Graduate Course Descriptions

Prerequisite: MT320 Introduction to Analysis or its equivalent.

The MT804-805 sequence is intended to emphasize the basic ideas and results of calculus and to provide an introduction to abstract analysis.

The course begins with an axiomatic introduction to the real number system. Metric spaces are then introduced. Theoretical aspects of convergence and continuity are then studied in the context of a metric space. Differentiation and integration are treated carefully as well. The sequence concludes with an introduction to the Lebesgue integral.

Prerequisite: MT320 Introduction to Analysis or its equivalent.

Topics for the MT 814-815 sequence include: differentiation and integration of a function of a complex variable, series expansions, residue theory, entire and meromorphic functions, multiple-valued functions, Riemann surfaces, and conformal mapping problems.

Prerequisite: MT310 Introduction to Abstract Algebra or its equivalent.

The MT 816-817 course sequence will study the basic structures of abstract algebra. Topics include groups, rings, ideal theory, unique factorization, homomorphisms, field extensions, and Galois theory.

Prerequisite: MT805 Analysis II.

This is a course in the classical theory of functions of a real variable. Topics include the Lebesgue integral, the classical Banach spaces, and integration in general measure spaces.

Prerequisite: MT816 and 817 Modern Algebra I & II.

An introduction to the linear representation theory of compact groups, especially finite groups and compact Lie groups, interacting with geometry, topology, harmonic analysis and other areas of mathematics.

Prerequisite: MT320 Introduction to Analysis.

Topology is the study of geometric phenomena of a very general sort, and, as such, topological notions appear throughout pure and applied mathematics.

The first semester of the MT840-841 sequence is devoted to General or Point-Set Topology with emphasis on those topics of greatest applicability. The subject will be presented in a self-contained and rigorous fashion with stress on the underlying geometric insights.

The content of the second semester varies from year to year. It will be an introduction to a specialized area of topology; for example algebraic, differential or geometric topology.

Prerequisites: MT210 Linear Algebra and MT410 Differential Equations.

This course is an introduction to the main techniques of classical applied mathematics: approximation, linearization, and orthogonality. Topics include advanced linear algebra, function spaces, transform theory, Fourier series, differential operators, integral equations, and calculus of variations.

Prerequisites: Multivariable calculus-based probability course (e.g., MT420 or MT426).

This course begins with a brief review of probability theory, random variables, and standard distributions, then studies conditional expectations, discrete time Markov chains, the Exponential distribution and Poisson processes, continuous-time Markov chains (including birth and death processes), renewal theory, and, time permitting, Brownian motion.

Prerequisite: Calculus-based probability and statistics (e.g., MT426-427, although some review will be included at the beginning of the semester). Computing experience would be helpful, but not required.

This course introduces the student to intermediate level statistics using classical (parametric), non-parametric, permutation and bootstrap methods. Topics include analysis of variance, regression, and analysis of contingency tables, as well as specialized applications of computer-intensive methods from a wide variety of fields.

Students interested in taking the course should consult with Professor Baglivo during the fall semester since it will be possible to tailor applications to the interests of the students. Calculus-based probability and statistics is prerequisite; some review will be included at the beginning of the semester. Computing experience would be helpful, but not required.

Prerequisite: MT310 Introduction to Modern Algebra, or MT 320 Introduction to Analysis, or permission of the instructor.

This two-semester sequence is a mathematical examination of the way mathematics is done and of axiom systems, logical inference, and the questions that can (or cannot) be resolved by inference from those axioms.

Topics in MT860 include propositional calculus, first order theories, decidability, and Godel's Completeness Theorem.

Topics for MT861 will be selected from one or more of the following areas: formal number theory, axiomatic set theory, effective computability, and recursive function theory.

Department permission is required.

This is an independent study course, taken under the supervision of a Mathematics Department faculty member. Interested students should see the Graduate Vice Chair.

This seminar is required of all candidates for the M.A. degree who are not in the joint M.A./M.B.A. program.