Return to Applied Mathematics | Mathematics Education | Course Index

## [1] Graduate Courses in Mathematics (MATH)

**5300 PROFESSIONALIZED SUBJECT MATTER** This course serves as an elective for the M.A. in mathematics education. The topics include algebra, geometry, and other mathematical topics from an advanced viewpoint. The subject matter is selected to strengthen the teaching skill and knowledge of secondary and beginning collegiate teachers. Prerequisite: MATH 1592 (Calculus II).

**5305 ORDINARY DIFFERENTIAL EQUATIONS II** This course serves as an elective for the M.A. in mathematics education. The topics include ordinary and partial differential equations, Fourier series, and numerical analysis with modeling applications in physics, biology, and other sciences. Lectures, computer labs, and projects are central to the course. Prerequisite: Linear Algebra (MATH 3320), and Differential Equations (MATH 3331).

**5306 MODELING AND SIMULATION** This course serves as an elective course for the MA in mathematics education. This project-oriented course applies differential equations and other methods to solve realistic problems from science, business, and industry. Lectures, computer labs, and projects. Prerequisites: MATH 2441, 3320, 3331, and 4371.

**5308 MATHEMATICAL THINKING FOR K-8 TEACHERS** This course is designed for the professional development of K-8 teachers and does not substitute for requirements in the MA degree. This course focuses on the Number, Property, and Operation Strand of the Arkansas Mathematics Framework. The importance of the structural properties of the rational number system will be investigated. Participants will be encouraged to develop and generalize algorithms within the system.

**5309 ALGEBRAIC THINKING FOR K-8 TEACHERS ** This course is required for candidates in the Elementary Mathematics Specialist program. It is designed to build both mathematical content knowledge and pedagogical content knowledge by developing a way of thinking about the mathematics that underlies both arithmetic and algebra. Class discussion, problem solving, and case studies will be central to the course. Prerequisite: MATH 5308.

**5315 INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS** This course serves as an elective course for the MA in mathematics education and introduces techniques for solving first and second order linear partial differential equations. Topics include quasi-linear first order partial differential equations, and the method of characteristics, second order linear partial differential equations, separation of variables of the heat equation, wave equation, and Laplace’s equation. Applications include heat conduction, steady state temperatures, and vibrating strings and membranes. Lecture. Prerequisites: MATH 2441, 2471, and 3331.

**5316 FUNDAMENTALS OF APPLIED MATHEMATICS FOR FLUID MECHANICS AND GRANULAR MATERIALS **This course is an introduction to applied mathematics in fluid mechanics and granular materials. It is an elective for all mathematics majors. Topics include dimensional analysis, perturbation methods for algebraic equations and differential equations, basic concepts and methods for fluid mechanics as well as granular materials. Prerequisite: Partial Differential Equations MATH 4315.

**5330 MATHEMATICAL MODELING IN BIOLOGY** This course is an introduction to mathematical modeling and analysis in biology and life sciences. Topics include dynamic system theory, feedback control, enzyme kinetics, Michaelis-Menten equation, the Hodgkin-Huxley model, mathematical models for calcium dynamics and blood glucose regulation, numerical solutions and mathematical analysis of the models. A contemporary textbook, research papers on this subject, and MATLAB will be used. Primary methods of delivery are lecture, student presentations, and discussion. Prerequisites: C or better in MATH 2441 and 3331.

**5335 GEOMETRY AND MEASUREMENT AND THEIR APPLICATIONS** This course is designed for the professional development of K-8 teachers and does not substitute for requirements in the MA degree. This course builds on and extends the preliminary understanding of the geometry and measurement developed in the undergraduate courses for K-8 teachers. The geometry topics include transformations, definition and classification, composition and decomposition of shapes, spatial visualization, and relationships between one, two and three-dimensional objects. The measurement topics include angles, linear, area, volume, capacity, mass, weight, time, money, temperature, and related rates. Instructional and assessment strategies for these areas will be explored. Applications of these topics and connections among Geometry, Measurement, and the other Strands of the Arkansas Mathematics Framework will be examined.

**5340 NUMERICAL METHODS** This course is a mathematics elective for the MA in mathematics education that introduces methods of numerical analysis with modern high speed computers. Topics include methods of solving nonlinear equations, linear and nonlinear systems, polynomial approximation, curve fitting, numerical differential equations, and numerical optimization. Lecture and computer activities. Prerequisites: MATH 2441 and 3320.

**5345 COLLEGE GEOMETRY** This course focuses on the elementary theory in foundations of geometry, advanced Euclidean geometry, and introduces transformations and non-Euclidean geometries. Problem solving, discovery, computer activities, and lecture. Prerequisite: Calculus I (MATH 1591).

**5362 ADVANCED CALCULUS I** This course is a mathematics elective for the M.A. in mathematics education. This rigorous theoretical treatment of calculus includes completeness, compactness, connectedness, sequences, continuity, differentiation, integration, and series. Lecture format and problem solving. Prerequisite: Calculus III (MATH 2371).

**5363 ADVANCED CALCULUS II** This course is an elective for the M.A. in mathematics education. This course is a multivariable treatment of Advanced Calculus topics that include a rigorous study of partial differentiation, multiple integrals, Implicit Function Theorem, Fubini’s Theorem, line integrals, and surface integrals. Lecture format and problem solving. Prerequisite: MATH 5362.

**5371 INTRODUCTION TO PROBABILITY** This course is required for the M.A. degree, if not previously taken at undergraduate level. This calculus-based introduction to probability and the distributions and properties of several discrete random variables includes hypergeometric, geometric, binomial, negative binomial, Poisson, and the distributions and properties of several continuous random variables, including normal, gamma, uniform, chi-squared, t, and F. Lecture format. Prerequisite: Calculus II (MATH 1592).

**5372 INTRODUCTION TO STATISTICAL INFERENCE** This course is required for the MA degree, if not previously taken at the undergraduate level. This introduction to the theory of statistical inference includes sampling distributions, point and interval estimation, hypothesis testing, and linear models. Lecture and projects. Prerequisites: MATH 2441 and 5371.

**5373 REGRESSION ANALYSIS** This course is an elective course for majors in mathematics and applied mathematics. It introduces simple and multiple linear models, and then more sophisticated regression models such as non-linear models, piecewise linear models, inverse prediction, weighted least squares, logistic, ridge and robust regression models. Principles in building regression models, pitfalls in regression models, and residual analysis are then discussed. Students learn basic designs of experiments and data analysis using ANOVA and examine applications in science, business, and industry through various examples. All illustrations are carried out using software such as R and STATA for various datasets. Prerequisite: MATH 5372 or consent of the instructor.

**5374 INTRODUCTION TO STOCHASTIC PROCESSES **This course is an introduction to applied mathematics in stochastic processes, and demonstrates how stochastic processes can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. It is an elective course for all mathematics majors. Topics include review of probability: conditional probabilities and conditional expectations. Markov chains, continuous-time Markov Introduction to Probability MATH 4371/5371 or consent of the instructor. Prerequisite(s): Math 4371/5371.

**5375 INTRODUCTION TO TOPOLOGY I** This course is an elective for the M.A. degree. This introduction to generalizations of the notion of continuity includes the study of minimum conditions on a set necessary to describe continuous functions. This study is accomplished via point set topology using examples including knots, surfaces, and function spaces. Lecture/seminar format. Prerequisite: Consent of instructor.

**5385 COMPLEX ANALYSIS** This course is an elective for the M.A. degree. The content of the course includes the arithmetic and geometry of the complex numbers, extension of transcendental functions to the field of complex numbers, analytic function theory, contour integration, the Cauchy Integral Theorem, series, calculus of residues, and harmonic functions. This course is fundamental to physics and engineering and is an extensive source of problems in pure mathematics. Lecture and discussion. Prerequisite: Calculus III (MATH 2371).

**5391 MACHINE LEARNING** This course serves as an elective for the MS in Applied Mathematics and the MA in Mathematics Education. The course is an introduction to common methods and algorithms used in machine learning. Content is broken down into supervised and unsupervised learning with an emphasis on using current cross-validation methods in either setting. Supervised topics include a variety of linear regression methods including ordinary, subset, and shrinkage. Unsupervised methods include cluster analysis, principal components, and independent component analysis. In all instances, the methods will be applied to data sets with a widely varying number of observations and variables. Prerequisite: MATH 5373 or consent of instructor.

**5392 TIME SERIES AND FORECASTING** This course serves as an elective for the MS in Applied Mathematics and the MA in Mathematics Education. It is an introduction to time series analysis and forecasting in data science. Time series data commonly occur in applications such as weather, share market, and medicine. Time series data are analyzed to understand the past and to predict the future, enabling managers or policy makers to make statistically guided decisions. Topics include autocorrelation analysis, filtering time-series data, basic stochastic models, univariate time-series models, stationary models, non-stationary models, long-memory processes, spectral analysis, multivariate time-series models, and state space models. Prerequisite: MATH 5373 or consent of instructor.

**6V80 MATHEMATICS SEMINAR** (Variable credit: 1-3 credit hours.) This course serves as a graduate elective for the MA or MS in mathematics. The purpose of this course is to study a chosen area of advanced mathematics or mathematics education. May be repeated for up to 6 hours when the theme of the course is changed. Prerequisite: Consent of the instructor.

**6V82 INDEPENDENT STUDY IN MATHEMATICS** (Variable credit: 1-3 credit hours.) This course serves as an elective for the MS in applied mathematics or the MA in mathematics education. The purpose of this course is to conduct independent study in a chosen area of advanced mathematics, applied mathematics, or mathematics education. May be repeated for up to 6 credit hours when the theme of the course is changed. Prerequisite: Consent of the instructor.

**6V85 RESEARCH IN MATHEMATICS** (Variable credit: 1-3 credit hours, predetermined by the instructor.) This course is a directed research project in a selected area of mathematics education, advanced mathematics, or applied mathematics. Prerequisite: Consent of instructor.

**6V96 THESIS** (Variable credit: 1-6 credit hours.) A requirement for the MS degree in Applied Mathematics (thesis option) and an option for the MA degree in Mathematics Education. Topics are chosen in consultation with an advisor. Course may be repeated.

**6305 FOUNDATIONS OF MATHEMATICS** This course is required in the M.A. program in mathematics education and is designed to introduce the fundamentals of mathematical logic and concepts of formal proof, including applications to fields such as elementary number theory and probability. Prerequisite: Consent of instructor.

**6307 ADVANCED TOPICS FOR MATHEMATICS EDUCATORS** This course is required in the M.A. program in mathematics education and includes advanced topics from functions, graphs, probability, statistics, and geometry which are relevant to mathematics in secondary schools and beginning collegiate programs. Other topics include technology, research, assessment, and curriculum leadership. Prerequisite: Consent of instructor.

**6310 ALGEBRAIC STRUCTURES** This course is required in the M.A. program in mathematics education and focuses on basic algebraic structures and their role in analyzing selected classical mathematical problems. The goal is to develop and apply the concepts of the algebraic theory of fields to prove the impossibility of classical constructions. Prerequisite: Consent of instructor.

**6312 DATA MODELING FOR K-8 TEACHERS** As a requirement in the Elementary Mathematics Specialist track of the ASTL Program, this graduate course is designed to prepare K-8 teachers to help students develop their understanding of data displays, measures of center, measures of variability, statistical generalization, chance, modeling measurements, and making inferences in light of uncertainty. Prerequisite: Teaching certification in a grade band within K-8.

**6315 INTRODUCTION TO NUMBER THEORY** This course serves as an elective for the M.A. in mathematics education and provides an introduction to number theory for secondary and beginning collegiate teachers of mathematics. Topics include divisibility, prime number theory, numerical functions, the algebra of congruence classes, higher degree congruence classes, number theory on the reals, Diophantine equations, and applications. Prerequisite: Consent of instructor.

**6340 HISTORICAL PERSPECTIVES OF MATHEMATICS** This course serves as an elective for the M.A. in mathematics education and provides a survey of the history and development of mathematical thought from ancient to modern times including philosophical, sociological, and biographical perspectives. Prerequisite: Consent of instructor.

**6342 MATHEMATICAL MODELING** This course is a required course for the M.S. in applied mathematics and an elective for the M.A. in mathematics education involving the mathematical concepts and techniques to model real-life problems from the physical, biological, social, and behavioral sciences. Graphics calculator and computer will be used. Prerequisite: Consent of instructor.

**6345 ADVANCED ORDINARY DIFFERENTIAL EQUATIONS** A required course for the MS degree in Applied Mathematics. Topics include linear systems of differential equations; existence and uniqueness; systems with constant coefficients; periodic systems and Floquet theory; existence, uniqueness, continuation of solutions of nonlinear systems; properties of solutions of linear and nonlinear systems; behaviors near equilibrium and the stability of equilibrium; stable/unstable manifolds, the Hartman-Grobman theorem and the center manifold theorem; the Poincare-Bendixson theorem. Prerequisites: MATH 3331 and MATH 4362 or equivalent.

**6348 NUMERICAL ANALYSIS** A required course for the MS degree in Applied Mathematics. Topics include direct methods for linear systems equations, roots of a single linear equation; interpolation using a variety of approximation techniques; numerical differentiation and integration with a focus on stability, convergence and error estimates of methods; the numerical solutions of linear and nonlinear equations and systems of equations; techniques in numerical linear algebra including matrix computation, elimination methods, matrix decomposition; orthogonalization and least-squares; iterative methods with a focus on error analysis. Prerequisites: MATH 2371, MATH 3320, and CSCI 1470.

**6350 MODERN GEOMETRY** This course is required in the M.A. program in mathematics education. This course involves Euclidean and non-Euclidean geometry including the utilization of technology and discussions of problems encountered in teaching geometry. Prerequisite: Consent of instructor.

**6355 ADVANCED PARTIAL DIFFERENTIAL EQUATIONS** An elective for the MS degree in Applied Mathematics. Topics include uniqueness, regularity, well-posedness and classification for elliptic, parabolic, and hyperbolic equations; Green’s functions, representation formulas, mean-value formulas, Duhamel’s method, weak and strong maximum principles, and energy methods. Prerequisites: MATH 4315/5315 and MATH 6345 or equivalent.

**6357 METHODS FOR SOLVING NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS** An elective for the MS degree in Applied Mathematics. Topics include Charpit’s method, Nonlinear separability, Compatibility, Variable transformations and Burger’s equation, Darboux transformations, First integrals, Similarity transformations, Hodograph transformations, Point and contact transformations, and Backlund transformations. Emphasis will be placed on solving nonlinear partial differential equations that arise in different areas of science and engineering. Prerequisites: MATH 4315/5315 or equivalent.

**6358 NUMERICAL DIFFERENTIAL EQUATIONS** An elective for the MS degree in Applied Mathematics. Topics include the numerical solutions of ordinary differential equations using single-step, multi-step, multivalue methods with a focus on convergence, error bounds, error estimates and stability of methods; finite difference methods for initial and boundary value problems for partial differential equations; consistency, stability, convergence of methods of methods for linear and nonlinear parabolic, hyperbolic, and elliptic partial differential equations. Prerequisite: MATH 3331, MATH 4315/5315, and CSCI 1470 or equivalent.

**6362 INFINITE DIMENSIONAL DYNAMICAL SYSTEMS** An elective for the MS degree in Applied Mathematics. Topics include semiflows, semigroups, evolutionary equations, reaction-convection-diffusion equations, wave equations, Navier-Stokes equations, existence and uniqueness of solutions, limit sets, invariant manifolds, stability, global attractors, numerical simulations, applications to fluid dynamics, physics, biology, and chemistry. Prerequisites: MATH 3331 and MATH 4315/5315.

**6365 CONTROL THEORY** An elective for the MS degree in Applied Mathematics. This course is an introduction to analysis and control design for both finite and infinite dimensional dynamical systems. It will focus on basic topics, including reachability, controllability, feedback, stabilization, Lyapunov functions, continuous semigroups, and boundary controls. Prerequisites: MATH 3331 and MATH 4315/5315.

**6370 DIFFERENTIAL CALCULUS** This course is required in the M.A. program in mathematics education. This course features key topics in elementary differential calculus in both historical and mathematical perspectives with emphasis on a teaching knowledge of these topics. Prerequisite: Consent of instructor.

**6372 INTEGRAL TRANSFORMS** An elective for the MS degree in Applied Mathematics. Topics include the Fourier, Laplace, and Hankel transforms; their operational properties, inversion formulas. Emphasis will be placed on solving ordinary and partial linear differential equations using the transform techniques. Applications include wave and heat equations. Prerequisites: MATH 3331 and 4315/5315.

**6375 INTEGRAL CALCULUS** This course is required in the M.A. program in mathematics education. This course features key topics in elementary integral calculus in both historical and mathematical perspectives with emphasis on a teaching knowledge of these topics. Prerequisite: Consent of instructor.

**6376 DESIGN OF EXPERIMENTS** An elective for the MS degree in Applied Mathematics and the MA degree in Mathematics Education. Major topics include, but are not limited to, fixed and random effects models, single-factor and factorial designs, block designs, response surface designs, nested and split-plot designs, and designs with covariates. Prerequisite: MATH 4373/5373 or consent of instructor.

**6378 SYMMETRY ANALYSIS OF DIFFERENTIAL EQUATIONS** Symmetry analysis is introduced as a method for the reduction and simplification of differential equations. Topics include: symmetry analysis of first order ordinary differential equations, second and higher order ordinary differential equations and systems of ordinary differential equations, nonlinear first order partial differential equations, linear and nonlinear second order partial differential equations and systems of partial differential equations. A computer algebra system such as Maple will be used as a tool in the construction of symmetries. Primary methods of delivery are lecture and demonstration. Prerequisite: MATH 4315/5315.