UT Dallas 2014 Undergraduate Catalog

Mathematical Science

MATH 1306 College Algebra for the Non-Scientist (3 semester credit hours) This course is intended for students NOT continuing on to precalculus or calculus. The course is designed to develop both abstract thinking and a practical approach to problem solving. The emphasis is on understanding rather than purely computational skills. Topics include logic, sets, the real numbers, linear equations and their applications, functions, and graphs. May not be used to satisfy major requirements for majors in the Schools of Natural Sciences and Mathematics or Management, or degree requirements for the School of Engineering and Computer Science. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A score of 20% on ALEKS math placement exam. (3-0) Y (2015-04-21 20:39:41)

MATH 1314 (MATH 1314) College Algebra (3 semester credit hours) Topics chosen from areas such as equations and inequalities, rational expressions, exponents, radicals and logarithms, functions, and graphs. Exam section required for MATH 1314. May not be used to satisfy major requirements for majors in the Schools of Natural Sciences and Mathematics or Management, or degree requirements for the School of Engineering and Computer Science. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A score of 35% on ALEKS math placement exam. (3-0) S (2015-04-21 20:39:41)

MATH 1316 (MATH 1316) Trigonometry (3 semester credit hours) Angular measure, trigonometric functions, their properties; trigonometric identities, equations, and applications; trigonometric form of complex number and related topics. May not be used to satisfy major requirements for majors in the School of Natural Sciences and Mathematics or Management, or degree requirements for the School of Engineering and Computer Science. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A score of 35% on ALEKS math placement exam, a grade of at least a C- in MATH 1314, or concurrent enrollment in MATH 1314. (3-0) S (2015-04-21 20:39:41)

MATH 1325 (MATH 1325) Applied Calculus I (3 semester credit hours) Functions and graphs, differentiation, maxima and minima, exponential and logarithmic functions, integration, applications of integrals. May not be used to satisfy degree requirements for majors in the School of Engineering and Computer Science or major requirements in the School of Natural Sciences and Mathematics. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Cannot be used to replace MATH 2417 or MATH 2413. Prerequisite: A score of 55% on ALEKS math placement exam or a grade of at least a C- in MATH 1314. (3-0) S (2015-04-21 20:39:41)

MATH 1326 Applied Calculus II (3 semester credit hours) Applications of differential equations, functions of several variables, least squares modeling, multiple integrals, infinite series. May not be used to satisfy degree requirements for BS majors in Schools of Engineering and Computer Science or Natural Sciences and Mathematics. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Cannot be used to replace MATH 2414 or MATH 2419. Prerequisite: A grade of at least a C- in MATH 1325. (3-0) S (2015-04-21 20:39:41)

MATH 2312 (MATH 2312) Precalculus (3 semester credit hours) Real numbers, subsets of real line, absolute value; algebra of functions, domain, range, composition, inverse; elements of analytical geometry including vectors in plane, conics, polar coordinates, translation and rotation of axes and related topics. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A score of 55% on ALEKS math placement exam or a grade of at least a C- in MATH 1314 and MATH 1316. (3-0) S (2015-04-21 20:39:41)

MATH 2333 Matrices, Vectors, and Their Application (3 semester credit hours) Matrices, vectors, determinants, inverses, systems of linear equations, and applications. May not be used to satisfy degree requirements for majors in the School of Engineering and Computer Science or major requirements in the School of Natural Sciences and Mathematics. Cannot be used to replace MATH 2418. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: MATH 1314 or equivalent. (3-0) S (2015-04-21 20:39:41)

MATH 2413 (MATH 2413) Differential Calculus (4 semester credit hours) Course covers topics in differential calculus of functions of one variable; topics include limits, continuity, derivative, chain rule, implicit differentiation, mean value theorem, maxima and minima, curve sketching, derivatives of inverse trigonometric functions, antiderivative, substitution method, and applications. Three lecture hours and two discussion hours a week; a problem section required with MATH 2413, and will also be registered for exam section. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A score of 70% on ALEKS math placement exam or a grade of at least a C- in MATH 2312. (3-2) S (2015-04-21 20:39:41)

MATH 2414 (MATH 2414) Integral Calculus (4 semester credit hours) Continuation of Math 2413. Course covers topics in integral calculus, sequences and series. Topics include techniques of integration, improper integrals, and applications. Polar coordinates, parametric equations, and arc length. Infinite sequences and series, tests for convergence, power series, radius of convergence and Taylor series. Three lecture hours and two discussion hours a week; registration in a problem section as well as the exam section is required with MATH 2414. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Cannot be used to replace MATH 2419. Prerequisite: A grade of C- or better in either MATH 2417 or in MATH 2413 or equivalent. (3-2) S (2015-04-21 20:39:41)

MATH 2415 (MATH 2415) Calculus of Several Variables (4 semester credit hours) The course covers differential and integral calculus of functions of several variables. Topics include vector valued and scalar functions, partial derivatives, directional derivatives, chain rule, Lagrange multipliers, multiple integrals, double and triple integrals, the line integral, Green's theorem, Stokes' theorem, Divergence theorem. Three lecture hours and two discussion hours a week; problem section required with MATH 2415, and will also be registered for exam section. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A grade of C- or better in MATH 2414. (3-2) S (2015-04-21 20:39:41)

MATH 2417 (MATH 2417) Calculus I (4 semester credit hours) Functions, limits, continuity, differentiation; integration of function of one variable; logarithmic, exponential, and inverse trigonometric functions; techniques of integration, and applications. Three lecture hours and two discussion hours a week; problem section required with MATH 2417, and will also be registered for exam section. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A minimal placement score 75% on ALEKS math placement exam or a grade of at least a C- in MATH 2312 or an equivalent course. (3-2) S (2015-04-21 20:39:41)

MATH 2418 (MATH 2418) Linear Algebra (4 semester credit hours) Systems of linear equations, determinants, vectors and vector spaces, linear transformations, eigenvalues and eigenvectors, quadratic forms. Three lecture hours and two discussion hours a week; problem section required with MATH 2418, and will also be registered for exam section. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A grade of at least a C- in either MATH 2417 or in MATH 2413. (3-2) S (2015-04-21 20:39:41)

MATH 2419 (MATH 2419) Calculus II (4 semester credit hours) Continuation of MATH 2417. Improper integrals, sequences, infinite series, power series, parametric equations and polar coordinates, vectors, vector valued functions, functions of several variables, partial derivatives and applications, multiple integration. Three lecture hours and two discussion hours a week; problem section required with MATH 2419, and will also be registered for exam section. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A grade of at least a C- in MATH 2417. (3-2) S (2015-04-21 20:39:41)

MATH 2420 (MATH 2420) Differential Equations with Applications (4 semester credit hours) Topics covered will be drawn from the following list: First order differential equations, system of linear differential equations, stability, series solutions, special functions, Sturm-Liouville problem, Laplace transforms and linear differential equations and applications in physical sciences and engineering using computers. Three lecture hours and two discussion hours a week; problem section required with MATH 2420, and will also be registered for exam section. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A grade of at least a C- in either MATH 2415 or in MATH 2419, and a grade of at least a C- in MATH 2418 or equivalent. (3-2) S (2015-04-21 20:39:41)

MATH 2451 Multivariable Calculus with Applications (4 semester credit hours) Vectors, matrices, vector functions, partial derivatives, divergence, curl, Laplacian, multiple integrals, line and surface integrals, Green's, Stokes', and Gauss' theorems, and applications in physical sciences and engineering. Topics drawn from implicit function theorem, differential forms and vector fields. Three lecture hours and two discussion hours per week; problem section required with MATH 2451. Not all MATH/STAT courses may be counted toward various degree plans. Please consult your degree plan to determine the appropriate MATH/STAT course requirements. Prerequisite: A grade of at least a C- in either MATH 2415 or in MATH 2419, and a grade of at least C- in MATH 2418 or equivalent. (3-2) S (2015-04-21 20:39:41)

MATH 2V90 Topics in Mathematics - Level 2 (1-6 semester credit hours) Special topics in mathematics outside the normal course of offerings. May be repeated for credit as topics vary (9 semester credit hours maximum). Instructor consent required. ([1-6]-0) S (2015-04-21 20:39:41)

MATH 3301 Mathematics for Elementary and Middle School Teachers (3 semester credit hours) This course is intended to develop future teachers' depth of mathematical understanding by examining concepts in school mathematics from an advanced perspective. Topics include: numeration systems; arithmetic algorithms, prime factorization and other properties of the integers; proportional reasoning involving fractions and decimals; counting methods; and basic ideas of geometry and measurement. Problem solving is stressed. May not be used to satisfy: [1] undergraduate mathematics core requirement, [2] degree requirements by students in Mathematics, [3] electives, or [4] certification requirements in 8-12 mathematics. Prerequisite: MATH 1306 or MATH 1314 or equivalent. (3-0) S (2015-04-21 20:39:41)

MATH 3303 Introduction to Mathematical Modeling (3 semester credit hours) An introduction to construction, use, and analysis of empirical and analytical mathematical models. Emphasis on using appropriate technology with tools such as curve fitting, probability and simulation, difference and differential equations, and dimensional analysis. May not be used to satisfy mathematics requirements by students in Mathematics and may not be used to satisfy electives. Prerequisites: MATH 2418 and a grade of at least a C- in either MATH 2415 or in MATH 2419. (3-0) Y (2015-04-21 20:39:41)

MATH 3305 Foundations of Measurement and Informal Geometry (3 semester credit hours) An analysis, from an advanced perspective, of the basic concepts and methods of geometry and measurement. Topics include visualization, geometric figures and their properties; transformations and symmetry; congruence and similarity; coordinate systems; measurement (especially length, area, and volume); and geometry as an axiomatic system. Emphasis on problem solving and logical reasoning. May not be used to satisfy: [1] undergraduate mathematics core requirement, [2] degree requirements by students in Mathematics, [3] electives, or [4] certification requirements in 8-12 mathematics. Prerequisite: MATH 2312 or MATH 3301 or equivalent. (3-0) Y (2015-04-21 20:39:41)

MATH 3307 Mathematical Problem Solving for Teachers (3 semester credit hours) Development of the ability to solve mathematical problems and communicate their solutions through the study of strategies and heuristics. Practice in solving problems involving ideas from number theory, algebra, combinatorics and probability, etc. Communicating mathematics, logical reasoning, and connections between mathematical topics will be emphasized. May not be used to satisfy degree requirements for Mathematics majors. Prerequisites: MATH 2312 and (MATH 3305 or MATH 3321). (3-0) Y (2015-04-21 20:39:41)

MATH 3310 Theoretical Concepts of Calculus (3 semester credit hours) Mathematical theory of calculus. Limits, types of convergence, power series, differentiation, and Riemann integration. Prerequisite: A grade of at least a C- in either MATH 2415 or in MATH 2419. (3-0) S (2015-04-21 20:39:41)

MATH 3311 Abstract Algebra I (3 semester credit hours) Groups, rings, fields, vector spaces modules, linear transformations, and Galois theory. Prerequisite: A grade of at least a C- in either MATH 2415 or in MATH 2419, and a grade of at least C- in MATH 2418 or equivalent. (3-0) S (2015-04-21 20:39:41)

MATH 3312 Abstract Algebra II (3 semester credit hours) Continuation of MATH 3311. Prerequisite: MATH 3311. (3-0) Y (2015-04-21 20:39:41)

MATH 3321 Geometry (3 semester credit hours) Elements of Euclidean, non-Euclidean, and projective geometry. Topics covered will be drawn from the following list: triangles and their distinguishing points, Euler line, nine point circle, extremum problems, circles and spheres, inversions, the circles of Apollonius, projective geometry, axioms of the projective plane, Desargues' theorem, conics, elementary facts of the non-Euclidean geometries. Prerequisite: A grade of at least a C- in either MATH 2415 or in MATH 2419. (3-0) Y (2015-04-21 20:39:41)

MATH 3379 Complex Variables (3 semester credit hours) Geometry and algebra of complex numbers, functions of a complex variable, power series, integration, calculus of residues, conformal mapping. Prerequisites: MATH 2451 and MATH 3310. (3-0) S (2015-04-21 20:39:41)

MATH 3380 Differential Geometry (3 semester credit hours) Curves and surfaces, multilinear algebra, alternating tensors, tangent vectors, tangent space, vector fields, differential forms; Curvature and torsion of curves, Riemannian metrics, curvature of surfaces, isometries, geodesics, Gauss map, First and Second Fundamental Forms, area on surfaces, Gauss-Bonnet Theorem, surfaces with constant negative curvature and elements of hyperbolic geometry. Prerequisites: MATH 2451 and MATH 2418 and MATH 2420 or equivalent courses. (3-0) Y (2015-04-21 20:39:41)

MATH 4301 Mathematical Analysis I (3 semester credit hours) Sets, real number system, metric spaces, real functions of several variables. Riemann-Stieltjes integration and other selected topics. Prerequisites: MATH 2451 and MATH 3310. (3-0) S (2015-04-21 20:39:41)

MATH 4302 Mathematical Analysis II (3 semester credit hours) Continuation of MATH 4301. Prerequisite: MATH 4301. (3-0) S (2015-04-21 20:39:41)

MATH 4332 Scientific Math Computing (3 semester credit hours) Topics covered include introduction to Unix shells, basic and advanced use of Matlab for mathematical and scientific problem solving. Course is conducted in a computer classroom and assignments include applications in numerical and statistical analysis, image processing, and signal processing. Prerequisites: MATH 2418 and a grade of at least a C- in either MATH 2415 or in MATH 2419. (3-0) S (2015-04-21 20:39:41)

MATH 4334 Numerical Analysis (3 semester credit hours) Solution of linear equations, roots of polynomial equations, interpolation and approximation, numerical differentiation and integration, solution of ordinary differential equations, computer arithmetic, and error analysis. Prerequisites: (CE 1337 or CS 1337 or TE 1337) and (MATH 2418 and MATH 2451). (Same as CS 4334) (3-0) Y (2015-04-21 20:39:41)

MATH 4341 Topology (3 semester credit hours) Elements of general topology, topological spaces, continuous functions, connectedness, compactness, completeness, separation axioms, and metric spaces. Prerequisites: MATH 2451 and MATH 3310. (3-0) S (2015-04-21 20:39:41)

MATH 4355 Methods of Applied Mathematics (3 semester credit hours) Topics include some frequently used tools in applied mathematics: Laplace and Fourier transforms, special functions, systems, signals, and their applications in physical sciences and engineering. Prerequisites: MATH 2418 and MATH 2420. (3-0) T (2015-04-21 20:39:41)

MATH 4362 Partial Differential Equations (3 semester credit hours) This course presents a survey of classical and numerical methods for the solution of linear and nonlinear boundary value problems governed by partial differential equations. Modeling and application-related issues are included throughout. Prerequisites: MATH 2420 and MATH 2451. (3-0) Y (2015-04-21 20:39:41)

MATH 4381 Structure of Modern Geometry (3 semester credit hours) The course is designed to familiarize students with the geometrical concepts which relate to two and three dimensional geometry and the mathematical techniques used in the study of geometry. The emphasis is both on the development of understanding of the concepts and the ability to use the concepts in proving theorems. The course includes study of axiom systems, transformational geometry, and an introduction to non-Euclidean geometries, supplemented by other topics as determined by the instructor. Prerequisite: A grade of at least a C- in MATH 2418 or equivalent. (3-0) Y (2015-04-21 20:39:41)

MATH 4390 Senior Research and Advanced Writing (3 semester credit hours) For students conducting independent research and scientific writing. Individual instruction course designed to develop skills for research and clear, precise and accurate scientific writing. Topics will vary from section to section depending upon the interests of the student, but will be selected from a specific area of mathematics. Subject and scope to be determined on an individual basis. Satisfies the School of Natural Sciences and Mathematics' advanced writing requirement. This course will retain core notation for a transition period - see http://go.utdallas.edu/core-curriculum-transition. Please consult advisors for more detailed information. Prerequisite: Senior level standing in Mathematics and instructor consent required. (3-0) S (2015-04-21 20:39:41)

MATH 4399 Senior Honors in Mathematics (3 semester credit hours) For students conducting independent research for honors theses or projects. Satisfies the School of Natural Sciences and Mathematics' advanced writing requirement. Instructor consent required. This course will retain core notation for a transition period - see http://go.utdallas.edu/core-curriculum-transition. Please consult advisors for more detailed information. (3-0) S (2015-04-21 20:39:41)

MATH 4V03 Independent Study in Mathematics (1-6 semester credit hours) Independent study under a faculty member's direction. Student must obtain approval from participating math sciences faculty member and the undergraduate advisor. May satisfy the School of Natural Sciences and Mathematics' advanced writing requirement if it has a major writing/report component. May be repeated for credit (9 semester credit hours maximum). Instructor consent required. ([1-6]-0) S (2015-04-21 20:39:41)

MATH 4V91 Undergraduate Topics in Mathematics (1-9 semester credit hours) May be repeated for credit as topics vary (9 semester credit hours maximum). Instructor consent required. ([1-9]-0) S (2015-04-21 20:39:41)

MATH 5301 Elementary Analysis I (3 semester credit hours) Real numbers, differentiation, integration, metric spaces, basic point set topology, power series, analytic functions, Cauchy's theorem. Prerequisite: MATH 2451 and MATH 3310 or equivalent. (3-0) Y (2015-04-21 20:39:41)

MATH 5302 Elementary Analysis II (3 semester credit hours) Continuation of MATH 5301. Prerequisite: MATH 5301. (3-0) Y (2015-04-21 20:39:41)

MATH 5304 Applied Mathematical Analysis for Non-Majors (3 semester credit hours) Techniques of mathematical analysis applicable to the social, behavioral and management sciences. Differential and integral calculus of one and many variables. May not be used to fulfill degree requirements. Prerequisite: MATH 1314. (3-1) S (2015-04-21 20:39:41)

MATH 5305 Higher Geometry for Teachers (3 semester credit hours) Topics in modern Euclidean geometry including distinguished points of a triangle, circles including the nine-point circle, cross ratio, transformations; introduction to projective geometry. May not be used to fulfill degree requirements for mathematical sciences majors except those in the Master of Arts in Teaching (MAT) program. Prerequisite: Junior-level mathematics course. (3-0) T (2015-04-21 20:39:41)

MATH 5306 Non-Euclidean Geometry for Teachers (3 semester credit hours) The relations among elliptic, Euclidean and hyperbolic geometries, Euclidean models of elliptic and hyperbolic geometries. May not be used to fulfill degree requirements for mathematical sciences majors except those in the Master of Arts in Teaching (MAT) program. Prerequisite: Junior-level mathematics course. (3-0) T (2015-04-21 20:39:41)

MATH 5313 Modern Algebra for Teachers (3 semester credit hours) Study of modern algebra involving groups, rings, fields and Galois Theory. May not be used to fulfill degree requirements for mathematical sciences majors except those in the Master of Arts in Teaching (MAT) program. Prerequisite: Junior-level mathematics course. (3-0) R (2015-04-21 20:39:41)

MATH 5390 Topics in Mathematics - Level 5 (3 semester credit hours) May be repeated for credit as topics vary (9 semester credit hours maximum). Instructor consent required. (3-0) R (2015-04-21 20:39:41)

MATH 6301 Real Analysis (3 semester credit hours) Lebesgue measure in finite- dimensional spaces, Abstract measures, measurable functions, convergence a.e., Egorov's Theorem, convergence in measure, Lebesgue integral, Lebesgue's bounded convergence theorem, Levi's monotone convergence theorem, Fatou's Lemma, Fubini's theorem, Lp-spaces. Prerequisite: MATH 5302. (3-0) Y (2015-04-21 20:39:41)

MATH 6302 Functional Analysis I (3 semester credit hours) Banach and Hilbert spaces, classical theorems of functional analysis, compact operators, Fredholm operators, elements of spectral theory, introduction to unbounded operators. Prerequisite: MATH 6301. (3-0) Y (2015-04-21 20:39:41)

MATH 6303 Theory of Complex Functions I (3 semester credit hours) Complex integration, Cauchy's theorem, calculus of residues, power series, entire functions, Riemann mapping theorems. Riemann surfaces, conformal mapping with applications. Prerequisite: MATH 4301 and MATH 4302. (3-0) Y (2015-04-21 20:39:41)

MATH 6304 Theory of Complex Functions II (3 semester credit hours) Riemann surfaces, meromorphic and holomorphic functions and differentials, the normalization theorem, the Riemann-Roch theorem, Abel theorem, applications to nonlinear equations. Prerequisite: MATH 6303. (3-0) T (2015-04-21 20:39:41)

MATH 6305 Mathematics of Signal Processing (3 semester credit hours) The course is devoted to a mathematical foundation of some of the key topics in signal processing: discrete and continuous signal transforms, least squares methods and adaptive filtering, compressed sensing and related topics. Prerequisites: (MATH 2418 and MATH 2451) or instructor consent required. (3-0) T (2015-04-21 20:39:41)

MATH 6307 Wavelets and Their Applications (3 semester credit hours) An introduction to windowed Fourier and continuous wavelet transforms, generalized frames, discrete wavelet frames, multiresolution analysis, Daubechies' orthogonal wavelet bases, and their applications in partial differential equations and signal processing. Prerequisite: (MATH 2418 and MATH 2420) or equivalent. (3-0) T (2015-04-21 20:39:41)

MATH 6308 Inverse Problems and Applications (3 semester credit hours) Exact and approximate methods of nondestructive inference, such as tomography and inverse scattering theory in one and several dimensions, with applications in physical and biomedical sciences and engineering. Prerequisite: (MATH 2418 and MATH 2420) or equivalent. (3-0) T (2015-04-21 20:39:41)

MATH 6309 Differential Geometry (3 semester credit hours) Smooth manifolds, tangent bundles, smooth partitions of unity, submanifolds, Sard's theorem, transversality, embeddings, Whitney theorem, differential forms, Frobenius Theorem, de Rham cohomology, degree theory on manifolds, Riemannian metric, Gauss-Bonnet theorem. Prerequisite: MATH 4301 or MATH 5301. (3-0) T (2015-04-21 20:39:41)

MATH 6310 Topology (3 semester credit hours) Metric spaces, introduction to topology, elements of homotopy theory, covering spaces, fundamental group, homotopy groups, fibrations, simplicial complexes and CW-complexes, degree theory. Prerequisite: MATH 4301 or MATH 5301. (3-0) Y (2015-04-21 20:39:41)

MATH 6311 Abstract Algebra I (3 semester credit hours) Basic properties of groups, rings, fields, and modules. Prerequisite: MATH 3311 or equivalent. (3-0) Y (2015-04-21 20:39:41)

MATH 6313 Numerical Analysis (3 semester credit hours) A study of numerical methods including the numerical solution of non-linear equations, linear systems of equations, interpolation, iterative methods and approximation by polynomials. Prerequisites: Knowledge of a high-level programming language and MATH 2418 and MATH 2451. (3-0) Y (2015-04-21 20:39:41)

MATH 6315 Ordinary Differential Equations (3 semester credit hours) The study of ordinary differential equations with emphasis on existence, uniqueness, linear systems, boundary value problems, and stability. Prerequisites: [MATH 2418 or equivalent and MATH 2420 and (MATH 4301 and MATH 4302)] or (MATH 5301 and MATH 5302). (3-0) Y (2015-04-21 20:39:41)

MATH 6316 Differential Equations (3 semester credit hours) Continuation of MATH 6315 and an introduction to partial differential equations. Prerequisite: MATH 6315. (3-0) T (2015-04-21 20:39:41)

MATH 6318 Numerical Analysis of Differential Equations (3 semester credit hours) Practical and theoretical aspects of numerical methods for both ordinary and partial differential equations are discussed. Topics selected from: initial value problems for ordinary differential equations, two-point boundary value problems, projection methods, finite difference, finite element and boundary element approximations for partial differential equations. Application of methods will be illustrated using Matlab. Prerequisite: MATH 6313 or equivalent. (3-0) T (2015-04-21 20:39:41)

MATH 6319 Principles and Techniques in Applied Mathematics I (3 semester credit hours) Mathematical methods usually used in applied sciences and engineering. Topics chosen from advanced linear algebra; Hilbert spaces; positivity; quaternions; integral equations; Fourier analysis; distributions; convexity; asymptotic methods; special functions. Prerequisites: MATH 2418 and MATH 2420 or equivalent. (3-0) T (2015-04-21 20:39:41)

MATH 6320 Principles and Techniques in Applied Mathematics II (3 semester credit hours) Continuation of Math 6319. Prerequisite: MATH 6319. (3-0) T (2015-04-21 20:39:41)

MATH 6321 Optimization (3 semester credit hours) Introduction to theoretical and practical concepts of optimization in finite and infinite dimensional setting, least-squares estimation, optimization of functionals, local and global theory of constrained optimization, iterative methods. Prerequisites: MATH 2420 and MATH 2418. (3-0) T (2015-04-21 20:39:41)

MATH 6331 Linear Systems and Signals (3 semester credit hours) Basic principles of systems and control theory: state space representations, stability, observableness, controllability, realization theory, transfer functions, feedback. Prerequisites: (MATH 2418 and MATH 2451) or instructor consent required. (3-0) T (2015-04-21 20:39:41)

MATH 6332 Advanced Control (3 semester credit hours) Theoretical and practical aspects of modern control methodologies in state space and frequency domain, in particular LQG and H-infinity control: coprime factorizations, internal stability, Kalman filter, optimal regulator, robust control, sensitivity minimization, loop shaping, model reduction. Prerequisite: MATH 6331. (3-0) T (2015-04-21 20:39:41)

MATH 6336 Nonlinear Control Systems (3 semester credit hours) Differential geometric tools, input-output maps, feedback linearization, nonlinear observers, input-output linearization, output tracking, and regulation, passivity based control, control systems on Lie groups. Prerequisites: (MATH 6315 and MATH 6331) or instructor consent required. (3-0) T (2015-04-21 20:39:41)

MATH 6339 Control of Distributed Parameter Systems (3 semester credit hours) Theoretical and technical issues for control of distributed parameter systems in the context of linear infinite dimensional dynamical systems: Evolution equations and control on Euclidean space, elements of functional analysis, semigroups of linear operators, abstract evolution equations, control of linear infinite dimensional dynamical systems, approximation techniques. Prerequisites: MATH 4362 and MATH 4301. (3-0) T (2015-04-21 20:39:41)

MATH 6340 Numerical Linear Algebra (3 semester credit hours) Topics include direct and iterative methods for solving linear systems; vector and matrix norms; condition numbers; least squares problems; orthogonalization, singular value decomposition; computation of eigenvalues and eigenvectors; conjugate gradients; preconditioners for linear systems; computational cost of algorithms. Topics will be supplemented with programming assignments. Recommended Prerequisites: MATH 4334 or equivalent and a prior programming course. Prerequisite: MATH 2418. (3-0) Y (2015-04-21 20:39:41)

MATH 6341 Bioinformatics (3 semester credit hours) Fundamental mathematical and algorithmic theory behind current bioinformatics techniques are covered and implemented. They include hidden Markov models, dynamic programming, genetic algorithms, simulated annealing, neural networks, cluster analysis, and information theory. Prerequisites: Knowledge of Unix and a high level programming language. (3-0) T (2015-04-21 20:39:41)

MATH 6342 Scientific Computing (3 semester credit hours) Introduction to scientific computing through projects in computational science and engineering. Topics include mathematical modeling; theoretical analysis of such models; numerical and symbolic computation; verification and validation; computational simulation. Representative projects will include applications of dynamical systems, Monte Carlo simulations, numerical optimization, and linear and nonlinear partial differential equations. The course includes an introduction to symbolic computation and to programming in MATLAB, Python, and/or C. Some prior programming experience is recommended. Prerequisites: MATH 4334 and MATH 4362 and MATH 6315 or instructor consent required. (3-0) T (2015-04-21 20:39:41)

MATH 6343 Computational Biology (3 semester credit hours) Mathematical and computation methods and techniques to analyze and understand problems in molecular biology are covered. Topics include sequence homology and alignment, genetic mapping, protein folding, and DNA computing. Prerequisite: MATH 2418 or equivalent. (3-0) T (2015-04-21 20:39:41)

MATH 6345 Mathematical Methods in Medicine and Biology (3 semester credit hours) Introduction to the use of mathematical techniques in solving biologically important problems. Some examples of topics that might be covered are biochemical reactions, ion channels, cellular signaling mechanisms, kidney function, and nerve impulse propagation. Recommended Prerequisite: MATH 2420. Prerequisites: MATH 2417 and MATH 2419. (3-0) T (2015-04-21 20:39:41)

MATH 6350 Quantum Computation and Information (3 semester credit hours) Quantum states, channels, measurements; entropy, subadditivity; entanglement measures, discord; teleportation, dense coding, quantum key distribution; Shor's algorithm, Grover's search algorithm, hidden subgroup algorithms. Prerequisite: MATH 2418 and instructor consent required. (3-0) T (2015-04-21 20:39:41)

MATH 6364 Stochastic Calculus in Finance (3 semester credit hours) Brownian Motion, Ito Calculus, Feynman-Kac formula and an outline of Stochastic Control, Black Scholes Analysis, Transaction Costs, Optimal Portfolio Investment. Prerequisites: STAT 4351 or equivalent and MATH 2451 or equivalent. (3-0) T (2015-04-21 20:39:41)

MATH 6390 Topics in Mathematics - Level 6 (3 semester credit hours) May be repeated for credit as topics vary (9 semester credit hours maximum). Instructor consent required. (3-0) R (2015-04-21 20:39:41)

MATH 6V81 Special Topics in Mathematics - Level 6 (1-9 semester credit hours) May be repeated for credit as topics vary. Instructor consent required. ([1-9]-0) S (2015-04-21 20:39:41)

MATH 6V98 Masters Thesis (3-9 semester credit hours) Pass/Fail only. May be repeated for credit. Instructor consent required. ([3-9]-0) S (2015-04-21 20:39:41)

MATH 7313 Partial Differential Equations I (3 semester credit hours) Classical and modern solution techniques for initial and boundary value problems for parabolic, elliptic, and hyperbolic linear partial differential equations. Existence, uniqueness, well-posedness, fundamental solutions, and Green's functions. First-order nonlinear equations, scalar conservation laws, and the method of characteristics. An introduction to weak solutions and the theory of Sobolev spaces. Prerequisite: MATH 6301 and Math 6315 or equivalent. (3-0) T (2015-04-21 20:39:41)

MATH 7314 Partial Differential Equations II (3 semester credit hours) Continuation of MATH 7313. Prerequisite: MATH 7313. (3-0) T (2015-04-21 20:39:41)

MATH 7316 Wave Propagation with Applications (3 semester credit hours) Study of the wave equation in one, two and three dimensions, the Helmholtz equation, associated Green's functions, asymptotic techniques for solving the propagation problems with applications in physical and biomedical sciences and engineering. Prerequisites: MATH 6303 and MATH 6318. (3-0) T (2015-04-21 20:39:41)

MATH 7319 Functional Analysis II (3 semester credit hours) Topological vector spaces, locally convex spaces, Frechet spaces, test function spaces and tempered distributions, Fourier transforms and applications to differential equations. Recommended Prerequisite: MATH 6303. Prerequisites: MATH 6301 and MATH 6302. (3-0) T (2015-04-21 20:39:41)

MATH 7390 Topics in Mathematics - Level 7 (3 semester credit hours) May be repeated for credit as topics vary (9 semester credit hours maximum). Instructor consent required. (3-0) R (2015-04-21 20:39:41)

MATH 8V02 Individual Instruction in Mathematics (1-6 semester credit hours) Pass/Fail only. May be repeated for credit as topics vary. Instructor consent required. ([1-6]-0) S (2015-04-21 20:39:41)

MATH 8V04 Topics in Mathematics - Level 8 (1-6 semester credit hours) Pass/Fail only. May be repeated for credit as topics vary. Instructor consent required. ([1-6]-0) R (2015-04-21 20:39:41)

MATH 8V07 Research (1-9 semester credit hours) Open to students with advanced standing subject to approval of the Graduate Advisor. Pass/Fail only. May be repeated for credit. Instructor consent required. ([1-9]-0) S (2015-04-21 20:39:41)

MATH 8V99 Dissertation (1-9 semester credit hours) Pass/Fail only. May be repeated for credit. Instructor consent required. Prerequisite: Open to PhD students only. ([1-9]-0) S (2015-04-21 20:39:41)