## GRADUATE COURSES IN MATHEMATICS

**Mathematics (MATH)**

**5111 Graduate Assistant Training. **(1-0) This course is concerned with techniques used in the teaching of mathematics. This course is required as a condition of employment for graduate teaching and instructional assistants. This course does not earn graduate degree credit. Repeatable with different emphasis. Graded on a credit (CR), no-credit (F) basis.

**5301 Partial Differential Equations.** (3-0) Theory and application of partial differential equations; deduction of the differential equation; use of vector and Tensor methods; equations of the first order; wave equations; vibrations and normal functions; Fourier series and integral; Cauchy’s methods, initial data; methods of Green; potentials; boundary problems; methods of Reimann-Volterra; characteristics.

Prerequisites: Mathematics 3323 and consent of the instructor.

**5303 History of Mathematics.** (3-0) A study of the development of mathematics and of the accomplishments of men and women who contributed to its progress. Cannot be used on a degree plan for M.S. degree.

Prerequisite: A grade of at least C in Mathematics 2472.

**5304 Topics in Mathematics for the Secondary Teacher.** (3-0) A study of the current trends and topics found in the secondary school mathematics curriculum with the goal of improving the mathematical background of the secondary teacher. Course content will be flexible and topics will be selected on the basis of student needs and interests. Cannot be used on degree plan for M.S. degree.

Prerequisite: A grade of C in Mathematics 2472.

**5305 Advanced Course in Probability and Statistics.** (3-0) Advanced topics in probability and statistics. May be repeated once with different emphasis for additional credit.

Prerequisite: Mathematics 3305.

**5306 Ring Theory. **(3-0) A course in ring theory. Commutative and non-commutative rings, examples, and applications adapted to the needs of the class.

Prerequisite: A grade of at least C in Mathematics 4307.

** 5307 Modern Algebra. **(3-0) Topics in modern algebra. Material will be adapted to the needs of the class.

Prerequisite: Mathematics 4307 or consent of the instructor.

**(3-0) A critical study of the foundations of derivation equations, operator spaces, and such basic topics. Recent developments in this field will be investigated and independent investigation will be encouraged.**

**5311 Foundations of Differential Equations.**Prerequisite: A grade of at least “C” in Mathematics 3323 and 3380.

**(3-0) Modern developments in the field of a complex variable.**

**5312 Functions of a Complex Variable.**Prerequisite: A grade of at least “C” in Mathematics 3373, 3380, and 4315.

**(3-0) Topics in field theory, separable extensions, and Galois Theory.**

**5313 Field Theory.**Prerequisite: A grade of at least “C” in Mathematics 4307.

**(3-0) Topics in algebra selected from quadratic forms, elementary number theory, algebraic or analytic number theory, with material adapted to the needs of the class.**

**5314 Number Theory.**Prerequisite: A grade of at least “C” in Mathematics 4307 or consent of instructor.

**(3-0) Open to graduate students on an individual basis by arrangement with the mathematics department. A considerable degree of mathematical maturity is required. May be repeated with different emphasis for additional credit. This course does not count toward any degree in the Department of Mathematics.**

**5317 Problems in Advanced Mathematics.****(3-0) A course in the theory of integration with special emphasis on the Lebesgue integrals. A course in the theory of real variables, with a knowledge of point set theory, is desirable as a background for this course. A considerable amount of mathematical maturity is required.**

**5319 The Theory of Integration.**Prerequisite: A grade of “C” or higher in MATH 4315 and 5373.

**(3-0) Point-set topology with an emphasis on general topological spaces; separation axioms, connectivity, the metrization theorem, and the C-W complexes.**

**5329 General Topology.**Prerequisite: A grade of at least “C” in Mathematics 4330.

**(3-0) Point-set topology with an emphasis on metric spaces and compactness but including a brief introduction to general topological spaces.**

**5331 Metric Spaces.**Prerequisite: A grade of least “C” in Mathematics 4330.

**(3-0) Topics selected from optimization and control theory, numerical analysis, calculus of variations, boundary value problems, special functions, or tensor analysis. May be repeated with different emphasis for additional credit.**

**5336 Studies in Applied Mathematics.**Prerequisites: Six hours of advanced mathematics pertinent to topic and consent of the instructor.

**(2-2) This course will involve the analysis of algorithms from science and mathematics, and the implementation of these algorithms using a computer algebra system. Symbolic numerical and graphical techniques will be studied. Application will be drawn from science, engineering, and mathematics.**

**5340 Scientific Computation.**Prerequisite: MATH 3323 or consent of instructor.

**(3-0) This course introduces formulation and statistical methodologies for simple and multiple regression, assessment of model fit, model design, and criteria for selection of optimal regression models. Students will develop skills with the use of statistical packages and the writing of reports analyzing a variety of real-world data**

**5345 Regression Analysis.**Prerequisite: MATH 2472.

**(3-0) This course, covers permutations, combinations, Stirling numbers, chromatic numbers, Ramsey numbers, generating functions, Polya theory, Latin squares and random block design.**

**5350 Combinatorics.**Prerequisite: MATH 3398 or consent of instructor.

**This course is designed to emphasize the close tie between the theoretical and algorithmic aspects. The topics may include basic concepts such as connectivity, trees, planarity, coloring of graphs, matchings, and networks. It also covers many algorithms such as Max-flow Min-cut algorithm, maximum matching algorithm, and optimization algorithms for facility location problems in networks.**

**5355 Applied and Algorithmic Graph Theory.**Prerequisite: MATH 5388 or MATH 3398.

**(3-0) Boolean algebra, counting techniques, discrete probability, graph theory, and related discrete mathematical structures that are commonly encountered in computer science.**

**5358 Applied Discrete Mathematics.**Prerequisite: A grade of at least “C” in Mathematics 2472.

**(3-0) This course introduces the process and techniques of mathematical modeling. It covers a variety of application areas from the natural sciences. Emphasis is placed on deterministic systems, stochastic models, and diffusion.**

**5360 Mathematical Modeling.**Prerequisite: MATH 3373, MATH 3323, and MATH 5301 or consent of instructor.

**(3-0) Discuss those topics that will enable the student to obtain a better grasp of the fundamental concepts of the calculus of real variables and the more recent developments of this analysis.**

**5373 Theory of Functions of Real Variables.**Prerequisite: A grade of at least “C” in Mathematics 4315.

**(3-0) This course is designed to introduce a wide range of topics in applied statistics, including, but not limited to, experimental design, stochastic modeling, time series, and computational statistics.**

**5376 Topics in Applied Statistics.**Prerequisite: Approval of instructor.

**(3-0) This course introduces fundamental concepts in the design of experiments, justification of linear models, randomization and principles of blocking. It also discusses the construction and analysis of basic designs including fractional replication, composite designs, factorial designs, and incomplete block designs.**

**5376A Design and Analysis of Experiments.**Prerequisite: Approval of instructor.

**(3-0) This course introduces basic methods, one-way, two-way ANOVA procedures, and multifactor ANOVA designs. Prerequisite: Approval of instructor.**

**5376B Analysis of Variance.****(3-0) A formal study of the theory of sets, relations, functions, finite and infinite sets, set operations and other selected topics. This course will also train the student in the understanding of mathematical logic and the writing of proofs.**

**5381 Foundations of Set Theory.**Prerequisite: A grade of at least “C” in Mathematics 2472.

**(3-0) A course covering the foundations of mathematical analysis. Topics include: real numbers, sequences, series, and limits and continuity of functions.**

**5382 Foundation of Real Analysis.**Prerequisite: Mathematics 5381.

**(3-0) Definitions and elementary properties of groups, rings, integral domains, fields and vector spaces with great emphasis on the rings of integers, rational numbers, complex numbers, polynomials, and the interplay between algebra and geometry.**

**5384 Geometric Approach to Abstract Algebra.**Prerequisite: Mathematics 5381.

**(3-0) Knot polynomials and other knot invariants. The topological classification of surfaces and topological invariants of surfaces.**

**5386 Knots and Surfaces, An Introduction to Low-Dimensional Topology.**Prerequisite: A grade of at least “C” in Mathematics 2472.

**(3-0) This course covers topics from: basic and advanced techniques of counting, recurrent relations, discrete probability and statistics, and applications of graph theory.**

**5388 Discrete Mathematics.**Prerequisites: A grade of at least “C” in Mathematics 2472.

**(3-0) This course will cover not only some of the basic statistical ideas and techniques but also the mathematical and probabilistic underpinnings of these techniques with an emphasis on simulations and modeling. The planning, conducting, analysis, and reporting of experimental data will also be covered.**

**5390 Statistics.**Prerequisite: A grade of at least “C” in Mathematics 2472.

**(3-0) A study of topics in geometry including geometrical transformations, the geometry fractals, projective geometry, Euclidean geometry, and non-Euclidean geometry.**

**5392 Survey of Geometries.**Prerequisite: A grade of at least “C” in Mathematics 2472.

**This course represents a student’s initial thesis enrollment. No thesis credit is awarded until student has completed the thesis in Mathematics 5399B. Graded on a credit (CR), progress (PR), no-credit (F) basis.**

**5399A Thesis.****This course represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding. Graded on a credit (CR), progress (PR), no-credit (F) basis.**

**5399B Thesis.**** **

**Mathematics Education (MTE)**

**Mathematics Education (MTE)**

** 5301 Topics in Mathematics for the Middle School Teacher. **(3-0) This topics course is designed to provide the general 4th-8th teacher with the content knowledge necessary to effectively teach mathematics at the middle level.

**(3-0) This topics course is designed to provide the general teacher with the pedagogical content knowledge necessary to effectively teach mathematics at the middle level.**

**5302 Topics in Teaching Mathematics for the Middle School Teacher.****(3-0) This course will focus on numerical reasoning and problem solving with particular attention being placed on strategies for solving problems, methods for mental computation and computational estimation, and algorithmic processes being taught in a student-centered atmosphere where teachers are free to take risks.**

**5311 Quantitative Reasoning.****(3-0) This course will focus on using spatial reasoning to investigate the concepts of direction, orientation, shape and structure; using mathematical reasoning to develop and prove geometric relationships; using logical reasoning and proof in relation to the axiomatic structure of geometry; using measurement of geometry concepts to solve real-world problems.**

**5313 Geometry and Measurement.****(3-0) This course will focus on using algebraic reasoning to investigate patterns, make generalizations, formulate mathematical models, and make predications; using properties, graphs, and applications of relations and function to analyze, model and solve problems; and making connections among geometric, graphic, numeric and symbolic representation of functions and relations.**

**5315 Algebraic Reasoning.****(3-0) This course will focus on modeling problems, applying appropriate mathematical analysis and drawing conclusions from the analysis; solving problems recursively, using linear and non-linear functions and using geometry and discrete mathematics to solve problems in Science, Music, and Art.**

**5317 Math Modeling.**Prerequisite: MTE 5315.

**(3-0) A first course in differential and integral calculus. The student will explore the slope of secant lines, average velocity, limit, instantaneous velocity, derivative, slope of a curve at a point, area under a graph, integrals, fundamental theorem of calculus, and applications.**

**5319 Concepts of Calculus.**Prerequisite: MTE 5317 or consent of department chair.

**(3-0) This course will deal with using graphical and numerical techniques to explore date, characterize patterns, and describe departures from patterns; designing experiments to solve problems; understanding the theory of probability and its relationship to sampling and statistical inference and its use in making and evaluating predication.**

**5321 Probability and Statistics.**Prerequisite: MTE 5315.

**(3-0) This course will consist of an introduction to fundamental mathematical structures and techniques of proof. Topics will include: logic, set theory, number theory, relations, and functions. Emphasis will be placed on communication about mathematics and construction of well-reasoned explanations.**

**5323 Logic and Foundations of Mathematics.**Prerequisite: MTE 5313 and 5319.