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2015-2016 Graduate Catalog
University of Tennessee, Knoxville
   
 
    
 
  Dec 16, 2017
 
2015-2016 Graduate Catalog [ARCHIVED CATALOG]

Course Descriptions

Contract All Courses |

 

Mathematics (MATH)

  
  •  

    MATH 400 - History of Mathematics

    3 Credit Hours
    Development of major ideas in mathematics from ancient to modern times and the influence of these ideas in science, technology, philosophy, art, and other areas. Includes at least one in-class essay examination and 3,000 words of writing outside classroom.
    (RE) Prerequisite(s): 251 or 257.
    (DE) Prerequisite(s): 300 or 307.
  
  •  

    MATH 403 - Mathematical Methods for Engineers and Scientists

    3 Credit Hours
    Matrix computations, numerical methods, partial differential equations, Sturm-Liouville Theory and special functions as used in engineering and science.
    (RE) Prerequisite(s): 231; 241 or 247.
    Comment(s): Knowledge of high-level programming language required.
  
  •  

    MATH 404 - Applied Vector Calculus

    3 Credit Hours
    Topics from multivariable and vector calculus; line and surface integrals, divergence theorem and the theorems of Gauss and Stokes.
    (RE) Prerequisite(s): 241 or 247.
  
  •  

    MATH 405 - Models in Biology

    3 Credit Hours
    Difference and differential equation models of biological systems.
    Cross-listed: (Same as Ecology and Evolutionary Biology 406.)

    Credit Restriction: May not be applied toward a mathematics graduate degree.
    (RE) Prerequisite(s): 142 or 148 or 152.
  
  •  

    MATH 411 - Mathematical Modeling

    3 Credit Hours
    Construction and analysis of mathematical models used in science and industry. Projects emphasized.
    (RE) Prerequisite(s): 231; 241 or 247; 200 or 251 or 257.
  
  •  

    MATH 421 - Combinatorics

    3 Credit Hours
    Introduction to problems of construction and enumeration for discrete structures such as sequences, partitions, graphs, finite fields and geometries, and experimental designs.
    (RE) Prerequisite(s): 300 or 307.
  
  •  

    MATH 423 - Probability

    3 Credit Hours
    Axiomatic probability, univariate and multivariate distributions, conditional distributions and expectations, moment generating functions, laws of large numbers and central limit theorem.
    (RE) Prerequisite(s): 241 or 247; 300 or 307.
    (DE) Prerequisite(s): 323.
  
  •  

    MATH 424 - Stochastic Processes

    3 Credit Hours
    Markov chains, Poisson processes and Brownian motion. Other topics as selected by instructor.
    (RE) Prerequisite(s): 423.
  
  •  

    MATH 425 - Statistics

    3 Credit Hours
    Standard statistical distributions, independence of mean and variance for a Gaussian sample, basic limit theorems; point and interval estimation, tests of statistical hypotheses, Neyman-Pearson theorem; likelihood ratio and other parametric and nonparametric tests.
    (RE) Prerequisite(s): 423.
  
  •  

    MATH 431 - Differential Equations II

    3 Credit Hours
    A second course in ordinary differential equations. Linear systems of differential equations, Frobenius method, Sturm-Liouville eigenvalue problems, phase plane analysis.
    (RE) Prerequisite(s): 231; 200 or 251 or 257.
  
  •  

    MATH 435 - Partial Differential Equations

    3 Credit Hours
    Separation of variables, Fourier series, solution of Laplace, wave, and heat equations.
    (RE) Prerequisite(s): 231; 241 or 247.
  
  •  

    MATH 443 - Complex Variables

    3 Credit Hours
    Introduction to the theory of functions of a complex variable, including residue theory and contour integrals.
    (RE) Prerequisite(s): 241 or 247.
  
  •  

    MATH 445 - Advanced Calculus I

    3 Credit Hours
    Introduction to the theory of sequences, series, differentiation, and Riemann integration of functions of one or more variables.
    (RE) Prerequisite(s): 241 or 247; 300 or 307.
  
  •  

    MATH 446 - Advanced Calculus II

    3 Credit Hours
    Continuation of 445.
    (RE) Prerequisite(s): 445.
  
  •  

    MATH 447 - Honors: Advanced Calculus I

    3 Credit Hours
    Honors version of 445.
    (RE) Prerequisite(s): 341.
  
  •  

    MATH 448 - Honors: Advanced Calculus II

    3 Credit Hours
    Continuation of 447.
    (RE) Prerequisite(s): 447.
  
  •  

    MATH 453 - Matrix Algebra II

    3 Credit Hours
    Advanced topics in matrix theory including Jordan canonical form.
    (RE) Prerequisite(s): 200 or 251 or 257.
  
  •  

    MATH 455 - Abstract Algebra I

    3 Credit Hours
    Introduction to algebraic structures such as groups, rings, fields, vector spaces, and linear transformations.
    (RE) Prerequisite(s): 251 or 257; 300 or 307.
  
  •  

    MATH 456 - Abstract Algebra II

    3 Credit Hours
    Continuation of 455.
    (RE) Prerequisite(s): 455.
  
  •  

    MATH 457 - Honors: Abstract Algebra I

    3 Credit Hours
    Honors version of 455.
    (RE) Prerequisite(s): 351.
  
  •  

    MATH 458 - Honors: Abstract Algebra II

    3 Credit Hours
    Continuation of 457.
    (RE) Prerequisite(s): 457.
  
  •  

    MATH 460 - Geometry

    3 Credit Hours
    Axiomatic and historical development of neutral, Euclidean, and hyperbolic geometry stressing proof technique and critical reasoning. Models of Non-Euclidean geometries.
    (RE) Prerequisite(s): 300 or 307.
  
  •  

    MATH 462 - Differential Geometry

    3 Credit Hours
    Classical differential geometry of curves and surfaces: Frenet frames, first and second fundamental forms, Gauss curvature and mean curvature, geodesics and parallel transport, the Gauss-Bonet theorem, geometry of the hyperbolic plane.
    (RE) Prerequisite(s): 241 or 247.
  
  •  

    MATH 467 - Honors: Topology

    3 Credit Hours
    Includes topology of line and plane, separation properties, compactness, connectedness, continuous functions, homeomorphisms, continua, and topological invariants.
    (RE) Prerequisite(s): 300 or 307.
    (DE) Prerequisite(s): 241 or 247.
  
  •  

    MATH 471 - Numerical Analysis

    3 Credit Hours
    Introduction to computation, instabilities, and rounding. Interpolation and approximation by polynomials and piecewise polynomials. Quadrature and numerical solution of initial and boundary value problems of ordinary differential equations, stiff systems.
    Cross-listed: (Same as Computer Science 471.)

    (RE) Prerequisite(s): 231; 200 or 251 or 257.
    (DE) Prerequisite(s): 371.
    Comment(s): Knowledge of a high-level programming language required.
  
  •  

    MATH 472 - Numerical Algebra

    3 Credit Hours
    Direct and iterative methods for systems of linear equations. Solution of single nonlinear equation and nonlinear systems. Orthogonal decomposition, least squares and algebraic eigenvalue problem.
    Cross-listed: (Same as Computer Science 472.)

    (RE) Prerequisite(s): 231; 200 or 251 or 257.
    (DE) Prerequisite(s): 371.
    Comment(s): Knowledge of a high-level programming language required.
  
  •  

    MATH 475 - Industrial Mathematics

    3 Credit Hours
    Modeling, analysis, and computation applied to scientific/technical/industrial problems.
    (RE) Prerequisite(s): 231.
    Recommended Background: Familiarity with operating system and programming language.
  
  •  

    MATH 490 - Readings in Mathematics

    1-3 Credit Hours
    Open to superior students. Independent study with faculty guidance.
    Repeatability: May be repeated. Maximum 9 hours.
    Comment(s): Consent of faculty mentor to supervise independent work required.
    Registration Permission: Consent of department head.
  
  •  

    MATH 499 - Seminar in Mathematics

    1-3 Credit Hours
    Topics vary. Requires out-of-class projects and in-class presentations by students. Students must register for the number of credit hours announced for a particular seminar.
    Repeatability: May be repeated. Maximum 9 hours.
    Registration Permission: Consent of instructor.
  
  •  

    MATH 500 - Thesis

    1-15 Credit Hours
    Grading Restriction: P/NP only.
    Repeatability: May be repeated.
    Credit Level Restriction: Graduate credit only.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 502 - Registration for Use of Facilities

    1-15 Credit Hours
    Required for the student not otherwise registered during any semester when student uses university facilities and/or faculty time before degree is completed.
    Grading Restriction: Satisfactory/No Credit grading only.
    Repeatability: May be repeated.
    Credit Restriction: May not be used toward degree requirements.
    Credit Level Restriction: Graduate credit only.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 504 - Discrete Mathematics for Teachers

    3 Credit Hours
    Mathematical logic and methods of argument, sets, functions and relations, combinatorics. Normally, the first graduate course for students seeking Master of Mathematics degree.
    Credit Restriction: May not apply toward mathematics major (Master of Science).
    Recommended Background: 1 year of calculus or equivalent.
    Comment(s): For students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences.
  
  •  

    MATH 505 - Analysis for Teachers

    3 Credit Hours
    Development of differential and integral calculus, proofs of basic theorems.
    Credit Restriction: May not apply toward mathematics major (Master of Science).
    Recommended Background: 1 year of calculus or equivalent.
    Comment(s): For students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences.
  
  •  

    MATH 506 - Algebra for Teachers

    3 Credit Hours
    Algebraic structures: integral domains and fields and their applications to algebra of integers and polynomials.
    Credit Restriction: May not apply toward mathematics major (Master of Science).
    Recommended Background: 1 year of calculus or equivalent.
    Comment(s): For students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences.
  
  •  

    MATH 507 - Probability and Statistics for Teachers

    3 Credit Hours
    Probability models. Discrete random variables. Binomial, hypergeometric, and Poisson distributions.
    Credit Restriction: May not apply toward mathematics major (Master of Science).
    Recommended Background: 1 year of calculus or equivalent.
    Comment(s): For Students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences.
  
  •  

    MATH 509 - Seminar for Teachers

    3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
    Credit Restriction: May not apply toward mathematics major (Master of Science).
    Comment(s): For Students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences.
    Registration Permission: Consent of instructor.
  
  •  

    MATH 511 - Methods in Applied Mathematics I

    3 Credit Hours
    Fundamentals and techniques associated with discrete models of physical, engineering and biological systems: difference equations, networks and graphs, optimization, and other topics.
    Recommended Background: Courses in advanced calculus and linear algebra.
  
  •  

    MATH 512 - Methods in Applied Mathematics II

    3 Credit Hours
    Fundamentals and techniques associated with continuous models of physical, engineering, and biological systems: development, solution and qualitative analysis of ordinary and partial differential equations, and calculus of variations.
    (DE) Prerequisite(s): 511.
  
  •  

    MATH 513 - Mathematical Principles of Fluid Mechanics I

    3 Credit Hours
    Equations of motion, incompressible and compressible potential flow, shock waves, viscous flows. Navier-Stokes equations.
    Recommended Background: Advanced courses in ordinary and partial differential equations and advanced calculus.
  
  •  

    MATH 514 - Mathematical Principles of Fluid Mechanics II

    3 Credit Hours
    Continuation of 513.
    (DE) Prerequisite(s): 513.
  
  •  

    MATH 515 - Analytical Applied Mathematics I

    3 Credit Hours
    Analysis of advanced techniques in modern context for applied problems: dimensional analysis and scaling, perturbation theory, variational approaches, transform theory, wave phenomena and conservation laws, stability and bifurcation, distributions, integral equations.
    Recommended Background: Courses in advanced calculus, linear algebra, and either advanced differential equations or 512.
  
  •  

    MATH 516 - Analytical Applied Mathematics II

    3 Credit Hours
    Continuation of 515.
    (DE) Prerequisite(s): 515.
  
  •  

    MATH 517 - Mathematical Methods in Physics I

    3 Credit Hours
    Cross-listed: (See Physics 571.)

  
  •  

    MATH 518 - Mathematical Methods in Physics II

    3 Credit Hours
    Cross-listed: (See Physics 572.)

  
  •  

    MATH 519 - Seminar in Applied Mathematics

    1-3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
  
  •  

    MATH 521 - Enumerative Combinatorics I

    3 Credit Hours
    Sieve methods, recursion, generating functions, and permutation groups applied to enumeration of discrete structures. Incidence algebras and combinatorics of partially ordered sets.
  
  •  

    MATH 522 - Enumerative Combinatorics II

    3 Credit Hours
    Continuation of 521.
    (DE) Prerequisite(s): 521.
  
  •  

    MATH 523 - Probability I

    3 Credit Hours
    Probability spaces and random variables, expectation, characteristic functions, convergence of random variables.
    Recommended Background: One year of advanced calculus and 323.
  
  •  

    MATH 524 - Probability II

    3 Credit Hours
    Continuation of 523. Law of large numbers, central limit theorem, conditional expectation, martingales. Other topics as selected by instructor.
    (DE) Prerequisite(s): 523.
  
  •  

    MATH 525 - Statistics I

    3 Credit Hours
    Formulation of statistical models, sufficiency; methods of estimation and optimal theory, asymptotic efficiency; the confidence procedures and hypothesis testing, uniformly most powerful tests; Bayesian statistics.
    Recommended Background: One year of advanced calculus and 425.
  
  •  

    MATH 526 - Statistics II

    3 Credit Hours
    Continuation of 525. Estimation and tests in general linear models; non-parametric models, rank methods for comparison, robust tests. Other topics as selected by instructor.
    (DE) Prerequisite(s): 525.
  
  •  

    MATH 527 - Stochastic Modeling

    3 Credit Hours
    Variable topics in probability applied to real world situations. Topics may include queuing theory, branching processes, Monte Carlo simulation, stochastic finance and other topics as selected by instructor.
    Recommended Background: One year of advanced calculus and one year of undergraduate probability or mathematical statistics.
  
  •  

    MATH 529 - Seminar in Stochastics

    1-3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
  
  •  

    MATH 531 - Ordinary Differential Equations I

    3 Credit Hours
    Existence, uniqueness, extendibility, and dependence on parameters for solutions of differential equations. The theory of linear systems of differential equations including boundary value problems and series methods.
    Recommended Background: One year of advanced calculus and undergraduate differential equations.
  
  •  

    MATH 532 - Ordinary Differential Equations II

    3 Credit Hours
    Continuation of 531. The nonlinear theory of differential equations including Liapunov stability, critical point analysis, and Poincare-Bendixson theory.
    (DE) Prerequisite(s): 531.
  
  •  

    MATH 534 - Calculus of Variations

    3 Credit Hours
    Necessary and sufficient conditions for weak and strong extrema in one-dimensional variation problems; Lagrangian mechanics. Multiple integrals. Basic elements of direct methods.
    Recommended Background: At least one senior-level course in differential equations or advanced calculus. Mathematical maturity.
  
  •  

    MATH 535 - Partial Differential Equations I

    3 Credit Hours
    First order partial differential equations, classification of second order partial differential equations, properties of elliptic, parabolic and hyperbolic partial differential equations.
    Recommended Background: One year of advanced calculus.
  
  •  

    MATH 536 - Partial Differential Equations II

    3 Credit Hours
    Continuation of 535. Properties and representation formulas for elliptic, parabolic and hyperbolic partial differential equations.
    (DE) Prerequisite(s): 535.
  
  •  

    MATH 537 - Mathematical Principles of Continuum Mechanics I

    3 Credit Hours
    Conservation principles, equations of equilibrium and motion for fluids and elastic solids, constitutive relations and stress, convexity properties, bifurcation phenomena, existence theory.
    Recommended Background: Courses in advanced calculus and advanced differential equations.
  
  •  

    MATH 538 - Mathematical Principles of Continuum Mechanics II

    3 Credit Hours
    Continuation of 537.
    (DE) Prerequisite(s): 537.
  
  •  

    MATH 539 - Seminar in Differential Equations

    1-3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
  
  •  

    MATH 545 - Real Analysis

    3 Credit Hours
    Measure theory, Lebesgue integration, Holder and Minkowski inequalities, Radon-Nikodym theorem, Fubini’s theorem.
    Recommended Background: One year of advanced calculus.
  
  •  

    MATH 546 - Complex Analysis

    3 Credit Hours
    Holomorphic functions, Cauchy’s theorem, Maximum Modulus theorem, Schwarz’s lemma, normal families, Riemann mapping theorem.
    (DE) Prerequisite(s): 545.
  
  •  

    MATH 547 - Applied Linear Analysis

    3 Credit Hours
    Banach and Hilbert spaces, linear operators and spectral theory, Sobolev spaces, applications.
    (DE) Prerequisite(s): 545.
  
  •  

    MATH 549 - Seminar in Analysis

    1-3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
  
  •  

    MATH 551 - Modern Algebra I

    3 Credit Hours
    Groups and rings.
    Recommended Background: One year of undergraduate abstract algebra.
  
  •  

    MATH 552 - Modern Algebra II

    3 Credit Hours
    Continuation of 551; modules, fields and Galois theory.
    (DE) Prerequisite(s): 551.
  
  •  

    MATH 555 - Number Theory I

    3 Credit Hours
    Introduction to algebraic number theory.
    Recommended Background: One year of undergraduate abstract algebra.
  
  •  

    MATH 556 - Number Theory II

    3 Credit Hours
    Continuation of 555.
    (DE) Prerequisite(s): 555.
  
  •  

    MATH 559 - Seminar in Algebra

    1-3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
  
  •  

    MATH 561 - Topology I

    3 Credit Hours
    Topological spaces and continuous functions, separation axioms, product and quotient topologies, connectedness, compactness, complete metric spaces.
    Recommended Background: One year of advanced calculus.
  
  •  

    MATH 562 - Topology II

    3 Credit Hours
    Continuation of 561. Fundamental group and covering spaces.
    (DE) Prerequisite(s): 561.
  
  •  

    MATH 567 - Riemannian Geometry I

    3 Credit Hours
    Riemannian and Lorentzian manifolds. Variations of arc length, Jacobi fields, comparison theorems. Constant curvature spaces. Curvature and topology of manifolds.
    Recommended Background: One year of advanced calculus.
  
  •  

    MATH 568 - Riemannian Geometry II

    3 Credit Hours
    Continuation of 567.
    (DE) Prerequisite(s): 567.
  
  •  

    MATH 569 - Seminar in Topology and Geometry

    1-3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
  
  •  

    MATH 571 - Numerical Mathematics I

    3 Credit Hours
    Direct and iterative methods for linear systems. The algebraic eigenvalue problem and the singular decomposition theorem. Newton and quasi-Newton methods for systems of nonlinear equations.
    Cross-listed: (Same as Computer Science 571.)

    Recommended Background: Courses in advanced calculus and basic numerical analysis.
  
  •  

    MATH 572 - Numerical Mathematics II

    3 Credit Hours
    Numerical techniques for initial value problems of ordinary differential equations. Two-point boundary value problems. Finite difference and finite element methods for selected partial differential equations. Fast Poisson solvers.
    Cross-listed: (Same as Computer Science 572.)

    (DE) Prerequisite(s): 571.
  
  •  

    MATH 574 - Finite Element Methods

    3 Credit Hours
    Finite element techniques for solution of boundary and initial-boundary value problems. Variational formulation. Finite dimensional subspaces and their approximating properties; rates of convergence. Computer implementation.
    Cross-listed: (Same as Computer Science 574.)

    Recommended Background: Courses in partial differential equations, linear algebra and numerical analysis.
  
  •  

    MATH 577 - Optimization

    3 Credit Hours
    Mathematical foundations of constrained and unconstrained optimization. Lagrange multipliers, the Farkas lemma, the Kuhn-Tucker-Karush theorem. Analysis of major algorithms and applications to real world problems.
    Recommended Background: Courses in numerical algorithms, linear algebra and advanced calculus.
  
  •  

    MATH 578 - Numerical Methods for Partial Differential Equations

    3 Credit Hours
    Numerical approximation of solutions of partial differential equations including conservation laws and hyperbolic, parabolic, and elliptic problems. Derivation, physical meaning, and implementation of schemes.
    Recommended Background: A course in partial differential equations or 512 or 515, and familiarity with an operating system and a programming language.
  
  •  

    MATH 579 - Seminar in Numerical Mathematics

    1-3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
  
  •  

    MATH 581 - Mathematical Ecology I

    3 Credit Hours
    Deterministic and stochastic models of populations, communities, and ecosystems.
    Cross-listed: (Same as Ecology and Evolutionary Biology 581.)

    (DE) Prerequisite(s): 431 and 453.
  
  •  

    MATH 582 - Mathematical Ecology II

    3 Credit Hours
    Continuation of 581.
    Cross-listed: (Same as Ecology and Evolutionary Biology 582.)

    (DE) Prerequisite(s): 581.
  
  •  

    MATH 583 - Mathematical Evolutionary Theory

    3 Credit Hours
    Population genetics and evolutionary ecology.
    Cross-listed: (Same as Ecology and Evolutionary Biology 585.)

    (DE) Prerequisite(s): 431 and 453.
  
  •  

    MATH 585 - Optimal Control Theory

    3 Credit Hours
    Deterministic optimal control. Examples involving calculus of variations, optimal trajectories, and engineering control problems. Introduction to stochastic control.
    Recommended Background: One year of advanced calculus and undergraduate differential equations.
  
  •  

    MATH 589 - Seminar in Mathematical Ecology

    1-3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
  
  •  

    MATH 590 - Seminar in Teaching College Mathematics

    1-3 Credit Hours
    Selected topics in research, theory, and techniques for teaching collegiate mathematics.
    Repeatability: May be repeated. Maximum 12 hours.
    Credit Restriction: May not be applied toward mathematics major (Master of Science).
    Registration Permission: Consent of department head.
  
  •  

    MATH 593 - Independent Study

    1-12 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
  
  •  

    MATH 598 - Graduate Reading in Mathematics

    1-3 Credit Hours
    Independent study with faculty guidance.
    Repeatability: May be repeated. Maximum 6 hours.
    Comment(s): Graduate standing required.
    Registration Permission: Consent of instructor.
  
  •  

    MATH 599 - Seminar in Mathematical Presentations

    1 Credit Hours
  
  •  

    MATH 600 - Doctoral Research and Dissertation

    3-15 Credit Hours
    Grading Restriction: P/NP only.
    Repeatability: May be repeated.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 619 - Seminar in Applied Mathematics

    1-3 Credit Hours
    Repeatability: May be repeated. Maximum 12 hours.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 623 - Advanced Probability I

    3 Credit Hours
    Selected topics in modern theory of probability and stochastic processes.
    Repeatability: May be repeated. Maximum 12 hours.
    (DE) Prerequisite(s): 523 and 524.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 624 - Advanced Probability II

    3 Credit Hours
    Continuation of 623.
    Repeatability: May be repeated. Maximum 12 hours.
    (DE) Prerequisite(s): 623.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 635 - Advanced Partial Differential Equations I

    3 Credit Hours
    Selected topics in classical and modern theoretical partial differential equations.
    Repeatability: May be repeated. Maximum 12 hours.
    (DE) Prerequisite(s): 535 and 536.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 636 - Advanced Partial Differential Equations II

    3 Credit Hours
    Continuation of 635.
    Repeatability: May be repeated. Maximum 12 hours.
    (DE) Prerequisite(s): 635.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 641 - Functional Analysis I

    3 Credit Hours
    Topological vector spaces, distributions, and Banach algebras with applications to Fourier analysis and differential equations: theorems of Krein-Milman, Paley-Wiener, Lax, Malgrange-Ehrenpreis, Gelfand-Naimark, and spectral theory of normal operators.
    Repeatability: May be repeated. Maximum 6 hours.
    (DE) Prerequisite(s): 545.
    (DE) Corequisite(s): 546 or 443.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 642 - Functional Analysis II

    3 Credit Hours
    Continuation of 641.
    Repeatability: May be repeated. Maximum 6 hours.
    (DE) Prerequisite(s): 641.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 645 - Advanced Analysis I

    3 Credit Hours
    Selected topics in real, complex, or discrete analysis.
    Repeatability: May be repeated. Maximum 12 hours.
    (DE) Prerequisite(s): 545 and 546.
    Registration Restriction(s): Minimum student level – graduate.
  
  •  

    MATH 646 - Advanced Analysis II

    3 Credit Hours
    Continuation of 645.
    Repeatability: May be repeated. Maximum 12 hours.
    (DE) Prerequisite(s): 645.
    Registration Restriction(s): Minimum student level – graduate.
 

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Contract All Courses |