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. Prerequisites: Mathematics 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. Prerequisites: Mathematics 161 with a minimum grade of C, or approval of the Mathematics Department Head.
403 Introduction to Graph Theory (3)
An overview of graph theory and its applications including trees, planar graphs and graphical invariants such as domination, coloring, and matchings. Prerequisites: Mathematics 300 with a minimum grade of C.
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. Prerequisite: Mathematics 255 with a 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. Prerequisite: Mathematics 407 with a 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. Prerequisite: Mathematics 300 with a minimum grade 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. Prerequisites: Mathematics 212, 300 with a minimum grades of C.
414 Operations Research (Linear) (3)
Introduction to linear programming, duality, transportation and assignment problems, integer programming. Prerequisites: Computer Science 118 or 150, Mathematics 212 with a minimum grade of C, or approval of the Mathematics Department Head.
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. This course is recommended for students planning to take actuarial exams. Prerequisite: Mathematics 307 or 407 or Engineering 322 with a minimum grade of C, or approval of the Mathematics Department Head.
422 Introduction to Point Set Topology (3)
Introductory set theory, topologies and topological spaces, continuous mappings, compactness, connectedness, separation axioms and metric spaces. Prerequisite: Mathematics 300 with a 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. Prerequisites: Computer Science 118 or 150 or equivalent, Mathematics 307 or 407 with minimum grades of C, or approval of the Mathematics Department Head.
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 approval of the department head; Mathematics 245 and Engineering 225 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. Prerequisite: Mathematics 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: Mathematics 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. Prerequisites: Mathematics 245, 255 with minimum grades of C.
446 Partial Differential Equations (3)
Classification and derivation of some elementary partial differential equations arising in applications. Separation of variables, Sturm-Liouville problems and orthogonality, Fourier Series. Diffusion, wave, and Laplace’s equations in various coordinate systems with various boundary and initial conditions. Laplace transform methods and D’Alembert’s solution. First order equations and weak solutions. On demand. Prerequisites: Mathematics 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: Mathematics 350 with a 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. Prerequisite: Mathematics 300 with a minimum grade of C, or approval of the Mathematics Department Head.
454 Abstract Algebra (3)
A study of special topics from advanced algebra, various algebraic structures, and the applications of algebra. On demand. Prerequisite: Mathematics 321 or 412 with a minimum grade of C, or approval of the Mathematics Department Head.
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. Prerequisites: Mathematics 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: Mathematics 212 and 245 with minimum grades of C, and Computer Science 118 or 150, or approval of the Mathematics Department Head.
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: Mathematics 465 with a minimum grade of C, or approval of the Math Department Head.
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. Prerequisites: Mathematics 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 the Mathematics Department Head. Graded satisfactory/no credit.
