## Mathematics (MTH) courses

### MTH 603 Advanced Calculus I

Prerequisite: MTH 280 and MTH 315.Concepts of limit, continuity, differentiation, Riemann integration, sequences and series, other related topics. May be taught concurrently with MTH 503. Cannot receive credit for both MTH 503 and MTH 603.

### MTH 604 Advanced Calculus II

Prerequisite: MTH 302; and MTH 503 or MTH 603.This is a continuation of MTH 603, including sequences and series of functions, uniform convergence, multivariate calculus, and other selected topics. May be taught concurrently with MTH 504. Cannot receive credit for both MTH 504 and MTH 604.

### MTH 605 Theory of Functions of a Complex Variable

Prerequisite: MTH 280 and MTH 315.Theory of elementary functions-polynomial, trigonometric, exponential, hyperbolic, logarithmic-of a complex variable; their derivatives, integrals; power series; other selected topics. May be taught concurrently with MTH 506. Cannot receive credit for both MTH 506 and MTH 605.

### MTH 607 Introduction to Partial Differential Equations

Prerequisite: MTH 302 and MTH 303 and MTH 315.Introduction to linear first and second order partial differential equations, including some formal methods of finding general solutions; the Cauchy problem for such equations, existence theorems, formal methods of finding the solution, and the role of characteristics; the classical boundary and initial value problems for the wave equation, heat equation and the boundary value problems for Laplace's equation. May be taught concurrently with MTH 507. Cannot receive credit for both MTH 507 and MTH 607.

### MTH 611 High School Mathematics from an Advanced Perspective

Prerequisite: permission of instructor.The focus of the course will be on relating what the mathematics students have learned in upper-level courses to what they will be teaching when they are in the high school classroom. The students' ability to reason and problem-solve mathematically and to model real-world problems in a mathematical context will be developed so they will be able to pass these abilities on to their own students. If there is a sufficient demand, an online component may be offered. May be taught concurrently with MTH 510. Cannot receive credit for both MTH 611 and MTH 510.

### MTH 631 Introduction to Abstract Algebra

Prerequisite: MTH 302 and MTH 315.Theory of groups, rings, integral domains, fields, polynomials. May be taught concurrently with MTH 532. Cannot receive credit for both MTH 532 and MTH 631.

### MTH 634 Linear Algebra II

Prerequisite: MTH 333.Topics include eigenvalue problems; Jordan normal form, linear functionals, bilinear forms, quadratic forms, orthogonal and unitary transformations, Markov processes, and other topics selected by the instructor. May be taught concurrently with MTH 534. Cannot receive credit for both MTH 534 and MTH 634.

### MTH 636 Theory of Numbers

Prerequisite: MTH 302 and MTH 315.Factorization, Euler totient function, congruences, primitive roots, quadratic residues and reciprocity law. May be taught concurrently with MTH 536. Cannot receive credit for both MTH 536 and MTH 636.

### MTH 637 Applied Abstract Algebra

Prerequisite: MTH 333 or MTH 532 or MTH 632.Topics typically include finite fields, block designs, error-correcting codes (nonlinear, linear, cyclic, BCH, and Reed-Solomon codes), cryptography, and computer implementation of these applications. May be taught concurrently with MTH 537. Cannot receive credit for both MTH 537 and MTH 637.

### MTH 640 Statistical Theory I

Prerequisite: MTH 302.Random variables, discrete and continuous probability functions, expectation, moment-generating functions, transformation of variables. May be taught concurrently with MTH 540. Cannot receive credit for both MTH 540 and MTH 640.

### MTH 643 Statistical Theory II

Prerequisite: MTH 540 or MTH 640 or equivalent.Estimation, complete and sufficient statistics, maximum likelihood estimation, hypothesis testing, nonparametric statistics. May be taught concurrently with MTH 541. Cannot receive credit for both MTH 541 and MTH 643.

### MTH 645 Applied Statistics

A course on statistical concepts, methods and data analysis with emphasis on assumptions and effects on violating those assumptions. Computer statistical packages will be used. Topics include statistical models, random sampling, normal distribution, estimation, confidence intervals, tests and inferences in single and two populations, and n-way analysis of variance. May be taught concurrently with MTH 545. Cannot receive credit for both MTH 545 and MTH 645.

### MTH 646 Analysis of Variance and Design of Experiments

Prerequisite: MTH 345 or MTH 541 or MTH 643 or MTH 545 or MTH 645.Topics include analysis of variance, estimation of variance components, randomized incomplete blocks, Latin squares, factorial nested, split-plot designs, fixed, random and mixed models. May be taught concurrently with MTH 546. Cannot receive credit for both MTH 546 and MTH 646.

### MTH 647 Applied Regression Analysis

Prerequisite: MTH 345 or MTH 541 or MTH 643 or MTH 545 or MTH 645.Topics include fitting a straight line, matrix models, residuals, selecting best equation, multiple regression, and nonlinear estimation. May be taught concurrently with MTH 547. Cannot receive credit for both MTH 547 and MTH 647.

### MTH 648 Applied Time Series Analysis

Prerequisite: MTH 540 or MTH 640; and MTH 345 or MTH 541 or MTH 643 or MTH 545 or MTH 645.This course will study the analysis of data observed at different points of time. Topics include stationary and non-stationary time series models, linear time series models, autoregressive models, autocorrelations, partial autocorrelations, moving average models, ARMA models, ARIMA models, forecasting, prediction limits, model specification, least square estimation, and seasonal time series models. Computer statistical packages will be used. May be taught concurrently with MTH 548. Cannot receive credit for both MTH 548 and MTH 648.

### MTH 653 Stochastic Modeling

Prerequisite: MTH 540 or MTH 640.This course will study applications of probability and statistics from a modeling point of view. Topics include generating functions, branching processes, discrete time Markov chains, classification of states, estimation of transition probabilities, continuous time Markov Chains, Poisson processes, birth and death processes, renewal theory, queuing systems, Brownian motion, and stationary processes. Computer statistical packages will be used. May be taught concurrently with MTH 543. Cannot receive credit for both MTH 543 and MTH 653.

### MTH 667 Introduction to Non-Euclidean Geometry

Prerequisite: MTH 302 and MTH 315.Development of non-Euclidean geometries; intensive study of hyperbolic geometry. May be taught concurrently with MTH 567. Cannot receive credit for both MTH 567 and MTH 667.

### MTH 670 Combinatorial Analysis

Prerequisite: MTH 280 and MTH 315.An introduction to combinatorial analysis including enumeration methods, combinatorial identities with applications to the calculus of finite differences and difference equations. May be taught concurrently with MTH 570. Cannot receive credit for both MTH 570 and MTH 670.

### MTH 675 History of Mathematics

Prerequisite: MTH 302 and MTH 315.Development of mathematics through the calculus; solution of problems of historical interest, problems which use historically significant techniques; problems whose solutions illuminate significant mathematical characteristics of elementary mathematics. May be taught concurrently with MTH 575. Cannot receive credit for both MTH 575 and MTH 675.

### MTH 680 Applied Mathematics

Prerequisite: MTH 303 and MTH 333.An introduction to several areas of applied mathematics including control theory, optimization, modeling of population dynamics, modeling of mathematical economics, minimax and game theory, and calculus of variations. May be taught concurrently with MTH 580. Cannot receive credit for both MTH 580 and MTH 680.

### MTH 682 Introductory Topology

Prerequisite: MTH 302 and MTH 315.Properties of abstract metric and topological spaces; discussion of concepts of compactness and connectedness. May be taught concurrently with MTH 582. Cannot receive credit for both MTH 582 and MTH 682.

### MTH 696 Readings

Prerequisite: permission of department head.Periodic conferences with an advisor are required. May be repeated to a total of 6 hours. May be taught concurrently with MTH 596. Cannot receive credit for both MTH 596 and MTH 696.

### MTH 701 Real Analysis

Prerequisite: MTH 503 or MTH 603.Topics include countable and uncountable sets, convergence, Lebesgue measure on the real line, the development of the Lebesgue integral, the fundamental theorem of calculus and Lp spaces.

### MTH 702 Real and Abstract Analysis

Prerequisite: MTH 701.A study of the theory of abstract measures and integration, and an introduction to functional analysis.

### MTH 706 Complex Analysis

Prerequisite: MTH 503 or MTH 603.Analytic functions, power series, Cauchy's theorem and its applications, residues. Selected topics from conformal mapping, analytic continuation, harmonic functions, Fourier series, and Dirichlet problems.

### MTH 710 Contemporary Mathematics for Secondary Teachers

Prerequisite: MTH 460 and MTH 333.Reports, research, and recent trends in secondary mathematics; recently developed programs in algebra and geometry.

### MTH 721 Theory of Ordinary Differential Equations I

Prerequisite: MTH 303; and MTH 503 or MTH 603.Existence and uniqueness theorems for first order differential equations; system of linear and nonlinear differential equations; continuous dependence of solutions on initial conditions and parameters; behavior of solutions of equations with constant coefficients, study of Lyapunov's theorems on stability; introduction to boundary value problems.

### MTH 722 Theory of Ordinary Differential Equations II

Prerequisite: MTH 721.Theory and application of boundary value problems; periodic solutions; linear systems with periodic coefficients (Floquet theory); two dimensional (autonomous) systems limit cycles. Differential equations under Caratheodory conditions; theory of differential and integral inequalities and other selected topics, if time permits.

### MTH 730 Abstract Algebra I

Prerequisite: MTH 532 or MTH 631; and MTH 333.Topics from group theory will include Cayley's Theorem, finite abelian groups, Cauchy's Theorem, the Sylow Theorems, and free groups.

### MTH 732 Abstract Algebra II

Prerequisite: MTH 730.Topics from ring theory will include the Chinese Remainder Theorem, Euclidean domains, rings of fractions, PID's and UFD's, and polynomial rings. Topics from field theory will include splitting fields, Galois Theory, separability, normality, and finite fields.

### MTH 741 Statistical Inference I

Prerequisite: MTH 540 or MTH 640 or equivalent.Formulation of statistical models, sufficiency and exponential families, methods of estimation, optimality theory. Uniformly minimum variance unbiased estimators, Fisher information, Cramer/Rao inequality, large sample theory, Bayes procedures and minimax procedures.

### MTH 742 Statistical Inference II

Prerequisite: MTH 741.Confidence intervals and regions, hypothesis testing, the Neyman-Pearson framework, uniformly most powerful tests, likelihood ratio criteria, power functions, similar regions, invariant tests, distribution free tests.

### MTH 750 Number and Operations for Elementary Mathematics Specialists

Prerequisite: Two years teaching experience and permission of program coordinator; and concurrently enrollment in ELE 730.This course is designed to develop an understanding of the learning and teaching of pre-number concepts, counting and cardinality, and numbers and operations in base ten. Emphasis will be given to how children think about and learn these concepts and how they fit into the elementary school curriculum. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 752 Rational Numbers and Proportional Thinking for Elementary Mathematics Specialists

Prerequisite: MTH 750 and permission of program coordinator; and concurrent enrollment in ELE 732.This course is designed to develop an understanding of the learning and teaching of rational numbers and ratio and proportional relationships. Emphasis will be given to how children think about and learn these concepts and how they fit into the elementary school curriculum. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 754 Algebraic Reasoning for Elementary Mathematics Specialist

Prerequisite: two years teaching experience and permission of program coordinator; and concurrently enrollment in ELE 734.This course will focus on the content and complexities of teaching and assessing algebraic reasoning in grade 1-6 settings. Course content will include examination of representation and analysis of mathematical situations and structures. Attention will be given to patterns, functions, and the transition from arithmetic to algebra. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 758 Data and Probability for Elementary Mathematics Specialist

Prerequisite: two years teaching experience and permission of program coordinator.This course is designed to develop understanding of probabilistic reasoning and the collection, exploration, and analysis of data. Emphasis will be given to how children think and learn about these concepts and how they fit into the elementary school curriculum. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 760 Geometry and Measurement for Elementary Mathematics Specialist

Prerequisite: two years teaching experience and permission of program coordinator; and concurrently enrollment in ELE 738.This course is designed to develop an understanding of the teaching and learning of geometry and measurement. Emphasis will be given to how children think about and learn these concepts and how they fit into an elementary curriculum. This course cannot be used within the MS Mathematics program or the MSEd Secondary Education (Mathematics) program.

### MTH 781 Topology

Point set topology in abstract spaces.

### MTH 791 Seminar I

Seminar in Mathematics.

### MTH 792 Seminar II

Seminar in Mathematics.

### MTH 796 Science Internship

Completion of an internship project (at least 80 hours per credit hour) at a discipline-related business, nonprofit organization, or government agency, approved and supervised by both the departmental and internship advisors. Includes a formal report in the appropriate professional format, and an oral presentation at an approved venue. Graded Pass/Not Pass only. No more than 6 hours may count toward a masters degree. This course may only be counted toward the PSM designation of the MNAS degree.

### MTH 797 Topics

Prerequisite: permission of department head.Material covered determined by the interests and backgrounds of the students. May be repeated for a maximum of 6 hours.

### MTH 798 Research

Supervised research in mathematics or mathematics education. May be repeated.

### MTH 799 Projects

Independent research for thesis preparation.