Online Degrees and Courses

Mathematics Courses For Graduate at Virginia Polytechnic Institute And State University

MATH 4024 - Axiomatic Set Theory
Peano postulates, cardinal arithmetic, axiom of choice, well orderings, ordinal arithmetic, continuum hypothesis.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4044 - History of Mathematics
Historical development of mathematics from antiquity to modern times. Senior standing in mathematics required. I.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4124 - Introduction to Abstract Algebra
An introduction to the theory of groups and rings. Topics include normal subgroups, permutation groups, Sylow’s Theorem, Abelian groups, Integral Domains, Ideals, and Polynomial Rings. I,II,III.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4134 - Number Theory
Divisibility, congruences, multiplicative functions, primitive roots, quadratic reciprocity. II
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4144 - Linear Algebra II
Second course in linear algebra. Similarity invariants, Jordan canonical form, inner product spaces, self-adjoint operators, selected applications.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4214 - Linear Analysis
Linear algebra of infinite dimensional spaces, inner product spaces, normed spaces, completeness, orthonormal bases, bounded and unbounded linear operators, adjoints, spectra, compact operators.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4225 - Elementary Real Analysis
Real number system, point set theory, limits, continuity, differentiation, integration, infinite series, sequences and series of functions. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4226 - Elementary Real Analysis
Real number system, point set theory, limits, continuity, differentiation, integration, infinite series, sequences and series of functions. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4234 - Elementary Complex Analysis
Analytic functions, complex integration, series representation of analytic functions, residues, conformal mapping, applications II
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4245 - Intermediate Differential Equations
Solution techniques, linear systems, the matrix exponential, existence theorems, stability, non-linear systems, eigenvalue problems.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4246 - Intermediate Differential Equations
Solution techniques, linear systems, the matrix exponential, existence theorems, stability, non-linear systems, eigenvalue problems.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4254 - Chaos and Dynamical Systems
Survey of basic concepts in chaotic dynamical systems. Includes material on bifurcation theory, conjugacy, stability, and symbolic dynamics.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4324 - Elementary Topology
Basic concepts of topological spaces, continuous functions, connected spaces, compact spaces, and metric spaces. I
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4334 - College Geometry
Transformational approach to Euclidean geometry including an in-depth study of isometries and their application to symmetry, geometric constructions, congruence, coordinate geometry, and non-Euclidean geometries. I,II.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4344 - Topics in Geometry
Selected topics in geometry for advanced undergraduates.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture, Online Course

MATH 4404 (AOE 4404) - Applied Numerical Methods
Interpolation and approximation, numerical integration, solution of equations, matrices and eigenvalues, systems of equations, approximate solution of ordinary and partial differential equations. Applications to physical problems. Partially duplicates 4554 and 3414. Mathematics majors or minors cannot take both 4404 and 3414.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture, Online Course

MATH 4425 - Fourier Series and Partial Differential Equations
Separation of variables for heat, wave, and potential equations. Fourier expressions. Application to boundary value problems. Bessel functions. Integral transforms and problems on unbounded domains. 4425: I, II. 4426: II.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4426 - Fourier Series and Partial Differential Equations
Separation of variables for heat, wave, and potential equations. Fourier expressions. Application to boundary value problems. Bessel functions. Integral transforms and problems on unbounded domains. 4425: I, II. 4426: II.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4445 - Introduction to Numerical Analysis
4445: Vector spaces and review of linear algebra, direct and iterative solutions of linear systems of equations, numerical solutions to the algebraic eigenvalue problem, solutions of general non-linear equations and systems of equations. 4446: Interpolation and approximation, numerical integration and differentiation, numerical solutions of ordinary differential equations. Computer programming skills required. I,III
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4446 - Introduction to Numerical Analysis
4445: Vector spaces and review of linear algebra, direct and iterative solutions of linear systems of equations, numerical solutions to the algebraic eigenvalue problem, solutions of general non-linear equations and systems of equations. 4446: Interpolation and approximation, numerical integration and differentiation, numerical solutions of ordinary differential equations. Computer programming skills required. II,IV
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4454 - Applied Mathematical Modeling- Continuous Mathematical Models
Analysis of classical and modern applications of mathematics in the physical, biological and social sciences. Emphasis on problem formulating, modeling, solving, simulating, and analyzing results. Programming language required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4514 - Applied Algebra
Binary relations, groups, semigroups, monoids, rings, fields, Boolean algebras, and Polya’s theory of Enumerations. Partially duplicates 3124.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4525 - Principles of Advanced Calculus
4525: Elementary calculus review, real number system, continuity of single variable functions, integration, sequences and infinite series. 4526: Differential calculus of several variable functions, multiple integration, curves and surfaces, line and surface integrals. For non-mathematics majors: 4525 partially duplicates 3224, 4526 partially duplicates 3214.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4526 - Principles of Advanced Calculus
4525: Elementary calculus review, real number system, continuity of single variable functions, Integration, sequences and infinite series. 4526: Differential calculus of several variable functions, multiple integration, curves and surfaces, line and surface integrals. For non-mathematics majors: 4525 partially duplicates 3224, 4526 partially duplicates 3214.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4544 - Ordinary and Partial Differential Equations
Ordinary differential equations: first order, second and higher order linear equations, power series and Laplace transform methods. Partial differential equations: Fourier series, separation of variables for heat, wave and potential equations. Sturm-Liouville theory. Bessel functions. Legendre polynomials. Partially duplicates 2214 and 4564.
Credit Hours: 5
Lecture Hours: 5
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4554 - Numerical Methods for Engineers
Root-finding, interpolation, linear algebraic systems, numerical integration, and numerical solution of ordinary and partial differential equations. Duplicates 3414 and 4404, and can not be taken by mathematics majors. Computer programming required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4564 - Operational Methods for Engineers
Laplace transformations, Fourier series, partial differential equations and separation of variables, boundary value problems, and Sturm-Liouville theory. Duplicates 4544. I,II,III,IV
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4574 - Vector and Complex Analysis for Engineers
Vector Analysis: Green’s theorem, potential theory, divergence, and Stokes’ theorem. Complex Analysis: Analyticity, complex integration, Taylor series, residues, conformal mapping, applications. I,II,III
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4584 (STAT 4584) - Advanced Calculus for Statistics
Introduction to those topics in advanced calculus and linear algebra needed by statistics majors. Infinite sequences and series. Orthogonal matrices, projections, quadratic forms. Extrema of functions of several variables. Multiple integrals, including convolution and nonlinear coordinate changes.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4625 - Mathematics for Secondary Teachers
Course activities will emphasize the curricular themes of problem solving, reasoning and proof, communication, connections, and representation. 4625: Topics in discrete mathematics and algebra from a secondary teaching perspective. 4626: Topics in trigonometry, geometry, measurement, statistics, and probability from a secondary teaching perspective.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4626 - Mathematics for Secondary Teachers
Course activities will emphasize the curricular themes of problem solving, reasoning and proof, communication, connections, and representation. 4625: Topics in discrete methematics and algebra from a secondary teaching perspective. 4626: Topics in trigonometry, geometry, measurement, statistics, and probability from a secondary teaching perspective.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 4644 - Secondary School Mathematics With Technology
Use and impact of technology in secondary mathematics curriculum. Various technologies including graphing calculators, calculator based laboratory and probes (CBLs), computer algebra systems, spreadsheets, dynamic geometry software and the Internet will be used to explore secondary mathematical concepts from an advanced viewpoint. I.
Credit Hours: 3
Lecture Hours: 3
Level(s): Undergraduate and Graduate
Instruction Type: Lecture

MATH 5114 - Specialized Topics in Algebra
Various graduate level topics in algebra such as field theory, non-commutative ring theory, group representation theory, Lie algebras. May be taken for credit more than once with departmental permission. II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5125 - Abstract Algebra
Groups, rings and ideals, modules, brief introduction to homological algebra. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5126 - Abstract Algebra
Groups, rings and ideals, modules, brief introduction to homological algebra. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5135 - Topics in Number Theory
Advanced topics in number theory such as algebraic number theory, analytic number theory, or theory of quadratic forms.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5136 - Topics in Number Theory
Advanced topics in number theory such as algebraic number theory, analytic number theory, or theory of quadratic forms.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5144 (GEOS 5144) (GEOL 5144) - Inverse Theory and Geoscience Applications
Overview of inverse theory, utilizing geophysical examples to illustrate the concepts of model construction, parameter estimation, resolution, and non-uniqueness. Emphasis is on the linear problem, concluding with an overview of nonlinear inversion.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5214 - Specialized Topics in Analysis
Various graduate level topics in analysis for graduate students in mathematics and qualified students in other areas. Consent required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5225 - Real Analysis
Basic set theoretic and topological notions, fundamental theorems of measure and integration, differentiation, applications to linear analysis. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5226 - Real Analysis
Basic set theoretic and topological notions, fundamental theorems of measure and integration, differentiation, applications to linear analysis. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5235 - Complex Analysis
Holomorphic functions, complex integration and residues, series expansions, normal families and the Riemann mapping theorem, entire functions, power series in the unit disk. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5236 - Complex Analysis
Holomorphic functions, complex integration and residues, series expansions, normal families and the Riemann mapping theorem, entire functions, power series in the unit disk. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5245 - Ordinary Differential Equations
Existence theorems, linear theory, stability theory, periodic solutions, Poincare-Bendixon theory, boundary-value problems, functional differential equations. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5246 - Ordinary Differential Equations
Existence theorems, linear theory, stability theory, periodic solutions, Poincare-Bendixon theory, boundary-value problems, functional differential equations. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5344 - Specialized Topics in Topology and Geometry
Various graduate level topics in topology and geometry. May be taken for credit more than once with department consent. II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5415 - Specialized Topics in Applied Math
Various graduate level topics in applied mathematics for graduate students in mathematics and qualified students in other areas. May be taken for credit more than once with department consent. Consent required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture, Lecture 1, Lecture 2, Lecture 3

MATH 5416 - Specialized Topics in Applied Math
Various graduate level topics in applied mathematics for graduate students in mathematics and qualified students in other areas. May be taken for credit more than once with department consent. Consent required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture, Lecture 1, Lecture 2, Lecture 3

MATH 5425 - Applied Partial Differential Equations
Partial differential equations of first and second order, hyperbolic equations, elliptic equations and Green’s functions, parabolic equations, canonic forms, application to physics and engineering. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5426 - Applied Partial Differential Equations
Partial differential equations of first and second order, hyperbolic equations, elliptic equations and Green’s functions, parabolic equations, canonic forms, application to physics and engineering. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5435 - Principles and Techniques of Applied Mathematics
Methods and techniques for obtaining approximate solutions to differential and integral equations that are not solvable exactly. Asymptotic and perturbation analysis, complex integration. Consent required. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5444 - Numerical Methods for Ordinary Differential Equations
Computational procedures for ordinary differential equations including Runge-Kutta methods, variable-step Runge-Kutta methods, predictor-corrector methods, applications to two-point boundary-value problems and parameter estimation. Error control, relative and absolute stability, methods for stiff equations; with computer assignments. Senior standing in engineering, science, or mathematics, and some programming ability required. IV
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5454 - Graph Theory
Graphs, trees, connectivity, Euler tours, matching, independent sets and cliques, planar graphs, directed graphs. Consent required. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5464 - Combinatorics
Counting problems, generating functions, recurrence relations, principle of inclusion and exclusion, experimental designs. Consent required. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5465 (CS 5465) - Numerical Analysis
A survey of the construction, analysis, and implementation of numerical algorithms in linear algebra, nonlinear equations and optimization, approximation by polynomials, quadrature, and ordinary differential equations. High-level programming language required. I
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5466 (CS 5466) - Numerical Analysis
A survey of the construction, analysis, and implementation of numerical algorithms in linear algebra, nonlinear equations and optimization, approximation by polynomials, quadrature, and ordinary differential equations. High-level programming language required. II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5474 (CS 5474) - Finite Difference Methods for Partial Differential Equations
Finite difference methods for initial and boundary value problems for partial differential equations. Consistency, stability, convergence, dispersion, and dissipation. Methods for linear and nonlinear elliptic and parabolic equations, first- and second-order hyperbolic equations, and nonlinear conservation laws. High-level programming language required. I
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5484 (CS 5484) - Finite Element Methods for Partial Differential Equations
Weak formulations of boundary-value problems for elliptic partial differential equations. Finite element spaces. Approximation theory for finite element spaces. Error estimates. Effects of numerical integration and curved boundaries. Nonconforming methods. Concrete examples of the application of the finite element method. Efficient implementation strategies. Time dependent problems. High-level programming language required. II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5485 (CS 5485) - Numerical Analysis and Software
Presentation and analysis of numerical methods for solving common mathematical and physical problems. Methods of solving large sparse linear systems of equations, algebraic eigenvalue problems, and linear least squares problems. Numerical algorithms for solving constrained and unconstrained optimization problems. Numerical solutions of nonlinear algebraic systems. Convergence, error analysis. Hardware and software influences. Efficiency, accuracy, and reliability of software. Robust computer codes. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5486 (CS 5486) - Numerical Analysis and Software
Presentation and analysis of numerical methods for solving common mathematical and physical problems. Methods of solving large sparse linear systems of equations, algebraic eigenvalue problems, and linear least squares problems. Numerical algorithms for solving constrained and unconstrained optimization problems. Numerical solutions of nonlinear algebraic systems. Convergence, error analysis. Hardware and software influences. Efficiency, accuracy, and reliability of software. Robust computer codes. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5495 - Mathematical Methods in Engineering I,ii
Linear algebra and matrix theory, vector calculus, complex variables and integral transforms, ordinary and partial differential equations, special functions, integral equations and calculus of variations. Facility with an existing math software package knowledge of senior level engineering mathematics required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5496 - Mathematical Methods in Engineering I,ii
Linear algebra and matrix theory, vector calculus, complex variables and integral transforms, ordinary and partial differential equations, special functions, integral equations and calculus of variations. Facility with an existing math software package knowledge of senior level engineering mathematics required. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5515 (GBCB 5515) - Mathematical Methods for Modeling and Simulation of Biological Systems
Introduction to mathematical techniques for modeling and simulation, parameter identification and analysis of biological systems. Emphasis on both theoretical and practical issues and methods of computation, with concrete applications. Suitable for students from the mathematical and life sciences who have a basic foundation in multivariate calculus and ordinary differential equations. 5515: Continuous models and methods. 5516: Discrete models and methods.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5516 (GBCB 5516) - Mathematical Methods for Modeling and Simulation of Biological Systems
Introduction to mathematical techniques for modeling and simulation, parameter identification and analysis of biological systems. Emphasis on both theoretical and practical issues and methods of computation, with concrete applications. Suitable for students from the mathematical and life sciences who have a basic foundation in multivariate calculus and ordinary differential equations. 5515: Continuous models and methods. 5516: Discrete models and methods.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5524 - Matrix Theory
Determinants, rank, linear systems, eigenvalues, diagonalization, Gram-Schmidt process, Hermitian and unitary matrices, Jordan canonical form, variational principles, perturbation theory, Courant minimax theorem, Weyl’s inequality, numerical methods for solving linear systems and for determining eigenvalues. science or engineering. III
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5545 - Calculus of Variations and Optimal Control Theory
Unified course in the calculus of variations and control theory including multiple integral problems and distributed parameter control systems. Necessary conditions, sufficient conditions, nonclassical problems, optimal control, distributed parameter control, computational methods. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5546 - Calculus of Variations and Optimal Control Theory
Unified course in the calculus of variations and control theory including multiple integral problems and distributed parameter control systems. Necessary conditions, sufficient conditions, nonclassical problems, optimal control, distributed parameter control, computational methods. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5614 - Topics for In-Service Teachers
Various topics in mathematics and its applications to real-life problems, presented in light of contemporary instructional technologies and standards of learning. The course is designed for in-service mathematics teachers at the high and middle school levels and is suitable for recertification credit. The specific topics covered will be tailored to the location and delivery mode of the course, as well as evolving standards and methodology. May be repeated for credit with different content. May not be applied toward graduate degrees in mathematics. In-service status required. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture, Online Course

MATH 5725 - Mathematics for Financial Modeling
Introduction to stochastic models used in financial market analysis and associated computational methods. 5725: Brownian motion, stochastic integration, Ito calculus, martingales, no-arbitrage pricing, Black-Scholes formula, basic term-structure models. 5726: PDE characterizations for American, Asian and various other path-dependent options, development and application of numerical methods for computation. Must meet pre-requisites or have instructor’s consent.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5726 - Mathematics for Financial Modeling
Introduction to stochastic models used in financial market analysis and associated computational methods. 5725: Brownian motion, stochastic integration, Ito calculus, martingales, no-arbitrage pricing, Black-Scholes formula, basic term-structure models. 5726: PDE characterizations for American, Asian and various other path-dependent options, development and application of numerical methods for computation. Must meet pre-requisites or have instructor’s consent.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5754 (ESM 5754) - Introduction to Perturbation Methods
Asymptotic expansions and series, approximate solutions of algebraic equations, straightforward expansions and their regions of nonuniformities, the Lindstedt-Poincare technique, the method of renormalization, the method of averaging, the method of matched asymptotic expansions. I
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5894 - Final Examination

Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 5974 - Independent Study

Credit Hours: 1 to 19
Lecture Hours: 1 to 19
Level(s): Graduate
Instruction Type: Independent Study, Independent Study 1, Independent Study 2

MATH 5984 - Special Study

Credit Hours: 1 to 19
Lecture Hours: 1 to 19
Level(s): Graduate
Instruction Type: Lecture, Lecture 1, Lecture 2, Lecture 3

MATH 5994 - Research and Thesis

Credit Hours: 1 to 19
Level(s): Graduate
Instruction Type: Research

MATH 6105 (STAT 6105) - Measure and Probability
Development of measure theoretic foundations of probability theory. 6105: sigma fields, probability, and general measures; random variables, measurability and distributions, integration, and expectation; product measures; Radon-Nikodym theorem and conditioning. 6106: Random variables and strong and weak laws of large numbers; characteristic functions, central limit theorem and martingales; stochastic processes and Brownian motion. 6105 parially duplicates Math 5225. I
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6106 (STAT 6106) - Measure and Probability
Development of measure theoretic foundations of probability theory. 6105: sigma fields, probability, and general measures; random variables, measurability and distributions, integration, and expectation; product measures; Radon-Nikodym theorem and conditioning. 6106: Random variables and strong and weak laws of large numbers; characteristic functions, central limit theorem and martingales; stochastic processes and Brownian motion. 6105 parially duplicates Math 5225. II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6125 - Topics in Algebra
Advanced topics in algebra for graduate students in mathematics. May be taken for credit more than once with department consent.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6126 - Topics in Algebra
Advanced topics in algebra for graduate students in mathematics. May be taken for credit more than once with department consent.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6225 - Topics in Analysis
Advanced analysis for graduate students in mathematics. May be taken for credit more than once with department consent. Consent required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6226 - Topics in Analysis
Advanced analysis for graduate students in mathematics. May be taken for credit more than once with department consent. Consent required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6255 - Functional Analysis
Banach spaces, Hilbert spaces, linear operators on Banach and Hilbert spaces, Riesz Representation Theorems, spectral theory, topological vector spaces, other topics in functional analysis. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6256 - Functional Analysis
Banach spaces, Hilbert spaces, linear operators on Banach and Hilbert spaces, Riesz Representation Theorems, spectral theory, topological vector spaces, other topics in functional analysis. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6324 - Topics in Topology and Geometry
Advanced topics in topology and geometry. May be taken for credit more than once with department consent, with different content.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6425 - Top in Applied Math
Advanced topics in applied mathematics for graduate students in mathematics, science, and engineering. May be taken for credit more than once with department consent. Consent required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6426 - Topics in Applied Mathematics
Advanced topics in applied mathematics for graduate students in mathematics, science, and engineering. May be taken for credit more than once with department consent. Consent required.
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture, Lecture 1

MATH 6755 (PHYS 6755) - Mathematical Foundations of Quantum Mechanics
Advanced course in mathematical physics which encompasses the frontiers of research in quantum theory. Content varies from year to year and includes scattering theory, spectral and perturbation theory, and many-body quantum dynamics. This course frequently taken concurrent with thesis research. The course alternates with Math 6745-6746 and may be taken a second time with instructor’s consent. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 6756 (PHYS 6756) - Mathematical Foundations of Quantum Mechanics
Advanced course in mathematical physics which encompasses the frontiers of research in quantum theory. Content varies from year to year and includes scattering theory, spectral and perturbation theory, and many-body quantum dynamics. This course frequently taken concurrent with thesis research. The course alternates with Math 6745-6746 and may be taken a second time with instructor’s consent. I,II
Credit Hours: 3
Lecture Hours: 3
Level(s): Graduate
Instruction Type: Lecture

MATH 7994 - Research and Dissertation

Credit Hours: 1 to 19
Level(s): Graduate
Instruction Type: Research

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Graduate Degree Courses of Macromolecular Science and Engineering at Virginia Polytechnic Institute and State University

Macromolecular Science and Engineering Courses For Graduate at Virginia Polytechnic Institute And State University MACR 5015 - Macromolecular Fundamentals Laboratory I and II The course will cover fundamentals and experimental techniques for

Undergraduate Degree Courses of Air Force ROTC at Virginia Polytechnic Institute and State University

Air Force ROTC Courses for Undergraduate at Virginia Polytechnic Institute and State University 1115-1116: INTRODUCTION TO THE AIR FORCE Introduction to the United States Air Force and Air Force Reserve Officer Training

Graduate Degree Courses of Education, Health and Physical Education at Virginia Polytechnic Institute and State University

Education, Health and Physical Education Courses For Graduate at Virginia Polytechnic Institute And State University EDPE 5104 - Analysis and Supervision for Teaching Physical Education Techniques for the analysis of teaching physical

List of all Schools at Virginia Polytechnic Institute and State University

List of all Schools at Virginia Polytechnic Institute and State University School of Architecture + Design (Part of the College of Architecture and Urban Studies) Architecture Industrial Design Interior Design School of Public and

List of Undergraduate Majors A to Z at Virginia Polytechnic Institute and State University

List of Undergraduate Majors A to Z at Virginia Polytechnic Institute and State University A Accounting and Information Systems Aerospace Engineering Agricultural and Applied Economics Agricultural Sciences Agricultural Technology Agriculture Undecided Animal and Poultry Sciences Apparel, Housing, and Resource

Undergraduate Degree Courses of Biological Systems Engineering at Virginia Polytechnic Institute and State University

Biological Systems Engineering Courses for Undergraduate at Virginia Polytechnic Institute and State University 2094: INTRODUCTION TO METAL FABRICATION Introduction to metal working tools, equipment, and processes. Fundamentals of gas and arc

See a list of all academic departments by college at Virginia Polytechnic Institute and State University

See a list of all academic departments by college at Virginia Polytechnic Institute and State University Agriculture and Life Sciences AHNR Information Technology Agricultural and Applied Economics Agricultural and Extension Education Agricultural Technology Animal & Poultry

Non-Degree Programs at Aquinas Institute Of Theology

Summer Preaching Institute Summer Studies Session Non-Degree Study

Graduate Degree Courses of Genetics, Bioinformatics, and Computational Biology at Virginia Polytechnic Institute and State University

Genetics, Bioinformatics, and Computational Biology Courses For Graduate at Virginia Polytechnic Institute And State University GBCB 5004 - Seminar in Genetics, Bioinformatics, and Computational Biology Review and discussion of current topics and

Graduate Degree Courses of Architecture at Virginia Polytechnic Institute and State University

Architecture Courses For Graduate at Virginia Polytechnic Institute And State University  ARCH 1015, 1016 Foundation Design Laboratory ARCH 2015, 2016 Architecture II ARCH 2034 The Art of Building ARCH 2974 Independent Study ARCH 2984 Special Study ARCH 3015, 3016 Architecture III ARCH 3045,

Graduate Degree Courses of Environmental Sciences and Engineering at Virginia Polytechnic Institute and State University

Environmental Sciences and Engineering Courses For Graduate at Virginia Polytechnic Institute And State University ENSC 4114 (CSES 4114) - Soil Physics Application of the principles of physics and mathematical analysis to the

Graduate Degree Courses of Theatre Arts at Virginia Polytechnic Institute and State University

Theatre Arts Courses For Graduate at Virginia Polytechnic Institute And State University TA 4315 - Directing Script analysis, theories, techniques, and practical applications of theatrical direction. 4315: Theories and aesthetics of directing,

Departments for Undergraduate Degree Courses at Virginia Polytechnic Institute and State University

Departments for for Undergraduate Studies at Virginia Polytechnic Institute and State University 2004: INTRODUCTORY STATISTICS Fundamental concepts and methods of statistics with emphasis on interpretation AAEC — Agricultural and Applied Economics AEE —