometry.

Random variables, probability distributions, expectation and limit theorems, confidence intervals.

Hypothesis testing, non-parametric methods, multivariate distributions, introduction to linear models.

This course emphasizes applications, using statistical computer packages (R, SPSS) and real data sets from a variety of fields. Topics include estimation and testing; stepwise regression; analysis of variance and covariance; design of experiments; contingency tables; and multivariate techniques, including logistic regression.

Partial differential equations and boundary value problems, inner product spaces, orthogonal functions, eigen value problems, Sturm-Liouville equations, Fourier series, Fourier transforms, Green’s functions, and classical equations of engineering and physics. 

Offered fall of odd years.

Topics from advanced calculus, including matrix representation of differentials and the multivariable chain rule, vector calculus, curvilinear coordinates, tensors, change of variables in higher dimensions, improper multiple integrals, applications of line and surface integrals, differential forms and the general Stokes’ theorem, potential theory, and Taylor’s formula for functions of several variables.

Offered fall of even years

A survey of operations research topics such as decision analysis, inventory models, queuing models, dynamic programming, network models,  and linear programming. Cross-listed with CS-463. Offered in the spring semester of odd-numbered years when demand warrants.

An introduction to numerical algorithms as tools to providing solutions to common problems formulated in mathematics, science, and engineering. Focus is given to developing the basic understanding of the construction of numerical algorithms, their applicability, and their limitations. (Cross-listed with CS-464)

Direct and iterative methods for the solution of systems of linear equations, matrix decompositions, computation of eigenvalues and eigenvectors, and relaxation techniques. The theoretical basis for error analysis including vector and matrix norms. Applications such as least squares and finite difference methods. Offered spring semester of even-numbered years. 

Measures, measurable functions, integration, convergence theorems, product measures, signed measures.

Topics include: Banach spaces, Lp-spaces, Hilbert spaces, topological vector spaces, and Banach algebra.

A study of group theory (including the Sylow Theorems and solvable groups); ring theory (including the Noetherian rings and UFDs); modules, tensor algebra, and semi-simple rings.

Polyhedra, simplicial homology theory, cohomology rings, and homotopy groups.