Course Descriptions — Master of Science in Mathematics

MTH5100 Foundations of Higher Mathematics
3 semester hours
The fundamentals of advanced mathematics and an introduction to mathematical proofs. Topics include logic, quantifier notation, set operations, functions, relations, the integers, and study of rational, real, and complex numbers as fields. Various types of proof techniques will be studied and applied to problems from number theory, geometry, analytic geometry, discrete mathematics, logic and calculus.
Prerequisite: Open to graduate students only.

MTH5200 Modern Geometries
3 semester hours
A study of absolute, finite, and non-Euclidean geometries from an axiomatic viewpoint.
Prerequisite: Open to graduate students only.

MTH5300 Number Theory
3 semester hours
Topics include the theory of mathematical induction, divisibility theory in the integers, prime numbers and their distribution, the theory of congruences and modular arithmetic, Fermat’s theorem, quadratic reciprocity, Diophantine equations, and number theoretic functions and their applications.
Prerequisite: Open to graduate students only.

MTH5400 Probability and Statistics
3 semester hours
This course includes probability for discrete sample spaces, probability distributions, Chebyshev’s theorem, moment generating functions, continuous random variables, sampling distributions, point and interval estimation, theory of hypothesis testing, regression and correlation, and introductory analysis of variance.
Prerequisite: Open to graduate students only.

MTH5500 Technology in the Mathematics Classroom
3 semester hours
Hands-on experiences working with current technology (scientific calculators, graphic calculators, computers, and computer software) for elementary, middle school, and secondary school mathematics. Presentation and evaluation of methods and strategies for employing technology as a regular part of instruction and assessment, including discussion of educational foundations.
Prerequisite: Open to graduate students only.

MTH5600 Assessment and Curriculum Development in Mathematics
3 semester hours
A balanced study of theoretical research-based foundations and classroom reform-based perspectives on assessment and evaluation in school mathematics. Consideration of alternate forms of assessment and evaluation of mathematics teaching and of students’ mathematical learning. Topics include assessment standards, scoring rubrics, performance assessment, and portfolios. Curriculum goals and issues are also addressed; recent developments in curriculum; learning research; alternate modes of presentation.
Prerequisite: Open to graduate students only.

MTH5701 Mathematics Education Research Seminar I
1 semester hour
This seminar serves as an introduction to methods of critical reading of research reports and to the structure and scope of mathematics education research.

MTH5702 Mathematics Education Research Seminar II
1 semester hour
Students will investigate recent developments and relevant research in mathematics education, and be introduced to the process of formal inquiry, as well as
the skills necessary to read and evaluate the research.
Prerequisite: MTH5701.

MTH5703 Mathematics Education Research Seminar III
1 semester hour
Students will read and evaluate original research, discuss issues of validity and reliability in research, and learn to assemble components for the writing of research.
Prerequisites: MTH5701 and MTH5702.

MTH5704 Mathematics Education Research Seminar IV
1 semester hour
Students will define a problem and begin investigation of it as a research project. The project must deal with a problem in mathematics education and may be local or national in scope.
Prerequisites: MTH5701; MTH5702 and MTH5703.

MTH6100 Abstract Algebra I
3 semester hours
Introduction to group theory. Topics include equivalence relations, groups, subgroups, cyclic groups, permutation groups, isomorphisms, cossets, external direct products, normal subgroups, factor groups, group homeomorphisms, rings, and integral domains.
Prerequisite: Open to graduate students in mathematics only.

MTH6200 Abstract Algebra II
3 semester hours
Continuation of MTH6100. Introduction to commutative rings, with emphasis on polynomial rings; fields vector spaces, and algebraic extensions.
Prerequisite: MTH6100.

MTH6300 Advanced Calculus I
3 semester hours
Reexamination of the calculus of functions of one variable: convergence, continuity, differentiation, the mean-value theorem, and the Riemann integral.
Prerequisite: Open to graduate students in mathematics only.

MTH6400 Advanced Calculus II
3 semester hours
Further study of sequences and series of functions, functions of several variables, and an introduction to complex analysis.
Prerequisite: MTH6300.

MTH6700 Mathematics Education Research II
3 semester hours
Students will determine a problem and investigate the problem as a research project. The project must deal with a problem in mathematics education and may be local or national in scope.
Prerequisite: MTH5700.