MATH 6010 Mathematical Biology
Credit Hours 3.0
Prerequisites MATH 2212 or MATH 1220 with grade of C or higher
Description

(Same as BIOL 6010.) This course provides an introduction to the use of continuous and discrete differential equations in the biological sciences. Biological topics will include single species and interacting population dynamics, modeling infectious and dynamic diseases, regulation of cell function, molecular interactions and receptor-ligand binding, biological oscillators, and an introduction to biological pattern formation. There will also be discussions of current topics of interest such as Tumor Growth and Angiogenesis, HIV and AIDS, and Control of the Mitotic Clock. Mathematical tools such as phase portraits, bifurcation diagrams, perturbation theory, and parameter estimation techniques that are necessary to analyze and interpret biological models will also be covered.

MATH 6030 Mathematical Music Theory
Credit Hours 3.0
Description

Specific aspects of group theory, algebraic combinatorics on words, similarity and distance measures,topology and geometry, and topos theory that are used in the analysis of general objects of music (scales, chords, rhythmic patterns) as well as in specific applications (development of software, music cognition, analysis of pieces from different time periods and genres). Acquire a repertoire of mathematical tools and techniques that are not always covered in the core courses of the major.

MATH 6211 Optimization
Credit Hours 3.0
Prerequisites MATH 3435 or MATH 3030 with a grade of C or higher
Description

Lagrange multipliers, gradient methods (steepest descent), search techniques, variational methods and control problems; other varying topics such as dynamic programming, nonlinear programming.

MATH 6250 Complex Analysis
Credit Hours 3.0
Prerequisites MATH 3000
Description

Complex numbers, analytic functions, complex series, Cauchy theory, residue calculus, conformal mapping.

MATH 6258 Vector Calculus
Credit Hours 3.0
Prerequisites MATH 2215
Description

(Same as PHYS 6510.) Vector algebra, curvilinear motion, vector fields, gradient, divergence, Laplacian, line and surface integrals, integral theorems.

MATH 6265 Partial Differential Equations
Credit Hours 3.0
Prerequisites A course in ordinary differential equations
Description

(Same as PHYS 6520.) First-order equations, classification of linear second-order equations, separation of variables, Fourier series, orthogonal functions, Green’s functions.

MATH 6275 Applied Dynamical Systems
Credit Hours 3.0
Description

Three lecture hours per week. An introduction to discrete and continuous dynamical systems. Topics include: phase space; linear and nonlinear systems; structural stability; classification of equilibrium states, invariant manifolds; poincare maps, fixed points and periodic orbits; stability boundaries; local bifurcations; homoclinic orbits; routes to chaos in dissipative systems; applications from physics, biology, population dynamics, economics.

MATH 6301 College Geometry
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Axioms of planar Euclidean Geometry. The 5th postulate. Congruence and Similarity. Theorem of Thales. Similar Triangles: SAS, AA, and SSS. Theorem of Ceva. The Pythagorean Theorem. Polgyons. Circles, secants, and tangents, measurement of an angle with respect to a circle. Perimeters, areas, circumference. Inscribed and circumscribed polygons. Coordinate Geometry in the plane. Mirror symmetries, rotations, translations, and dilations. Isometries and the fundamental theorem of Euclidean Geometry. Transformations in the plane and tessellations.

MATH 6371 Modern Geometry
Credit Hours 3.0
Prerequisites MATH 3000
Description

Euclidean and non-Euclidean geometry, including incidence, order, and the parallel postulate.

MATH 6381 General Topology
Credit Hours 3.0
Prerequisites Grade of C or higher in MATH 3000
Description

This course will provide an introduction to general topology, which is the study of spaces and how to classify spaces according to their characteristic properties. The class will begin with a brief review of basic set theory and metric spaces. Topics covered include topological spaces, continuous functions, topological properties (connectedness, compactness, countability, and separation axioms), the fundamental group, and covering spaces.

MATH 6382 Algebraic Topology
Credit Hours 3.0
Prerequisites Grade of C or higher in General Topology (MATH 4381/6381) and Modern Algebra I (MATH 4441)
Description

This course will provide an introduction to methods in algebraic topology. Topics covered include fundamental groups, covering space theory, simplicial complexes, simplicial homology, singular homology, singular cohomology, and higher homotopy groups.

MATH 6391 Introduction to Differential Geometry and its Applications
Credit Hours 3.0
Prerequisites MATH 2215
Description

(Same as PHYS 6391.) Three lecture hours a week. The theory of curves and surfaces in parametric and implicit form. Curvature and torsion of a curve; the shape operator and the total and mean curvature of a surface. The Gauss-Weingarten equations; the Egregium Theorem; surfaces of constant curvature and non-Euclidean geometry. Minimal surfaces; the Gauss Bonnet Theorem; submanifolds in Euclidian spaces, vector fields, differential forms, and the theorems of Frobenius and Stokes. Applications to Physics.

MATH 6420 Graph Theory
Credit Hours 3.0
Prerequisites MATH 3000
Description

Introduction to graph theory; topics include structure of graphs, trees, connectivity, Eulerian and Hamiltonian graphs, planar graphs, graph colorings, matchings, independence, and domination. Additional topics may include symmetry of graphs, directed graphs, extremal graph theory and Ramsey theory, graph embeddings, and probabilistic methods in graph theory.

MATH 6435 Linear Algebra II
Credit Hours 3.0
Prerequisites MATH 3435 with grade of C or higher
Description

Theory and applications of matrix algebra, vector spaces, and linear transformations. Topics include matrix representations of linear transformations, eigenvalues and eigenvectors, similarity, the spectral theorem, and orthogonality. 3.0 Credit hours.

MATH 6441 Modern Algebra I
Credit Hours 3.0
Prerequisites MATH 3435 and MATH 3000 with grades of C or higher, or equivalents
Description

Axiomatic approach to algebraic structures, groups, permutations, homomorphisms, and factor groups.

MATH 6442 Modern Algebra II
Credit Hours 3.0
Prerequisites MATH 4441/6441
Description

Rings, integral domains, and fields; polynomials over a field, matrices over a field, algebraic numbers and ideals.

MATH 6444 Polynomials
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Three lecture hours a week. The topic of polynomials is one of the oldest in mathematics and has applicability to almost every area of mathematics. The course will use algebra and analysis to study polynomials. Among topics to be covered: roots of polynomials (inequalities, relationship between the root of a polynomial and its derivative), resultants, discriminant, irreducible polynomials, special classes of polynomials (symmetric, cyclotomic, Chebysev).

MATH 6450 Theory of Numbers
Credit Hours 3.0
Prerequisites MATH 3000
Description

Properties of integers, divisibility, congruence of numbers. Lagrange’s theorem, residues, Diophantine problems.

MATH 6455 Error Correcting Codes
Credit Hours 3.0
Prerequisites MATH 3030 or MATH 3435
Description

Three lecture hours a week. This course provides and elementary, yet rigorous introduction to the theory of error correcting codes. Topics include survey of groups, finite fields and polynomials, linear algebra, Huffman codes, data compression and entropy, linear codes, Reed-Muller codes, cyclic codes, BCH codes, and fast decoding BCH codes.

MATH 6460 Cryptography
Credit Hours 3.0
Prerequisites MATH 3030 or MATH 3435, and the ability to program in a high-level language
Description

Three lecture hours a week. This course covers the mathematical background of computational and algorithmic methods for cryptography. This includes information theory, computational complexity and number theory. Methods covered include public key cryptosystems and secure methods for authentication and digital signatures.

MATH 6544 Biostatistics
Credit Hours 3.0
Prerequisites BIOL 1107K, BIOL 1108K, and MATH 2211
Description

Principles and methods of statistics as applied to biology and medicine.

MATH 6547 Introduction to Statistical Methods
Credit Hours 3.0
Prerequisites a course in calculus
Description

Data analysis, sampling, and probability; standard methods of statistical inference, including t-tests, chi-square tests, and nonparametric methods. Applications include use of a statistical computer package.

MATH 6548 Methods of Regression and Analysis of Variance
Credit Hours 3.0
Prerequisites a course in calculus and a course covering methods of statistical inference
Description

Simple and multiple regression, model selection procedures, analysis of variance, simultaneous inference, design and analysis of experiments. Applications include use of a statistical computer package.

MATH 6610 Numerical Analysis I
Credit Hours 3.0
Prerequisites MATH 2215 and the ability to program in a high-level language
Description

(Same as CSC 6610.) Nature of error; iteration; techniques for nonlinear systems; zeros of functions; interpolation; numerical differentiation; Newton-Cotes formulae for definite integrals; computer implementation of algorithms.

MATH 6620 Numerical Analysis II
Credit Hours 3.0
Prerequisites MATH 3030 or MATH 3435, and the ability to program in a high-level language
Description

(Same as CSC 6620.) Gaussian Elimination for linear systems; least squares; Taylor, predictor-corrector and Runge-Kutta methods for solving ordinary differential equations; boundary value problems; partial differential equations.

MATH 6650 Inverse and Ill-Posed Problems
Credit Hours 3.0
Prerequisites Math/CSC 6610 or Math/CSC 6620
Description

Three lecture hours a week. Ill-posed problems that arise in astrophysics, geophysics, spectroscopy, computerized tomography, and other areas of science and engineering are considered in this course. Topics to be covered: a general regularization theory; variational regularization and the discrepancy principle; iterative regularization; convergence analysis and stopping rules; numerical aspects.

MATH 6661 Analysis I
Credit Hours 3.0
Prerequisites Corequisite: 4435/6435
Description

The real number system, basic topology of metric spaces, sequences and series, limits and continuity.

MATH 6662 Analysis II
Credit Hours 3.0
Prerequisites MATH 4661/6661 with grade of C or higher
Description

Differentiation of real functions, Riemann integrals, sequences and series of functions, differentiation and integration of functions of several variables.

MATH 6671 Transforms in Applied Mathematics
Credit Hours 3.0
Prerequisites MATH 3030 or MATH 3435
Description

The Laplace transform, discrete and continuous Fourier Transforms, z-transforms, discrete filters, and wavelets.

MATH 6751 Mathematical Statistics I
Credit Hours 3.0
Prerequisites MATH 2215
Description

Probability, random variables and their distributions, mathematical expertation, moment generating functions, sampling distributions.

MATH 6752 Mathematical Statistics II
Credit Hours 3.0
Prerequisites MATH 4751/6751
Description

Theory of estimation and hypothesis testing, applications of statistical inference, introduction to regression and correlation.

MATH 6767 Statistical Computing
Credit Hours 3.0
Prerequisites MATH 4752/6752 or MATH 4548/6548, and MATH 3435 with grades of C or higher and the ability to program in a high-level language
Description

Computational implementation of statistical methods such as descriptive statistics and graphs, testing for normality, one and two sample tests, Wilcoxon rank sum tests, Wilcoxon signed rank tests, basic regression and analysis of variance (ANOVA). Standard statistical packages (SAS) will be used as well as user-written programs. 3.0 credit hours.

MATH 7000 Thinking Mathematically: Introduction to Proof
Credit Hours 3.0
Prerequisites Admission to a graduate program for the preparation of Secondary Mathematics teachers (this requires at a minimum the complete calculus sequence)
Description

This course is designed to provide a transition to higher-level mathematics through a hands-on approach to creative problem-solving, formal mathematical concepts, and proofs. Topics include logic, proofs, induction, formal systems, and set theory.

MATH 7008 Foundations of Numbers and Operations
Credit Hours 3.0
Description

This course is an introductory mathematics course for pre-service middle childhood educators. This course will emphasize the understanding and use of the major concepts of number and operations. As a general theme, strategies of problem solving will be used and discussed in the context of various topics.

MATH 7050 Geometry and Spatial Sense
Credit Hours 3.0
Prerequisites MATH 7008 with grade of C or higher or consent of instructor
Description

Building on Euclidean geometry this course is designed to develop a more visual understanding of geometry and enhance geometric intuition in two- and three-dimensions. Topics include measurement, two-dimensional geometry, three-dimensional geometry, spherical geometry, symmetry, tessellations, efficient shapes, transformations.

MATH 7070 Introduction to Probability and Statistics
Credit Hours 3.0
Prerequisites MATH 7008 with grade of C or higher or consent of instructor
Description

This course is intended to provide an overview of the basics of probability and descriptive statistics. Various forms of technology will be used.

MATH 7090 Algebraic Concepts
Credit Hours 3.0
Prerequisites MATH 7008 with grade of C or higher
Description

This course is designed to broaden understanding of fundamental concepts of Algebra with particular attention given to specific methods and materials of instruction. The principle algebra topics to be taught in this course are: the Language of Algebra; Patterns, Relations and Functions; and Balance, Equations, and Inequalities.

MATH 7300 Problem Solving with Computers
Credit Hours 3.0
Prerequisites MATH 3000
Description

Three lecture hours a week. This course explores various mathematical contexts and develops mathematical knowledge necessary to solve, or attempt to solve, mathematical problems in the computer enhanced environment. The problems come from many sources and contexts. Computer programs such as Maple, Matlab, spreadsheets, Geometer’s Sketch Pad, Study Works, etc. will be used. No previous experience with computers is required.

MATH 7400 Discrete Mathematics for Teachers
Credit Hours 3.0
Prerequisites MATH 1220 or MATH 2211 or consent of instructor
Description

Topics covered include logic, sets, functions, sequences, mathematical reasoning, graph theory, problem solving.

MATH 7420 Applied Combinatorics
Credit Hours 3.0
Prerequisites MATH 2212 or MATH 2420 with grade of C or higher
Description

Counting principles including combinations, permutations, generating functions, recurrence relations, the principle of inclusion exclusion, and Polya’s theory of counting. This course is for high school mathematics teachers in the M.A.T. or M.Ed. programs who have had a full sequence of calculus courses and a first course in linear algebra.

MATH 7610 Special problems and solving strategies
Credit Hours 3.0
Prerequisites MATH 2212 with a grade of B or better or permission from the instructor
Description

The course will concentrate on developing solving strategies of difficult mathematical problems which require creativity and profound understanding of mathematics. Among topics to be covered: induction and pigeonhole principle, arithmetic, algebra, summation of series, intermediate real analysis, inequalities.

MATH 7820 Historical and Cultural Development of Mathematics I
Credit Hours 3.0
Description

Three lecture hours a week. Exploration of the historical and cultural development of mathematics between ~3000 B.C. and ~1600 A.D. Mathematics topics to include the development of arithmetic, geometry (practical, deductive, and axiomatic), number theory, trigonometry, syncopated and symbolic algebra, probability, and statistics. This course is for high school mathematics teachers in the M.A.T. or M.Ed. programs who have had a full sequence of calculus courses and a first course in linear algebra.

MATH 7821 Historical and Cultural Development of Mathematics II
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Three lecture hours a week. Exploration of the historical and cultural development of mathematics from ~A.D. 1600 to the present. Mathematics topics to include the development of algebraic geometry, logarithms, calculus, non-Euclidean geometry, abstract algebra, probability, and analysis.

MATH 8110 Real Analysis I
Credit Hours 3.0
Prerequisites MATH 4662/6662
Description

Topological and metric spaces, measures, and abstract integration.

MATH 8120 Real Analysis II
Credit Hours 3.0
Prerequisites MATH 8110
Description

Topics include: function spaces, general measure and integration theory, elements of Banach and Hilbert space theory.

Credit Hours 3.0
Prerequisites Prerequisite: MATH 4435 or MATH 6435 with a grade of C or higher, or equivalent
Description

Topics oriented to applications of linear algebra; topics may include unitary similarity and normal matrices, simultaneous diagonalization, Jordan canonical form, variational characterizations of eigenvalues of Hermitian matrices, eigenvalue location and Gersgorin theory, positive definite matrices, nonnegative matrices, and the Perron-Frobenius theorem.

MATH 8201 Combinatorial Matrix Theory
Credit Hours 3.0
Prerequisites MATH 8200 with grade of C or higher
Description

The course covers the basic results and methods of combinatorial matrix theory. It is concerned with the use of matrix theory and linear algebra in providing combinatorial theorems and in describing and classifying combinatorial constructions. The course includes a lot of graph theory, in particular, matrix connections with undirected graphs, bipartite graphs, directed graphs, and special graphs.

MATH 8210 Topics in Applied Matrix Analysis
Credit Hours 3.0
Prerequisites MATH 8200 with grade of C or higher
Description

Applications of selected topics in matrix analysis to other areas of mathematics, as well as statistics, engineering, biology, physics, computational and social sciences are considered in this course. The course covers topics such as: Boolean matrices with applications; Generalized inverses; Applications of the Singular Value Decomposition (SVD); Matrix inequalities with applications; Semidefinite programming. The course may be taken more than once if topics vary.

MATH 8220 Abstract Algebra I
Credit Hours 3.0
Prerequisites MATH 4442/6442 with grade of C or higher
Description

Group actions and Sylow Theorems, solvable and nilpotent groups, algebraic, separable, and normal field extensions, symmetric polynomials, Galois theory.

MATH 8221 Abstract Algebra II
Credit Hours 3.0
Prerequisites MATH 8220 with grade of C or higher
Description

A continuation of MATH 8220, this course covers module theory, theory of multilinear forms and determinants, finitely generated modules over Principal Ideal Domains and other advanced topics in abstract algebra.

MATH 8230 Topics in Algebra
Credit Hours 3.0
Description

May be taken more than once if topics are different.

MATH 8240 Introduction to Commutative Algebra and Algebraic Geometry
Credit Hours 3.0
Prerequisites MATH 8220 with grade of C or higher
Description

The course provides a rigorous foundation in commutative algebra and algebraic geometry. Topics such as algebraic varieties, Zariski topology, localization, dimension theory will be covered.

MATH 8250 Commutative Ring Theory
Credit Hours 3.0
Prerequisites MATH 8220 with grade of C or higher
Description

This course studies main classes of rings in commutative algebra such as regular rings, Cohen-Macaulay rings, Gorenstein rings. The topics involve depth, projective dimension, injective dimension, local cohomology, Hilbert-Samuel multiplicity and other advanced concepts in commutative algebra.

MATH 8310 Theory of Functions of a Complex Variable
Credit Hours 3.0
Prerequisites MATH 4662/6662
Description

Basic theory of complex numbers and of analytic functions, conformal mapping, integration, power series, theory of residues, analytic continuation, theory of singularities, univalent functions, multiple-valued functions, Riemann surfaces.

MATH 8320 Functional Analysis
Credit Hours 3.0
Prerequisites MATH 8110 with grade of C or higher
Description

This course is an introduction to the fundamental concepts of functional analysis and operator theory. Its topics include: Hilbert spaces, Banach spaces, Frechet spaces, bounded linear operators on Banach spaces, Riesz and Fredholm theory of compact operators, the spectral theorem for normal operators, the three pillars of linear analysis (Hahn-Banach, open mapping, Banach-Steinhaus theorems), Krein-Milman theorem, Gelfand’s theory of commutative C*-algebras.

MATH 8330 Harmonic Analysis
Credit Hours 3.0
Prerequisites MATH 8110 with grade of C or higher
Description

This course is an introduction to the fundamental concepts of harmonic and Fourier analysis. Its topics include: Fourier series and integrals in one and several dimensions; convolutions; Poisson summation; Fourier analysis on locally compact Abelian groups; commutative Banach algebras; selected applications to number theory, partial differential equations, engineering, numerical methods (such as fast Fourier tranform and fast multiplication).

MATH 8340 Several Complex Variables
Credit Hours 3.0
Prerequisites MATH 8110 with grade of C or higher
Description

This course is an introduction to the fundamental concepts of complex analysis and complex geometry in two or more variables. Its topics include: local and global analysis and algebra of holomorphic functions, power series in several complex variables, plurisubharmonic functions, domains of holomorphy, pseudoconvex domains, Reinhardt domains, Cauchy-Riemann equations, Stein manifolds, open and closed Riemann surfaces, embeddings into affine or projective space.

MATH 8350 Differential Manifolds
Credit Hours 3.0
Prerequisites MATH 4662 with grade of C or higher
Description

This course is an introduction to the fundamental concepts of analysis, geometry and topology of differential manifolds. Its topics include: local and global analysis and algebra of smooth functions (implicit function theorem, inverse function theorem, smooth partition of unity, rank theorem, Sard’s lemma, Morse lemma), embedding into Euclidean space, differential forms (Stokes theorem, de Rham cohomology, orientation class, cohomology of spheres and projective spaces, harmonic forms, Hodge decomposition), tensor analysis, curvature, Lie groups, homogeneous spaces.

MATH 8360 Topics in Analysis
Credit Hours 3.0
Prerequisites MATH 8110 with grade of C or higher
Description

This course is a topics course in analysis whose content may vary from semester to semester and from instructor to instructor. Possible topics include advanced themes in functional analysis (orthogonal functions, positive functions on groups, Bochner’s theorem, operator theory, operator algebras), Lie groups and Lie algebras (basic theory, representations of compact Lie groups, structure theory of semi-simple Lie algebras), analysis of linear elliptic and parabolic differential equations (existence and regularity for Dirichlet problem, Neumann problem in Holder and Sobolev spaces).

Credit Hours 3.0
Prerequisites MATH 6420
Description

Advanced topics in graph theory that may include symmetry of graphs, directed graphs, graph embeddings, graph colorings, matchings, factors, decompositions, domination, extremal graph theory, Ramsey Theory, and probabilistic methods in graph theory.

MATH 8440 Combinatorics
Credit Hours 3.0
Prerequisites MATH 6420
Description

Topics in combinatorics that may include enumeration techniques, principle of inclusion exclusion, partitions, recurrence relations, generating functions, Mobious inversion, Ramsey numbers, finite geometries, block designs, error correcting codes.

MATH 8450 The Probabilistic Method in Combinatorics
Credit Hours 3.0
Prerequisites MATH 8440 with grade of C or higher
Description

This advanced course discusses the probabilistic method on combinatorics. Topics include linearity of expectation, the second moment method, the local lemma, correlation inequalities, martingales, large deviation inequalities, pseudo-randomness and random graphs.

MATH 8460 Topological Graph Theory
Credit Hours 3.0
Prerequisites MATH 6420 (Graph Theory) with a grade of C or higher
Description

This course studies embeddings of graphs in surfaces, and graphs as topological spaces. The topics may include planar graphs, surfaces, combinatorial embeddings, contractibility of cycles, the genus problem, the width of embeddings, embedding extensions and obstructions, tree-width and the excluded minor theorem, colorings of graphs on surfaces. Credit Hours: 3.0.

MATH 8500 Systems Biology
Credit Hours 3.0
Prerequisites Grade of C or higher in MATH 6010 or MATH 6275
Description

Cross-listed with NEUR 8500. This course provides an introduction to systems biology from mathematical modeling point of view. It will introduce biology students to mathematical modeling, and mathematical students to systems biology. Biological topics will include gene systems, protein systems, metabolic systems and signaling systems. Mathematical tools will include basic modeling concepts, approximation, static networks, linear vs. nonlinear systems and how to linearize nonlinear systems, and parameter estimation and optimization. Specific case studies will include integrative analysis of genome, protein, and metabolite data, systems biology in medicine and drug development, and synthetic biology.

Credit Hours 3.0
Prerequisites Grade of C or higher in MATH 6010 (BIOL 6930) or MATH 6275 or MATH 8510, or with permission from the instructor
Description

Cross-listed with NEUR 8395 and BIOL 8505. This graduate level course extends mathematical methods and models of biological systems, covered in MATH 4010/6010 (BIOL 6930) Â“Mathematical BiologyÂ”. The main focus will be on multidimensional and spatial models of biological systems. The topics will include the dispersal of biological populations and age structure on population growth; rates of spread of invading organisms and population persistence; branching random walks and chain reactions; stochastic and Markov models of biological systems; cellular automata models with deterministic and stochastic rules, related to the infectious disease transmission and control; the Game of Life, and pattern formation in biological networks of different nature.

MATH 8510 Applied Mathematics
Credit Hours 3.0
Prerequisites MATH 4661/6661
Description

Topics in mathematics applicable to natural and social sciences, engineering, business, or the arts. Topics selected from differential and difference equations, integral equations, transform theory, numerical analysis, approximation theory, optimization and calculus of variations, and continuum mechanics.

MATH 8515 Dynamical Foundations of Neuroscience
Credit Hours 3.0
Prerequisites MATH 4010/6010, MATH 4275/6275, or PHYS 4180/6180 with grade of C or higher
Description

(Same as NEUR 8340.) This course deals with computational and mathematical neuroscience with the emphasis on models of neurons and neural networks described in terms of dynamical systems, time continuous and discrete. Topics include biophysics and dynamics of single and coupled neurons, bifurcations and transitions between various types of neuronal activities; modeling of synapses, dendrites and axons; locomotion and small networks; neural coding in single cells and at the population level; dynamics of large networks, including spike computing with population codes; networks learning and behavioral changes.

MATH 8520 Applied Combinatorics and Graph Theory
Credit Hours 3.0
Prerequisites CSC 6520
Description

(Same as CSC 8520.) Development of combinatorial and graphical algorithms. Techniques for the study of complexity with application to algorithms in graph theory, sorting and searching.

MATH 8525 Applied Stochastic Processes
Credit Hours 3.0
Prerequisites Math 4752/6752 Mathematical Statistics II or MATH 4010/6010 Mathematical Biology
Description

This course deals with stochastic processes taking place at different spatial and temporal scales, with the emphasis on simulation and analysis of biological processes. Topics include Probabilistic and deterministic models, Discrete and Continuous Probability Distributions, Poisson processes, Discrete and Continuous Markov Chains, Discrete Time Branching Processes, Continuous Birth and Death Processes, Population Dynamics, and Stochastic Differential Equations. The potential biological applications include logistic growth processes, epidemic models, enzyme kinetics, competition processes, stochastic ion channels and random walk models for neural spike trains. 3.0 Credit Hours.

MATH 8530 Topics in Applied Mathematics
Credit Hours 3.0
Description

May be taken more than once if topics are different.

MATH 8535 Applied Matrix Algebra
Credit Hours 3.0
Prerequisites MATH 4435/6435 with a grade of C or higher
Description

Matrix algebra: its concepts, results, techniques and methods applicable to statistics, bioinformatics, neuroscience, systems biology, economics, and related fields. The topics may include advanced operations on matrices, projectors and idempotent operators, generalized inverses, inequalities for eigenvalues, matrix approximations, optimization problems in statistics and econometrics, quadratic subspaces, inequalities with applications in statistics, non-negative matrices and their models in applied sciences.

MATH 8540 Advanced Topics in Ordinary Differential Equations and Dynamic Systems
Credit Hours 3.0
Prerequisites MATH 4275 or MATH 6275 with grade of C or higher
Description

(Same as PHYS 8540.) This course is a graduate-level presentation of the mathematical theory of ordinary differential equations and nonlinear dynamical systems. It is designed for students who want to study the advanced topics of qualitative theory of ordinary differential equations and do research in dynamical systems Topics include existence and uniqueness theorems; IVP and Picard iterates; stability; variational equation and Floquet theory; Jordan normal form; the center manifold theorem; relaxation oscillations and method of averaging; Smale horseshoe and transverse homoclinic orbits; Lyapunov exponents and topological entropy.

MATH 8550 Biologic Networks
Credit Hours 3.0
Prerequisites MATH 6420 with grade of C or better
Description

This course will be a comprehensive introduction of graph theory to the structural analysis of biological networks at the interface of biology and discrete mathematics. The course covers graph structure properties and graph algorithms with applications to biology problems such as protein interaction networks, metabolic networks, ecological networks, and correlation networks. The course provides knowledge on establishing mathematical models and tools on solving these models for various bioinformatic related problems.

MATH 8560 Informatics of Neural and Cardiovascular Systems
Credit Hours 3.0
Prerequisites MATH 4010/6010 or MATH 6275 or MATH 4751/6751 with grades of C or higher
Description

(Same as NEUR 8360). This course studies informatics in application to biological systems, the emerging fields of science that appeared at a cross-road of mathematics, biology, and medicine. It is designated for graduate students. Biological topics will include gating properties of ion channels, with particular application to cardiac diseases and cancer. The models of ion channels, neural and cardiac cells will be introduced. Electrical activity of biological cells will be analyzed with modern mathematical methods. The role of stochasticity in information processing by biological systems will be analyzed. Application of the mathematical modes for genetic diseases (epilepsy, arrhythmias) will be discussed.

MATH 8570 Computational Methods and Modeling for the Life Sciences
Credit Hours 3.0
Prerequisites MATH 6010 (Mathematical Biology) or MATH 6275 (Applied Dynamical Systems) with a grade of C or higher
Description

Advanced computational and mathematical modeling methods for generating and analyzing deterministic dynamic models in the context of scientific data. Biological case studies may be drawn from many areas involving all scales of inquiry, from molecules to ecosystems.

Credit Hours 3.0
Prerequisites MATH 4435/6435 and MATH 4610/6610 or CSC 4610/6610
Description

(Same as CSC 8610.) Advanced topics in numerical analysis. Stability and conditioning, discretization error, convergence. Examples are drawn from linear algebra, differential and nonlinear equations.

MATH 8620 Numerical Linear Algebra
Credit Hours 3.0
Prerequisites MATH 4435/6435; and MATH 4610/6610 or CSC 4610/6610
Description

(Same as CSC 8620.) Computational aspects of linear algebra. Matrix factorization, least squares, orthogonal transformations, eigen-values; and methods for sparse matrices.

MATH 8800 Topics in Mathematics
Credit Hours 3.0
Description

May be taken more than once if topics are different.

MATH 8801 Graduate Research in Mathematics
Credit Hours 1.0 TO 15.0
Description

May be repeated for credit.

MATH 8802 Graduate Laboratory in Mathematics
Credit Hours 1.0 TO 15.0
Description

May be repeated for credit.

MATH 8820 Research
Credit Hours 3.0
Prerequisites consent of the instructor and chair of department
Description

Independent investigation of topics of common interest to student and instructor.

MATH 8950 Directed Research in Mathematics
Credit Hours 1.0 TO 15.0
Prerequisites consent of the instructor
Description
MATH 8999 Thesis Research
Credit Hours 1.0 TO 15.0
Prerequisites thesis option
Description
MATH 9116 Teaching College Mathematics
Credit Hours 3.0
Prerequisites consent of instructor
Description

Research-based investigation of teaching college-level mathematical sciences courses: placement, prerequisites, remedial courses, services courses, preparing syllabi, grading, technology, pedagogical strategies.

MATH 9126 Epistemology of Advanced Mathematics Concepts
Credit Hours 3.0
Prerequisites consent of instructor
Description

An investigation of various epistemological frameworks in the context of collegiate level mathematics courses. Constructivism, Platonism, Cognitivism, Empiricism, and Information Processing. Comparison of the epistemologies as as they apply to post-secondary mathematics concepts.

MATH 9136 Learning Theories Relevant to Collegiate Mathematics Education
Credit Hours 3.0
Prerequisites MATH 9126 with grade of C or higher
Description

The course focuses on a variety of learning theories relevant to collegiate mathematics education and advanced mathematical thinking including: cognitive, social, constructivists, semiotics, situated learning, behaviorist, etc. The course will look at the influence of learning theories on how mathematics educators view learning, conduct research about learning, and subsequently develop teaching methodologies.

MATH 9166 Internship in Teaching College Mathematics
Credit Hours 3.0
Prerequisites consent of instructor and approval to teach in the Department of Mathematics and Statistics
Description

Teaching of at least one undergraduate mathematics course using at least two distinct pedagogical strategies.

MATH 9185 Research Seminar in Undergraduate Mathematics Education
Credit Hours 3.0
Prerequisites consent of instructor
Description

Student will read, discuss, and report on current publications in the field. Can be taken more than once for credit.

MATH 9999 Dissertation Research
Credit Hours 1.0 TO 18.0
Prerequisites consent of department
Description

Doctoral Dissertation Research.