The Department of Mathematics, Physics, Computer Science, and Geomatics supports graduate programs in Mathematics and General Science Education.   The College of Education offers a Master of Science in Education, M.S.Ed., A-level certification program in secondary education in the teaching fields of mathematics and general science, a Master of Science in Education, M.S. Ed., A-level certification, alternative fifth-year program in secondary education in the areas of mathematics and general science, and a Masters of Education, M.Ed., non-certification program with concentrations in mathematics and general science.    Visit the College of Education’s web page at the Troy State site for more information on admission and degree requirements.

The following graduate courses are offered through the Department of Mathematics, Physics, Computer Science, and Geomatics.    

MTH 5512 (3 SH) Discrete Mathematical Methods

Graph theory, tress, algorithms, recurrence relations, and Boolean algebra.  Prerequisites:  MTH 2227 and MTH 3302.

MTH 5522 (3 SH) Numerical Analysis

Finite differences, interpolation, numerical integration and differentiation, solutions of equations of one variable, linear systems, and numerical solutions or ordinary differential equations.  Prerequisite:  MTH 2227, MTH 3331.

MTH 5523 (3 SH) Probability and Statistics I

Fundamentals of probability theory, sample spaces, mutual exclusion, independence, conditional probability, permutations and combinations, common discrete and continuous distributions, expected value, mean, variance, multivariate distributions, covariance, Central Limit Theorem.  Prerequisites:  MTH 2227 or permission of instructor. 

MTH 5524 (3 SH) Real Analysis I

Basic propositions of real variable theory to include the structure of the real number system, sequences, Bolzano Weierstrass theorem, Cauchy sequences, Heine-Borel and related theorems, differentiation, and the Riemann integral.  Prerequisite:  MTH 2227 and MTH 3302.

MTH 5525 (3 SH) Real Analysis II

Basic propositions of real variable theory to include metric and normed spaces, compactness and continuity, Fundamental Theorem of Calculus, pointwise and uniform convergence, power series, Lebesgue and Riemann integrals.  Prerequisite:  MTH 4424.

MTH 5526 (3 SH) Complex Analysis

Complex numbers, analytic functions, elementary functions and their mappings, integrals, contour integral, and Cauchy integral formula.  Prerequisite:  MTH 2227.

MTH 5536 (3 SH) Theory of Numbers

Divisibility, congruence, prime numbers, Fermat’s theorem, number theoretic functions.  Prerequisite:  MTH 2227 and MTH 3302.

MTH 5541 (3 SH) Algebraic Structures I

Equivalence relations and partitions.  Properties of the integers, modular arithmetic.  Elementary theory of groups, finite groups, subgroups, cyclic groups, permutation groups.  Isomorphisms.  Cosets and factor groups.  Direct products.  Prerequisites:  MTH 2227, 3302, 3331. 

MTH 5542 (3 SH) Algebraic Structures II
            Elementary theory of rings, polynomial rings, divisibility, unique factorization

domains.  Integral domains, ideals, factor rings, divisibility in integral domains.  Elementary theory of fields.  Extension fields.  Polynomials. Prerequisite:  MTH 4441.

MTH 5543 (3 SH) Probability and Statistics II

Fundamentals of the theory of statistics, the Central Limit Theorem, point estimation, sufficiency, consistency, hypothesis testing, sampling distributions, confidence intervals, linear regression models, interpretation of experimental results, Bayesion Estimation.  Prerequisite:  MTH 4423.

MTH 5560 (3 SH) Topology

An introduction to metric and topological spaces and associated topics, including interior and closure operators, separation axioms, compactness, and connectedness.  Prerequisite:  MTH 3302.

MTH 5581 (3 SH) Methods and Materials for Teaching Mathematics

Teaching methods, selection, organization, and use of mathematics material in secondary schools.  Observation and teaching experiences will be included.  Prerequisites:  EDU 3300, 3346, MTH 2227 or permission of instructor.  Credit will not count toward a non-teaching major or minor in mathematics.

MTH 6600 (3 SH) Modern Topics in Mathematics

An investigation of current topics in mathematics, that is generally not covered in regularly offered graduate courses in the mathematic graduate curriculum.

MTH 6610 (3 SH) History of Mathematics

The course is designed to acquaint the secondary mathematic teacher with the historical development of mathematics with particular attention given to the techniques of the periods studied.

MTH 6612 (3 SH) Advanced Discrete Mathematics

Trees, network models and Petri nets, Boolean algebra and combinatorial circuits, automata, grammars, and languages.  Prerequisite:  Discrete Mathematical Methods or permission of instructor.

MTH 6616 (3 SH) Mathematical Models

An introduction to the modeling process.  Students will practice creative and empirical model constructions, analyze models and do independent model research.  Applications using paired data will be included.

MTH 6620 (3 SH) Advanced Concepts of Algebra

            Study of rings, integral domain fields, factorization, ideals, field extensions.

MTH 6621 (3 SH) Foundations of Mathematics

Study of the axiomatic nature of mathematics, theory of sets, cardinal and ordinal numbers, linear continuum, real numbers, zorn’s lemma, and axiom of choice

MTH 6624 (3 SH) Applied Combinatorics

A study of the use of generating functions in problem solving, method of Inclusion-Exclusion, Polya’s Enumeration Formula, Burnside’s Theorem.

MTH 6625-7  (1-3 SH) Specialized Study in Area of Mathematics

Study of a problem or problems using research techniques.  Selection of problem must be approved by student’s advisor, instructor under whom the study is to be made, and the appropriate director of the Graduate School.  Total credit for any combination of enrollments in these courses may not exceed six semester hours.

MTH 6631 (3 SH) Advanced Matrix Analysis

Special classes of matrices, congruence, bounds of characteristic roots, regions containing characteristic roots, the Moore-Penrose inverse, the c-inverse, and the inertia of some special classes of matrices.  Emphasis on theory and theorem proving.  Prerequisite:  Linear Algebra of permission of instructor.

MTH 6632 (3 SH) Non-Euclidean Geometry

Study of non-Euclidean geometries with emphasis given to their logical development.

MTH 6650 (3 SH) Trends in Technology and Problem Solving in Secondary Mathematics Instruction

A comprehensive study of contemporary teaching strategies that incorporate current technologies and effective problem solving approaches for use by the mathematics education in the modern secondary school mathematics program.  Emphasis will be placed upon the effective use of calculators, writing, and computer software in the mathematics curriculum.

MTH 6691 (3 SH) Research in Education (Mathematics)

A study of a variety of research and evaluation methods in the teaching of mathematics.

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