# Courses

#### Mathematics

*Note:Unless otherwise noted, all prerequisite
courses must be passed with a grade of C- or
higher. *

**0414. Introduction to
Numerical Analysis (3 s.h.) **

Roots of nonlinear equations, errors, their source and propagation, linear systems, approximation and interpolation of functions, numerical integration. Offered every two years in the spring.

**0415. Advanced Engineering (3
s.h.) **

**0417. Concepts of Analysis (3
s.h.) **

Advanced calculus in one and several real variables. Topics include topology of metric spaces, continuity, sequences and series of numbers and functions, convergence, including uniform convergence. Ascoli and Stone-Weierstrass theorems. Integration and Fourier series. Inverse and implicit function theorems, differential forms, Stokes theorem. Offered every year.

**0418. Concepts of Analysis (3
s.h.) **

Advanced calculus in one and several real variables. Topics include topology of metric spaces, continuity, sequences and series of numbers and functions, convergence, including uniform convergence. Ascoli and Stone-Weierstrass theorems. Integration and Fourier series. Inverse and implicit function theorems, differential forms, Stokes theorem. Offered every year.

**0433. Math Prob Theory (3
s.h.) **

**0434. Mathematical
Statistics (3 s.h.) **

**0453. Numerical Analysis
I (3 s.h.) **

**0462. Ordinary Differential
Equations (3 s.h.) **

Existence and uniqueness theorems, continuous and smooth dependence on parameters, linear differential equations, asymptotic behavior of solutions, isolated singularities, nonlinear equations, Sturm-Liouville problems, numerical solution of ODEs. Offered every spring.

**0471. Special Topics
in Math (3 s.h.) **

**0477. Linear Algebra (3
s.h.) **

Vector spaces and subspaces over the real and complex numbers; linear independence and bases; linear mappings; dual and quotient spaces; fields and general vector spaces; polynomials, ideals and factorization of polynomials; determinant; Jordan canonical form. Fundamentals of multilinear algebra. Offered every fall.

**0499. Master's Thesis
Project (3 s.h.) **

**0501. Seminar (3
s.h.) **

Challenging problems from many different areas of mathematics are posed and discussed. Offered sporadically.

**0502. Seminar (3
s.h.) **

Challenging problems from many different areas of mathematics are posed and discussed. Offered sporadically.

**0503. Number Theory (3
s.h.) **

An introduction to the ideas and techniques of number theory, elementary, analytic, and algebraic. Dirichlet's theorem on primes in an arithmetic progression, the prime number theorem, algebraic number fields. Offered every year.

**0504. Number Theory (3
s.h.) **

An introduction to the ideas and techniques of number theory, elementary, analytic, and algebraic. Dirichlet's theorem on primes in an arithmetic progression, the prime number theorem, algebraic number fields. Offered every year.

**0513. Numerical Linear
Algebra (3 s.h.) **

The syllabus includes iterative methods, classical methods, nonnegative matrices. Semi-iterative methods. Multigrid methods. Conjugate gradient methods. Preconditioning. Domain decomposition. Direct Methods. Sparse Matrix techniques. Graph theory. Eigenvalue Problems. Offered every two years.

**0514. Numerical Linear
Algebra (3 s.h.) **

The syllabus includes iterative methods, classical methods, nonnegative matrices. Semi-iterative methods. Multigrid methods. Conjugate gradient methods. Preconditioning. Domain decomposition. Direct Methods. Sparse Matrix techniques. Graph theory. Eigenvalue Problems. Offered every two years.

**0515. Methods of Applied
Mathematics (3-6 s.h.) **

Various applied mathematical methods and topics discussed: Laplace and Fourier transforms, calculus of variations, integral equations, boundary value problems. Offered sporadically.

**0516. Methods of Applied
Mathematics (3-6 s.h.) **

Various applied mathematical methods and topics discussed: Laplace and Fourier transforms, calculus of variations, integral equations, boundary value problems. Offered sporadically.

**0519. Numerical Differential
Equations (3-6 s.h.) **

Various methods for numerical integration of ordinary and partial differential equations are discussed. Offered every two years.

**0520. Numerical Differential
Equations (3-6 s.h.) **

Various methods for numerical integration of ordinary and partial differential equations are discussed. Offered every two years.

**0535. Differential
Geometry and Topology (3-6 s.h.) **

*Prerequisite: Prerequisites: Math 247, 248, 365.*

Elementary theory of smooth manifolds. Singular cohomology and DeRham's theorem. Fundamental group and covering spaces. Hodge theory. Offered every two years.

**0536. Differential
Geometry and Topology (3-6 s.h.) **

*Prerequisite: Prerequisites: Math 247, 248, 365.*

Elementary theory of smooth manifolds. Singular cohomology and DeRham's theorem. Fundamental group and covering spaces. Hodge theory. Offered every two years.

**0540. Probability Theory (3
s.h.) **

*Prerequisite: Math 233 or permission of instructor.*

With a rigorous approach the course covers the axioms, random variables, expectation and variance. Limit theorems are developed through characteristic functions. Offered every year.

**0548. Stochastic Processes (3
s.h.) **

*Prerequisite: Math 540.*

Random sequences and functions; linear theory; limit theorems; Markov processes; branching processes; queuing processes. Offered every two years in the spring.

**0557. Real Analysis (3-6
s.h.) **

*Prerequisite: Math 417 or equivalent.*

The syllabus coincides with the syllabus for the Ph.D. Examination in Real Analysis. Offered every year.

**0558. Real Analysis (3-6
s.h.) **

*Prerequisite: Math 417 or equivalent.*

The syllabus coincides with the syllabus for the Ph.D. Examination in Real Analysis. Offered every year.

**0559. Functions of
a Complex Variable (3-6 s.h.) **

*Prerequisite: Math 347 or equivalent.*

Analytic functions. Conformal mapping. Analytic continuation. Topics in univalent functions, elliptic functions, Riemann surfaces, analytic number theory. Nevanlinna theory, several complex variables. Offered every year.

**0560. Functions of
a Complex Variable (3-6 s.h.) **

*Prerequisite: Math 347 or equivalent.*

Analytic functions. Conformal mapping. Analytic continuation. Topics in univalent functions, elliptic functions, Riemann surfaces, analytic number theory. Nevanlinna theory, several complex variables. Offered every year.

**0561. Partial Differential
Equations (3 s.h.) **

The classical theory of partial differential equations. Elliptic, parabolic, and hyperbolic operations. Offered every two years.

**0562. Partial Differential
Equations (3 s.h.) **

The classical theory of partial differential equations. Elliptic, parabolic, and hyperbolic operations. Offered every two years.

**0563. Topics in Applied
Mathematics (3 s.h.) **

Variable content course. Offered sporadically.

**0564. Math Programming (3
s.h.) **

**0565. Topology (3
s.h.) **

*Prerequisite: Math 417.*

Point set topology through the Urysohn Metrization Theorem; fundamental group and covering spaces. Differential forms; the DeRham groups. Offered every year.

**0566. Topology (3
s.h.) **

*Prerequisite: Math 417.*

Point set topology through the Urysohn Metrization Theorem; fundamental group and covering spaces. Differential forms; the DeRham groups. Offered every year.

**0573. Topics in Applied
Mathematics (3-6 s.h.) **

*Prerequisite: Permission of instructor.*

Variable topics, such as control theory and transform theory, will be treated. Offered sporadically.

**0574. Topics in Applied
Mathematics (3-6 s.h.) **

*Prerequisite: Permission of instructor.*

Variable topics, such as control theory and transform theory, will be treated. Offered sporadically.

**0575. Abstract Algebra (3-6
s.h.) **

*Prerequisite: Math 205 or equivalent..*

Groups, rings, modules, fields; Galois theory; linear algebra. Offered every year.

**0576. Abstract Algebra (3-6
s.h.) **

*Prerequisite: Math 205 or equivalent..*

Groups, rings, modules, fields; Galois theory; linear algebra. Offered every year.

**0584. Topics Computer
Program (3 s.h.) **

**0591. Independent Study (1-3
s.h.) **

Note: Under normal circumstances it is assumed that a student has taken basic courses on the 500 level before entering any of the 600-level courses. Except when noted to the contrary, 600-level courses are offered sporadically.

**0592. Independent Study (1-3
s.h.) **

Note: Under normal circumstances it is assumed that a student has taken basic courses on the 500 level before entering any of the 600-level courses. Except when noted to the contrary, 600-level courses are offered sporadically.

**0593. Independent Study (1-3
s.h.) **

Note: Under normal circumstances it is assumed that a student has taken basic courses on the 500 level before entering any of the 600-level courses. Except when noted to the contrary, 600-level courses are offered sporadically.

**0594. Independent Study (1-3
s.h.) **

Note: Under normal circumstances it is assumed that a student has taken basic courses on the 500 level before entering any of the 600-level courses. Except when noted to the contrary, 600-level courses are offered sporadically.

**0601. Theory of Groups (3
s.h.) **

*Prerequisite: .*

**0603. Topics in Algebra (3-6
s.h.) **

*Prerequisite: Variable topics in theory of commutative and non-commutative rings, groups, algebraic number theory, algebraic geometry..*

**0604. Topics in Algebra (3-6
s.h.) **

*Prerequisite: Variable topics in theory of commutative and non-commutative rings, groups, algebraic number theory, algebraic geometry..*

**0605. Lie Groups (3-6
s.h.) **

*Prerequisite: The theory of Lie groups, from the analytic, algebraic, and applied point of view..*

**0606. Lie Groups (3-6
s.h.) **

*Prerequisite: The theory of Lie groups, from the analytic, algebraic, and applied point of view..*

**0613. Calculus of Variations (3
s.h.) **

**0615. Selected Topics
in Complex Variable Theory (3-6
s.h.) **

*Prerequisite: .*

**0616. Selected Topics
in Complex Variable Theory (3-6
s.h.) **

*Prerequisite: .*

**0617. Topics in Number
Theory (3-6 s.h.) **

Analytic and algebraic number theory. Classical results and methods and special topics such as partition theory, asymptotic, Zeta functions, transcendence, modular functions. Offered every two years.

**0618. Topics in Number
Theory (3-6 s.h.) **

Analytic and algebraic number theory. Classical results and methods and special topics such as partition theory, asymptotic, Zeta functions, transcendence, modular functions. Offered every two years.

**0619. Riemann Surfaces (3
s.h.) **

**0621. Functional Analysis (3-6
s.h.) **

*Prerequisite: Prerequisites: Math 557, 558, and Math 565 or permission of instructor.*

Offered sporadically.

**0622. Functional Analysis (3-6
s.h.) **

*Prerequisite: Prerequisites: Math 557, 558, and Math 565 or permission of instructor.*

Offered sporadically.

**0624. Topics in Analysis (3
s.h.) **

Variable content course. Offered sporadically.

**0625. Topics in Functional
Analysis **

**0626. Topics in Functional
Analysis **

**0629. Seminar in Real
Analysis (3-6 s.h.) **

*Prerequisite: .*

**0630. Seminar in Real
Analysis (3-6 s.h.) **

*Prerequisite: .*

**0631. Seminar in Complex
Analysis (3-6 s.h.) **

*Prerequisite: .*

**0632. Seminar in Complex
Analysis (3-6 s.h.) **

*Prerequisite: .*

**0635. Topics in Differential
Equations (3-6 s.h.) **

Variable content course. Offered sporadically.

**0636. Topics in Differential
Equations (3-6 s.h.) **

Variable content course. Offered sporadically.

**0637. Modular Functions (3
s.h.) **

Modular forms, Einsenstein and Poincaré series, Theta series, Dirichlet series, Hecke operators. Offered every two years.

**0638. Modular Functions (3
s.h.) **

Modular forms, Einsenstein and Poincaré series, Theta series, Dirichlet series, Hecke operators. Offered every two years.

**0643. Algebraic Topology (3-6
s.h.) **

Advanced topics in algebraic topology. Offered sporadically.

**0644. Algebraic Topology (3-6
s.h.) **

Advanced topics in algebraic topology. Offered sporadically.

**0651. Advanced Probability
Theory (3 s.h.) **

Variable content course.

**0657. Harmonic Analysis (3
s.h.) **

A year long course to explore the real-variable techniques developed in Harmonic Analysis to study smoothness properties of functions and the behavior of certain spaces under the action of some operators. These techniques are also essential in many applications to PDE's and several complex variables. Offered every two years.

**0658. Harmonic Analysis (3
s.h.) **

A year long course to explore the real-variable techniques developed in Harmonic Analysis to study smoothness properties of functions and the behavior of certain spaces under the action of some operators. These techniques are also essential in many applications to PDE's and several complex variables. Offered every two years.

**0659. Several Complex
Variables (3 s.h.) **

Holomorphic functions of several complex variables, domains of holomorphy, pseudoconvexity, analytic varieties, CR manifolds. Offered sporadically.

**0660. Several Complex
Variables (3 s.h.) **

Holomorphic functions of several complex variables, domains of holomorphy, pseudoconvexity, analytic varieties, CR manifolds. Offered sporadically.

**0673. Topics in Differential
Geometry (3-6 s.h.) **

Advanced topics in differential geometry. Offered sporadically.

**0674. Topics in Differential
Geometry (3-6 s.h.) **

Advanced topics in differential geometry. Offered sporadically.

**0681. Topics in Numerical
Analysis (3-6 s.h.) **

**0682. Topics in Numerical
Analysis (3-6 s.h.) **

**0683. Combinatorial
Mathematics (3-6 s.h.) **

Variable content course. Offered sporadically.

**0684. Combinatorial
Mathematics (3-6 s.h.) **

Variable content course. Offered sporadically.

**0697. Seminar in Probability (3-6
s.h.) **

*Prerequisite: .*

**0698. Seminar in Probability (3-6
s.h.) **

*Prerequisite: .*

**0799. Preliminary Examination
Preparation (1-6 s.h.) **

*Prerequisite: .*

**0899. Pre-Dissertation
Research (1-6 s.h.) **

*Prerequisite: .*

**0950. Dissertation (1-6
s.h.) **

*Prerequisite: .*

**0999. Dissertation
Research (1-6 s.h.) **