## Graduate Courses

### MTH 505 Mathematical Problem Solving (A)

*Prerequisite - Instructor's Permission.*

Develops problem-solving ability in mathematics. Includes how to get started, methods of proof, devising a strategy, and "looking back." Places strong emphasis on critical reasoning and clarity of written expression. *3 Cr. Summer.*

### MTH 512 History of Mathematics (A)

*Prerequisite: MTH 202 and either MTH 245 or MTH 281.*

Covers the history and development of mathematical ideas from primitive origins to today. Includes topics such as arithmetic, number theory, geometries, algebra, calculus and selected advanced topics. *3 Cr. *

### MTH 521 Number Theory (A)

*Prerequisites: MTH 202 and MTH 281.*

Topics include but are not limited to: mathematical induction, divisibility, primes, arithmetic functions, congruencies, modular arithmetic, Diophantine problems and the distribution of primes. *3 Cr. *

### MTH 522 Introduction to Coding Theory (A)

*Prerequisites: MTH 324.*

Provides an introduction to error-correcting codes emphasizing the theory behind code constructions as well as explicit computation with specific codes. Covers linear codes, encoding and decoding, bounds on codes, finite fields and codes designed using finite fields. *3 Cr. *

### MTH 525 Modern Algebra (A)

Provides a study of algebraic systems, with special attention to groups and their classification properties. Emphasizes theory and proofs, but clarifies that ideas by means of specific examples involving modular arithmetic, real and complex numbers, permutations, and matrices. Requires extensive writing. *3 Cr. Every Semester.*

### MTH 529 Topics in Algebra (A)

*Prerequisite: Instructor's permission.*

Addresses specific topics in abstract algebra not covered in other courses. A list of topics to be covered will be announced before course is offered. *3 Cr. *

### MTH 530 Topology (A)

*Prerequisites - MTH324.*

Provides a study of topologies on various spaces. Emphasizes theory, abstraction, proof techniques and clarifies these by means of many specific examples. Bridges topics such as geometry, analysis and algebra. Topics include, but are not limited to set theory, continuous functions, connectedness, compactness, and separation. *3 Cr. Spring.*

### MTH 532 College Geometry (A)

*Prerequisite: MTH 324.*

Studies geometry from the synthetic, analytic, transformational and vector viewpoints. Includes these topics: axiomatic systems, finite geometries, absolute geometry, Euclidean geometry, non-Euclidean geometries, geometric transformations and projective geometry. *3 Cr. *

### MTH 539 Topics in Geometry (A)

Prerequisite - Instructor's Permission. *3 Cr. *

### MTH 541 Statistical Methods (A)

*Prerequisites: MTH 446 or MTH 456.*

This course focuses on investigative statistics, emphasizing the process of data collection and data analysis. It will incorporate case studies from current events and interdisciplinary research, taking a problem-based approach to learn how to determine which statistical techniques are appropriate. Topics will typically include making connections between the two-sample t-test, Regression and ANOVA; Multiple Regression; Design and Analysis of Experiments; Logistic Regression and Survival Analysis. *3 Cr. *

### MTH 542 Statistical Computing (A)

*Prerequisites: MTH 446 or MTH 456.*

This course is an introduction to the methods of Simulation and Monte Carlo estimation. In Part-1 of the course we will study methods for generating random variables. In Part-2 we will simulate statistical models for a given system, formulate them in terms of appropriate random variables and then using Monte Carlo methods we will estimate various quantities of interest for the simulated systems. *3 Cr. *

### MTH 543 Regression Analysis (A)

*Prerequisites - MTH346.*

General linear model in matrix form, simple and multiple regression analysis, transformations, variable selection, multicollinearity, analysis of variance, robust regression, logistic regression, principal components and factor analysis, and statistical software applications. *3 Cr. *

### MTH 546 Probability and Statistics II (A)

*Prerequisites: MTH 203 and MTH 346.*

Covers the Central Limit Theorem, maximum likelihood estimation, method of moments, unbiased and sufficient statistics, minimum variance, Cramer-Rao lower bound, confidence intervals, Neyman-Pearson Lemma, power calculations, likelihood ratio tests. *3 Cr. *

### MTH 547 Time Series (A)

*Prerequisites - MTH243 or MTH346.*

This course introduces the theory and practice of Time Series Analysis. Students will learn how to model and forecast a time series as well as read papers from the literature. *3 Cr. *

### MTH 551 Experimental Mathematics (A)

*Prerequisites: MTH281&324.*

Listed as a swing course with MTH451. Students will be exposed to a brief theory in each topic and will be given weekly projects. They will experiment using SAGE and formulate a conjecture based on the analysis of data resulting from the experiments. Then, alone with the professor's assistance, they will try to prove or, using more in depth experiments, to disprove, the conjecture. The assessment will be based on the number of completed projects. Graduate students will be required to assist undergraduates with proofs and to complete at least one proof. *3 Cr. *

### MTH 556 Advanced Differential Equations (A)

*Prerequisites: MTH 255, MTH 324 or some exposure to matrix theory.*

Covers series solutions about singular points, systems of linear first-order differential equations, plane autonomous systems, Fourier series, Sturm Liouville problems, partial differential equations of physics including the heat, wave and Laplace equation. *3 Cr. *

### MTH 557 Real Analysis (A)

*Prerequisites: MTH 203 and MTH 324.*

Provides a study of functions of a real variable. Emphasizes theory and proof techniques. Includes: real numbers, denseness of the rational numbers, convergence of sequences of real numbers, Cauchy sequences, Bolzano-Weierstrass theorem, continuous functions, uniform continuity, differentiable functions and integrable functions. Enhances understanding of the topics through a series of required writing tasks. *3 Cr. *

### MTH 558 Complex Analysis (A)

*Prerequisites: MTH203 and MTH324.*

Provides a study of functions of a complex variable. Focus on the theory of analytic functions. Includes: Cauchy-Rienmann equations, Cauchy’s Theorem, Cauchy’s integral formula, the Fundamental Theorem of Algebra, Laurent series, Residue Theorem, Contour intergration and applications to real integrals. *3 Cr. *

### MTH 560 Mathematical Modeling (A)

*Prerequisites: MTH 202 and MTH 281.*

Topics covered include Linear Programs, Duality Theory and Sensitivity Analysis, Simplex Method, Integer Programs, Branch and Bound, Markov chains (Ergodic and Absorbing), Critical Path Method, Birth and Death Processes, Intro to Queuing: M/M/1 queues; M/M/1 queues with finite capacity; M/M/s queues; finite source models; general distribution service models. Optimization and Algebra software will be used. *3 Cr. *

### MTH 563 Graph Theory (A)

*Prerequisite: MTH324 or instructor's permission.*

An introduction to graph theory, including distance concepts, symmetry and structure, trees and connectivity, Eulerian and Hamiltonian Graphs, planar graphs and imbeddings and applications of graphs. *3 Cr. *

### MTH 565 Combinatorics (A)

*Prerequisites: MTH 324 and instructor's permission.*

An introduction to combinatorics, including basic counting techniques involving permutations, combinations, compositions, and partitions; binomial coefficients; the twelve-fold way; recursions and generating functions. Other topics may include a more advanced study of permutations, sequences in combinatorics, magic squares, the probabilistic method, etc. *3 Cr. *

### MTH 571 Numerical Analysis I (A)

*Prerequisites: MTH 203.*

Covers the development of methods used to numerically approximate the solutions to mathematical problems, with consideration given to generation and propagation of round-off errors, convergence criteria and efficiency of computation. Includes these topics: roots of nonlinear equations, systems of nonlinear and linear equations, polynomial approximations, numerical differentiation and integration, and curve fitting. Mathematical software, such as MAPLE, will be used. *3 Cr. *

### MTH 581 Discrete Mathematics II (A)

*Prerequisites: MTH 201 and MTH 281.*

A second course in discrete mathematics. Includes: study of algorithms, recurrence relations, inclusion-exclusion principle, partial order and equivalence relations, graph theory, and trees. *3 Cr. *

### MTH 592 Mathematics Internship (A)

*(Prerequisite - Instructor's Permission) Allows for a supervised experience in applying mathematical skills and techniques in a practical work environment.*

Requires projects that may include applications in business, the social sciences, or physical sciences. A maximum of three credits can be applied toward the mathematics major. *1-6 Cr. Every Semester.*

### MTH 599 Independent Study in Mathematics (A)

(Prerequisite - Instructor's Permission) To be defined in consultation with the instructor/ sponsor prior to registration. *1-3 Cr. *

### MTH 605 Problem Solving in Mathematics (A)

*Prerequisite - Instructor's Permission.*

Develops problem-solving ability at the graduate level. Emphasis on meaning, strategies and written communication. Especially appropriate for adolescence mathematics teachers. *3 Cr. *

### MTH 621 Algebra (A)

*Prerequisite: MTH 425.*

Includes these topics: groups and subgroups, normal subgroups and quotient groups, permutation groups, finite Abelian groups, some special classes of rings, homomorphisms, ideals and quotient rings Euclidean rings and polynomial rings. *3 Cr. *

### MTH 628 Applications of Algebra (A)

*Prerequisite: MTH 425 and either MTH 621 or permission of instructor.*

Applies group theory and ring theory to the solution of polynomial equations and to problems in number theory, geometry, coding theory, combinatorics and selected areas of computer science. *3 Cr. *

### MTH 629 Topics in Algebra and Number Theory (A)

*Prerequisite: permission of instructor.*

Introduces topics of current interest in research or topics not covered in other courses in algebra and number theory. An outline of selected topics will be announced before the course is offered. *3 Cr. *

### MTH 639 Topics in Geometry (A)

*Prerequisite: MTH 324.*

Introduces topics of current interest in research or topics not covered in other courses in geometry. An outline of selected topics will be announced before the course is offered. *3 Cr. *

### MTH 641 Mathematical Statistics (A)

*Prerequisite: MTH 446 or MTH546.*

Allows for rigorous development of probability concepts in the sample space and models for discrete and continuous random variables. Introduces bivariate normal distribution, transformation of variables, statistics and sampling distributions, Central Limit Theorem, parametric estimation, Rao-Cramer inequality, hypothesis tests, power functions, Neyman-Pearson Theorem and both UMP and Likelihood Ratio tests. *3 Cr. *

### MTH 651 Real Analysis (A)

*Prerequisite: MTH 457.*

Includes topics such as uniform continuity and the Weierstrass Approximation Theorem, theory of differentiation and the Riemann integral, convergence of series of functions, uniform convergence of series of functions, functions of bounded variation, Riemann-Stieltjes integration, Lebesque measure and Lebesque integration. *3 Cr. *

### MTH 659 Topics in Analysis (A)

*Prerequisite: permission of instructor.*

Introduces topics of current interest in research or topics not covered in other courses in analysis. An outline of selected topics will be announced before the course is offered. *3 Cr. *

### MTH 669 Topics in Applicable Mathematics and Statistics (A)

*Prerequisite: permission of instructor.*

Introduces topics of current interest in research or topics not covered in other courses in applicable mathematics and statistics. An outline of selected topics will be announced before the course is offered. *3 Cr. *

### MTH 681 Topics in Discrete Mathematics (A)

*Prerequisite - Instructor's Permission.*

Includes topics of current interest in areas of discrete mathematics not covered (in depth) in other discrete math courses. An outline of selected topic(s) will be announced before the course begins. *3 Cr. *

### MTH 699 Independent Study in Mathematics (A)

To be defined in consultation with the instructor/sponsor prior to registration. *1-3 Cr. *