Mathematics

Courses of Instruction

Available on the Master of Arts in Teaching degree.

Program for the M.A.T. degree


Prerequisites:
A baccalaureate degree with the equivalent of a major in mathematics consisting of courses through elementary calculus of one and several variables, linear algebra, and at least 8 hours of approved advanced courses.

Graduate Program:
At the graduate level the program includes 24 hours of graduate mathematics courses and 12 hours of graduate education courses. A thesis of 6 hours may be substituted for 6 hours of the required mathematics. The MAT program totals at least 36 hours.

Mathematics course work must include: (i) 50253, 50503, and 60023, (ii) at least one of Math 50263 and 50513. All 50000-level courses count towards the MAT degree, subject to university limitations.

The required courses in Education are EDUC 60213: Advanced Educational Psychology, EDUC 60253: Historical and Philosophical Foundations of Education, EDUC 60313: Educational Assessment, and EDUC 60153: Microcomputers in Education.

The following is a complete list of courses offered by this department. Go to Class Search to see which courses are being taught this semester.

Courses of Instruction

50073 HISTORY OF MATHEMATICS
. Prerequisite: Advanced standing in mathematics, or permission. The history of mathematics from the times of ancient Egypt and Mesoptamia until the advent of calculus in the seventeenth century.

50253 ABSTRACT ALGEBRA I
. Prerequisite: Math 10123 and Math 30224 or equivalent. Introduction to groups and rings. Homomorphisms, isomorphisms, subgroups, and ideals. Quotient and product structures.

50263 ABSTRACT ALGEBRA II
. Prerequisite: Math 50253. A continuation of Math 50253. Introduction to field extensions and Galois theory. Advanced topics in groups and rings.

50303 STUDIES IN GEOMETRY AND TOPOLOGY.
Prequisite: Twelve semester hours of mathematics, and permission of the instructor. Topics include topology surfaces, convex sets, networks, and non-Euclidean geometry.

50323 DIFFERENTIAL GEOMETRY
. Prerequisite: Math 30224 and Math 30524 or equivalent. Calculus on euclidean space. Geometry of curves and surfaces. Connections and curvature.

50403 COMPLEX ANALYSIS
. Prerequisite: Math 30524. Analytic functions, harmonic functions, and the Cauchy-Riemann equations. Conformal mappings. Cauchy's integral theorem and formula, with applications. Power series and analytic continuation.

50503 REAL ANALYSIS I
. Prerequisite: Math 10123, Math 30224, and Math 30524, or equivalent. A rigorous development of elementary limit processes. Continuity, sequences, series, differentiation, integration.

50513 REAL ANALYSIS II
. Prerequisite: Math 50503. A continuation of Math 50503. Multivariable calculus, including the Implicit Function Theorem and change of variables. Other selected topics.

50613 PARTIAL DIFFERENTIAL EQUATIONS
. Prerequisite: Math 30613 or equivalent. Basic theory of hyperbolic, parabolic, and elliptic partial differential equations.

50623 APPLIED MATHEMATICS I
. Prerequisite: Math 30224, Math 30524 and Math 30613, or equivalent. Selected topics, such as linear and nonlinear systems, equilibria, Fourier series, computational graph theory, optimization and linear programming, calculus of variations, complex integration.

50633 APPLIED MATHEMATICS II.
Prerequisite: Math 50623. A continuation of Math 50623.

50703 NUMBER THEORY
. Prerequisite: Math 10123 and Math 30224 or equivalent. Properties of the integers. Divisibility, prime numbers, modular arithmetic, Chinese Remainder Theorem, Diophantine equations.

60003 THE TEACHING OF MATHEMATICS.
Teaching methods, including both general principles and specific techniques, and supervised teaching. Focus is on teaching topics from upper secondary level and entry level college courses.

60023 SURVEY OF MATHEMATICAL PROBLEMS I.
Prerequisite: Math 30224 or equivalent. Mathematical reasoning and proof techniques from various areas of mathematics such as logic, probability, graph theory, cryptography and constructibility.

60033 SURVEY OF MATHEMATICAL PROBLEMS II.
Prerequisite: Math 60023. Mathematical reasoning and proof techniques from various areas of mathematics such as game theory, set theory, limits, functions, plane Geometry and extensions of the real numbers.

60053 FOUNDATION OF MATHEMATICS.
Naïve set theory, including cardinality, the Axiom of Choice, Zorn's Lemma, and other topics.

60223 LINEAR ALGEBRA.
Prerequisite: 18 semester hours of mathematics and permission. Vector spaces, linear transformations and selected topics from multilinear algebra, spectral theory and related subjects.

60250 THEORY OF NUMBERS.
Prerequisite: Mathematics 30224 (or equivalent) and permission. Topics selected from the following: The natural numbers developed from the Peano postulates. Prime number theory, including units and associates. Divisibility and integral domains. Modular arithmetic and algebra. Diophantine equations and quadratic residues. (1-3 sem. hrs.)

60313 TOPOLOGY.
Prerequisite: 50503. Topological spaces, including separation properties, compactness, and connectedness. Metric spaces.

60403 HIGHER GEOMETRY.
Prerequisite: Graduate standing in mathematics. The foundations of geometry. The basic concepts of Euclidean and non-Euclidean geometry. Geometric transformations. Geometric constructions.

60500 INTRODUCTION TO APPROXIMATION THEORY.
Prerequisite: The equivalent of Mathematics 50503, and permission. Topics from the theory of uniform, or Tchebycheff, approximation, including uniform approximation by polynomials and other linear families, the Weierstrass theorem and the Haar unicity theorem. (1-6 sem. hrs.)

60653 INTEGRAL TRANSFORMS.
Prerequisite: One semester of complex analysis, or permission. Laplace transforms. Inversion formulas and methods of residues. Applications to systems of ordinary and partial differential equations. Problems in heat conduction and mechanical vibrations. Other transforms, including the Fourier.

60970 SPECIAL TOPICS.
Prerequisite: Graduate standing in mathematics. (1-12 sem. hrs.)

70200 ALGEBRA.
Prerequisite: The equivalent of Mathematics 50263. Groups with operators. Modules and ideals. Elementary field theory. (1-9 sem. hrs.)

70350 INTRODUCTION TO ALGEBRAIC TOPOLOGY.
Prerequisite: One semester of General Topology, and permission. Homotopy theory, including natural algebraic structures, the fundamental group of a space and covering spaces. Fibrations and higher homotopy groups. (1-6 sem. hrs.)

70403 PROJECTIVE GEOMETRY.
Prerequisite: Graduate standing in mathematics and permission.

70420 DIFFERENTIAL GEOMETRY.
Prerequisite: Mathematics 50513 and permission. Differential structures on manifolds. Differential forms and integration. Stokes' Theorem. Vector fields and flows. Poisson brackets and Lie derivatives. Affine connections and Riemannian metrics. Geodesics and completeness. (1-9 sem. hrs.)

70500 REAL AND COMPLEX ANALYSIS.
Prerequisite: Mathematics 50513, and permission. (1-12 sem. hrs.)

70550 OPERATORS IN HILBERT SPACE.
Prerequisite: A knowledge of the Lebesgue integral, and permission. Topology of Hilbert space. Projections and closed linear subspaces. General properties of normal, Hermitian and unitary operators. Compact operators. Spectral analysis of bounded and unbounded operators. Applications. (1-6 sem. hrs.)

70650 FUNCTIONAL ANALYSIS.
Prerequisite: Five semester hours of Mathematics 70500, Mathematics 50253, and Math 60313. Linear topological spaces. Convex sets. Normed linear spaces. Banach spaces, and Hilbert spaces. Linear operators. Spectral analysis. Banach algebras, C*-algebras, and von Neumann algebras. Representations and decomposition theory. (1-9 sem. hrs.)

70771.
Selected when enrolling only for non-thesis examination or preparation for the examination.

70980 THESIS.
Prerequisite: Written permission of the Chair of the Department.

70990 THESIS.
Prerequisite: Admission to candidacy. Continuation of 70980.