College of Arts and Sciences
321 Introduction to Modern Algebra (3)
Integral domains, rings, fields, groups, elementary number theory, and other selected topics. Spring semester. Prerequisites: Math 212 and 300 (or approval of instructor) with minimum grades of C.
350 Fundamental Concepts in Analysis (3)
Classical treatment of the basic concepts of calculus: limits, continuity, differentiation, Riemann integration, sequences and series of numbers and functions. Fall semester. Prerequisites: Math 245, 255, and 300 with minimum grades of C.
401 Mathematics of Interest (3)
Mathematical theory of interest with applications, including accumulated and present value factors, annuities, yield rates, amortization schedules and sinking funds, depreciation, bonds and related securities. Recommended for students planning to take actuarial exams. Fall semester alternate years. Prerequisites: Math 160 or 161 with a minimum grade of C, or approval of the instructor.
403 Graph Theory and Combinatorics (3)
Planar graphs, circuits, graph coloring, trees, general counting principles, generating functions, recurrence relations with applications to computer science including tree traversal, grammars, languages, and finite-state machines. Fall semester. Prerequisites: Math 300 with a minimum grade of C, and either Computer Science 118 or 150 or equivalent. Credit not allowed in both Math 403 and 303.
407 Introduction to Probability and Statistics (3)
Introduction to the theory of probability and its applications, counting techniques, sample spaces, random variables and their distributions, mathematical expectation, moment generating functions, binomial, Poisson, and normal distributions, Central Limit Theorem. Fall semester. Prerequisite: Math 255 with minimum grade of C.
408 Mathematical Statistics (3)
A continuation of Math 407 with an introduction to the theories of point and interval estimation, hypothesis testing, regression and correlation analysis, goodness of fit, chi-square, t and F distributions. Spring semester. Prerequisite: Math 407 with minimum grade of C.
410 Number Theory (3)
Divisibility, primes, congruencies, Fermat’s Theorem, number theoretic functions, primitive roots and indices, the quadratic reciprocity law. Summer on demand. Prerequisite: Math 300 with minimum grades of C.
412 Linear Algebra and Matrix Theory (3)
Vector spaces, linear transformations, eigenvalue and similarity transformations, orthogonal and unitary transformations, normal matrices, Jordan form. Fall semester. Prerequisites: Math 212, 245, 300 with minimum grades of C.
414 Operations Research (Linear) (3)
Introduction to linear programming, duality, transportation and assignment problems, integer programming. Spring semester alternate years. Prerequisites: Computer Science 118 or 150 or equivalent, Math 212 with minimum grade of C, or approval of instructor.
420 Applied Statistical Methods (3)
Intermediate applied statistical analysis and model building. Covers One and Two Factor Analysis of Variance, Simple and Multiple Regression and Correlation, and Time Series Analysis. Spring semester. This course is recommended for students planning to take actuarial exams. Prerequisites: Math 307 or 407 or Engineering 322 with a minimum grade of C, or approval of the instructor.
422 Introduction to Point Set Topology (3)
Introductory set theory, topologies and topological spaces, continuous mappings, compactness, connectedness, separation axioms and metric spaces. Summer on demand. Prerequisite: Math 300 with minimum grade of C.
424 Operations Research (Non-Linear) (3)
Network flows, Markov chains and applications, queuing theory and applications, inventory theory, decision theory, and games. Spring semester alternate years. Prerequisites: Computer Science 118 or 150 or equivalent, Mathematics 307 or 407 with minimum grade of C, or approval of instructor.
428 Packages for Mathematical Computations (3)
The nature of libraries of procedures for solving mathematical problems, including the design parameters, selection of algorithms, problems with reliability and transportation. Several major mathematical packages will be examined in detail, including IMSL, LINPACK , EISPACK , MINPACK. On demand. Prerequisites: Computer Science 118 or consent of instructor; Math 212/245, and one of the following: Math 308, Engineering 225, Computer Science 231 with minimum grades of C.
430 The Historical Development of Mathematics (3)
Examination of central ideas, major developments, and important issues in mathematics from ancient times to the present. Historical overview of the evolution of the discipline through comparative examination of specific theories and results. Alternate fall and summer. Prerequisite: Math 300 with a minimum grade of C.
440 Applied Analysis (3)
Vector analysis through Stokes’ Theorem and the Divergence Theorem. Topics in advanced calculus including implicit functions, Jacobians, interchange of limit processes, and uniform convergence of series of functions; introduction to power series solutions of differential equations. Prerequisites: Math 245, 255 with minimum grades of C.
445 Advanced Differential Equations (3)
Systems of differential equations; existence and uniqueness theorems; linear systems; phase plane analysis; stability theory; applications. Fall semester alternate years. Prerequisite: Math 245, 255 with minimum grades of C.
450 Modern Analysis (3)
Differentiation; inverse and implicit function theorems; functions of bounded variation. Integration and measure; integration on manifolds; Stokes’ and Green’s Theorems; other selected topics. On demand. Prerequisite: Math 350 with minimum grade of C.
452 Basic Concepts of Geometry (3)
Deficiencies in Euclidean geometry, Euclid’s parallel postulate, introduction to non-Euclidean geometry, consistency and validity of non-Euclidean geometry, incidence geometries, affine geometries, linear, planar, and spatial order properties. Alternate fall and summer semesters. Prerequisite: Math 300 with minimum grade of C or approval of instructor.
454 Abstract Algebra (3)
A study of special topics from advanced algebra, various algebraic structures, and the applications of algebra. On demand. Prerequisite: Math 321 or 412 with minimum grade of C or approval of instructor.
460 Techniques of Applied Mathematics (3)
Additional topics in vector calculus; series of orthogonal functions; integral transforms; treatment of some elementary partial differential equations arising in applications. Spring semester alternate years. Prerequisite: Math 245, 255 with minimum grades of C.
465 Numerical Analysis I (3)
Numerical solutions of equations in one variable; interpolation and polynomial approximation; numerical differentiation and integration; initial value problems for ordinary differential equations; direct methods for solving systems of linear equations. Prerequisites: Math 212 and 245 with minimum grades of C, and a background in computer programming (for example, Computer Science 150).
466 Numerical Analysis II (3)
Iterative techniques for solving systems of linear equations; approximation theory; eigenvalue and eigenvector approximation; boundary value problems for ordinary differential equations; numerical solution to partial differential equations. Prerequisite: Math 465 with a minimum grade of C, or approval of instructor.
470 Introductory Complex Variables (3)
Complex numbers; differentiation and integration of functions of a complex variable; analytic functions; Cauchy’s Theorem; power series; residues and poles; conformal mapping; contour integration. Fall semester alternate years. Prerequisites: Math 245, 255 with minimum grades of C.
475 Research Seminar (1)
Investigation of special topics in mathematics using the directed research technique. On demand. Prerequisite: approval of department. Graded satisfactory/no credit.
495r Departmental Honors (1-3 hours per term, 4 hours for the two terms)
On demand. See “Departmental Honors,” page 39.
497r Research (1-4)
On demand.
498r Individual Studies (1-4)
On demand.
499r Group Studies (1-4)
On demand.
