VCU Department of Mathematics

MATH COURSES 501-591

MATH 501 Introduction to Abstract Algebra

Prerequisites: MATH 211 and 310.
Semester course; 3 lecture hours. 3 credits.

An introduction to groups, rings, and fields from an axiomatic point of view. Coset decomposition and basic morphisms.

MATH 504 Algebraic Structures and Functions

Prerequisite: MATH 200-201, MATH 300 and one additional mathematical science course and permission of instructor.
Semester course; 3 lecture hours. 3 credits.

Semigroups, groups, rings, integral domains and fields. Exponential, logarithmic and trigonometric functions. Graphing in parametric and polar coordinates. Arithmetic and geometric sequences and series. Not applicable toward M.S. in Mathematical Sciences.

MATH 505 Modern Geometry

Prerequisite: MATH 307; corequisite: MATH 310.
Semester course; 3 lecture hours. 3 credits.

Topics in Euclidean, projective, and non-Euclidean geometries from a modern viewpoint.

MATH 507-508 Analysis I, II

Prerequisites: MATH 211, 307, and 310 or permission of instructor.
Continuous course; 3 lecture hours. 3-3 credits.

Theoretical aspects of calculus: sequences, limits, continuity, infinite series, series of functions, integration, differential geometry.

MATH 509-510 General Topology I, II

Prerequisite: MATH 211 and 307.
Continuous course; 3 lecture hours. 3-3 credits.

Foundations and fundamental concepts of point-set topology. Topological spaces, convergence, connected sets, compactness, product spaces, quotient spaces, function spaces, separation properties, metrization theorems, mappings, and compactification.

MATH 511 Applied Linear Algebra

Prerequisite: MATH 310.
Semester course; 3 lecture hours. 3 credits.

The algebra of matrices, the theory of finite dimensional vector spaces, and the basic results concerning eigenvectors and eigenvalues, with particular attention to applications.

MATH 512 Complex Analysis for Applications

Prerequisite: MATH 307.
Semester course; 3 lecture hours. 3 credits.

The algebra and geometry of complex numbers, analytic functions, integration, series, contour integration, analytic continuation, conformal mapping, with particular attention to applications.

MATH 515 Numerical Analysis I

Prerequisites: MATH 310 or (MATH 201 and MATH 185) and a knowledge of a programming language.
Semester course; 3 lecture hours. 3 credits.

Solutions of equations, interpolation and approximation, numerical integration, iterative methods for solving linear equations, calculation of eigenvalues and eigenvectors. Selected algorithms may be programmed for solution on computers.

MATH 516 Numerical Analysis II

Prerequisite: MATH 515.
Semester course; 3 lecture hours. 3 credits.

Numerical solution of initial value problems in ordinary differential equations, 2 point boundary value problems. Introduction to numerical techniques for solving partial differential equations. Selected algorithms may be programmed for solution on computers.

MATH 517-518 Methods of Applied Mathematics

Prerequisite: MATH 301 and MATH 307.
Continuous course; 3 lecture hours. 3-3 credits.

Vector analysis, matrices, complex analysis, special functions. Legendre and Hermite polynomials, Fourier series, Laplace transforms, integral equations, partial differential equations, boundary-value and initial value problems.

MATH 520 Game Theory and Linear Programming

Prerequisite: MATH 310.
Semester course; 3 lecture hours. 3 credits.

The mathematical basis of game theory and linear programming. Matrix games, linear inequalities and convexity, the minimax theorems in linear programming, computational methods, and applications.

MATH 521 Introduction to Algebraic Number Theory

Prerequisite: MATH 501.
Semester course; 3 lecture hours. 3 credits.

Introduction to algebraic numbers and algebraic number fields with emphasis on quadratic and cyclotomic fields. Units, primes, unique factorization.

MATH 523 Discrete Event Simulation

Prerequisites: STAT 212 and MATH 309 or their equivalents, or permission of instructor.
Semester course; 3 lecture hours. 3 credits.

An introduction to the theory and practice of discrete event simulation. Topics include random variable generation, model development and validation, variance reduction techniques, and statistical analysis of output. Applications will be taken from areas such as queueing theory and manufacturing systems. A high level simulation language will be utilized.

MATH 525 Introduction to Combinatorial Mathematics

Prerequisites: MATH 211, 310, or permission of instructor.
Semester course; 3 lecture hours. 3 credits.

Introduction to the problems and methods of solution in the enumeration, existence, and construction of some discrete mathematical structures. Discussion of generating functions, recurrence relations, Ramsey's theorem, matching theory, combinatoral designs, Latin squares, and linear coding theory.

MATH 527-528 Mathematical Foundations of Operations Research

Prerequisites: CMSC 255 or 201, MATH 310 and 309 (second semester); STAT 503 strongly recommended for second semester.
Continuous course; 3 lecture hours. 3-3 credits.

Introduction to the mathematical foundations of deterministic and stochastic operations research, including the simplex method for linear programming, nonlinear optimization, dynamic programming, and some stochastic models. Real world applications will be discussed throughout.

MATH 530 The History of Mathematics

Prerequisite: 17 credits at the 200-level or above in mathematical sciences or permission of instructor.
Semester course; 3 lecture hours. 3 credits.

Surveys major trends in the development of mathematics from ancient times through the nineteenth century and considers the cultural and social contexts of mathematical activity.

Either MATH 530 or MATH 531 (but not both) may be applied to the master's degree in mathematical sciences or the MS degree in computer science. Both MATH 530 and MATH 531 may be applied to the MEd degree in mathematics education.

MATH 531 Expositions in Modern Mathematics

Prerequisite: six credits at the 400-level or above in mathematical sciences.
Semester course; 3 lecture hours. 3 credits.

Studies descriptively several major ideas relevant to present-day mathematics, such as the advent of pure abstraction, difficulties in the logical foundations of mathematics, the impact of mathematics and statistics in the twentieth century, and the computer revolution.

Either MATH 530 or MATH 531 (but not both) may be applied to the master's degree in mathematical sciences or the MS degree in computer science. Both MAT 530 and MAT 531 may be applied to the MEd degree in mathematics education.

MATH 532 Ordinary Differential Equations I

MATH 301 and 310 or the equivalent. MATH 507 is recommended.
Semester course; 3 lecture hours. 3 credits.

Existence and uniqueness for systems, linear systems, fundamental matrix solutions, matrix exponential, nonlinear systems, plane autonomous systems and introduction to stability.

MATH 554 Using Technology in the Teaching of Mathematics

MATH 200 and STAT 212 and six additional credits of mathematical science courses and permission of the instructor.
Semester course; 2 lecture hours and 2 laboratory hours. 3 credits.

Using graphing calculators, CBLs (calculator based labs) and computer software packages in teaching topics in algebra, geometry, trigonometry, statistics, finance and calculus. Not applicable toward M.S. in Mathematical Sciences.

MATH 555/ENGR 555 Dynamics and Multivariable Control I

MATH 301 and 310 or the equivalent.
Semester course; 3 lecture hours. 3 credits.

Systems of differential equations with controls, linear control systems, controllability, observability, introduction to feedback control and stabilization.

MATH 591 Topics in Mathematics

Open to qualified undergraduates.
Semester course; 1-3 credits per semester.
May be repeated for credit.
See the Schedule of Classes for specific topics and prerequisites.

A study of selected topics in mathematics.