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Graduate Course DescriptionsCollage of Graduate Course Offerings Concepts

Mathematics (MA, STAT)

Note: Prerequisites in mathematics and statistics are intended as a guide and may be satisfied through completion of equivalent or more advanced courses. Consent of the course instructor can substitute for completion of specified prerequisites, and students are invited to discuss their eligibility for enrollment with their advisors or the instructor of the course.

Dual Level, Undergraduate-Graduate

MA 510 Vector Calculus, Cr. 3.
P: 261 (or 263). Calculus of functions of several variables and of vector fields in orthogonal coordinate systems; optimization problems; the implicit function theorem; Green’s, Stokes’, and the Divergence theorems; applications to engineering and the physical sciences.
MA 511 Linear Algebra with Applications, Cr. 3.
P: 351. Real and complex vector spaces; linear transformations; Gram-Schmidt process and projections; least squares; QR and LU factorization; diagonalization, real and complex spectral theorem; Schur triangular form; Jordan canonical form; quadratic forms.
MA 521 Introduction to Optimization Problems, Cr. 3.
P: 510, and 351 or 511. Necessary and sufficient conditions for local extrema in programming problems and in the calculus of variations. Control problems, statement of maximum principles, and applications. Discrete control problems.
MA 525 Introduction to Complex Analysis, Cr. 3.
P: 263 or 441 or 510. Complex numbers and complex-valued functions of one variable; differentiation and contour integration; Cauchy’s theorem; Taylor and Laurent series; residues; conformal mapping; applications.
MA 540 Analysis I, Cr. 3.
P: 441. Metric spaces, compactness and connectedness, sequences and series, continuity and uniform continuity, differentiability, Taylor’s Theorem, Riemann-Stieltjes integrals.
MA 541 Analysis II, Cr. 3.
P: 540. Sequences and series of functions, uniform convergence, equicontinuous families, the Stone-Weierstrass Theorem, Fourier series, introduction to Lebesgue measure and integration.
MA 553 Introduction to Abstract Algebra, Cr. 3.
P: 453. Group theory: Sylow theorems, Jordan-Holder theorem, solvable groups. Ring theory: unique factorization in polynomial rings and principal ideal domains. Field theory: straightedge and compass constructions, roots of unity, finite fields, Galois theory, and solubility of equations by radicals.
MA 554 Linear Algebra, Cr. 3.
P: 453. Review of basics: vector spaces, dimension, linear maps, matrices determinants, linear equations. Bilinear forms; inner product spaces; spectral theory; eigenvalues. Modules over a principal ideal domain; finitely generated abelian groups; Jordan and rational canonical forms for a linear transformation.
MA 556 Introduction to the Theory of Numbers, Cr. 3.
P: 263 (or 261). Divisibility, congruences, quadratic residues, Diophantine equations, and the sequence of primes.
MA 560 Fundamental Concepts of Geometry, Cr. 3.
P: 305. Foundations of Euclidean geometry, including a critique of Euclid’s Elements and a detailed study of an axiom system such as that of Hilbert. Independence of the parallel axiom and introduction to non-Euclidean geometry.
MA 571 Elementary Topology, Cr. 3.
P: 441. Fundamentals of point-set topology with a brief introduction to the fundamental group and related topics; topological and metric spaces; compactness and connectedness; separation properties; local compactness; introduction to function spaces; basic notions involving deformations of continuous paths.
MA 575 Graph Theory, Cr. 3.
P: 305 (or 351) or equivalent. Introduction to graph theory with applications.
MA 580 History of Mathematics, Cr. 3.
P: two semesters of calculus and MA 305 or consent of instructor. The origins of mathematical ideas and their evolution over time, from early number systems and the evolution of algebra, geometry, and calculus to 20th-century results in the foundations of mathematics. Connections between mathematics and society, including the role of applications in the development of mathematical concepts.
MA 581 Introduction to Logic for Teachers, Cr. 3.
P: 351 or consent of instructor. Sentential and general theory of inference and nature of proof, elementary axiom systems.
MA 598 Topics in Mathematics, Cr. 1–5. (V.T.)
Supervised reading courses as well as dual-level special topics courses are given under this number.

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