MATH 4110 Number Theory
Credit: 3 hours
Prerequisite: At least a "C" in MATH 2252
Topics in this course include elementary properties of integers, including divisibility, unique factorization, progressions and prime numbers; linear congruences and residue classes’ complete and reduced residue systems; Chinese Remainder Theorem; quadratic residues, law of quadratic reciprocity; the theorems of Fermat and Wilson; Fibonacci and perfect numbers; sums of squares; and elementary theory of continued fractions. Three hours per week.
MATH 4150 Linear Algebra
Credit: 3 hours
Prerequisites: At least a "C" in both MATH 2260 and MATH 3040
Topics in this course include an introduction to the theory of vector spaces, with emphasis on finite-dimensional vector spaces, linear systems, matrices, linear transformations, eigenvalues, and related subjects. Three hours per week.
MATH 4260 Mathematical Analysis
Credit: 3 hours
Prerequisites: At least a "C" in MATH 3040
This course is a study of the principles of mathematical analysis; point set topology of real numbers, numerical sequences and series, continuity, differentiation, integration, sequences and series of functions, and metric spaces. Three hours per week.
MATH 4300 Regression Analysis
Credit: 3 hours
Prerequisites: At least a "C" in MATH 3600
Topics in this course include simple and multiple regression; model selection procedures; analysis of variance; simultaneous inference; and design and analysis of experiments. Three hours per week.
MATH 4480 Graph Theory
Credit: 3 hours
Prerequisites: At least a "C" in MATH 2252
Topics in this class include structure of graphs, directed graphs, trees, and connectivity; Eulerian and Hamiltonian graphs; planar graphs; graph colorings; matchings; independence; and domination. Additional topics may include symmetry of graphs, external graph theory, graph embeddings, and probabilistic methods in graph theory. Three hours per week.
MATH 4621 Mathematical Statistics I
Credit: 3 hours
Prerequisites: At least a "C" in both MATH 2253 and MATH 3600
This is the first in a two-course sequence. Topics in this course include distributions of random variables; conditional probability and stochastic independence; multivariate and some special distributions; and distributions of functions of random variables. Three hours per week.
MATH 4622 Mathematical Statistics II
Credit: 3 hours
Prerequisite: At least a "C" in MATH 4621
This is the second in a two-course sequence. Topics in this course include statistical inference, sufficient statistics, estimation theory, theory of statistical tests, and inferences about normal models. Three hours per week.
MATH 4630 Topics in Applied Statistics
Credit: 3 hours
Prerequisite: At least a "C" in MATH 3600
Topics in applied statistics will be selected from quality control, sampling theory, nonparametric statistics, experimental design, computational statistics, and regression analysis. Three hours per week.
MATH 4651 Numerical Analysis I
Credit: 3 hours
Prerequisites: At least a "C" in both MATH 2252 and CPSC 1301
This is the first in a two-course sequence. Topics in this course include the development and implementation of efficient numerical methods; locating roots of nonlinear equations; solving systems of linear equations; numerical differentiation and integration; interpolation; and approximation of functions. Three hours per week.
MATH 4652 Numerical Analysis II
Credit: 3 hours
Prerequisites: At least a "C" in both MATH 4651 and MATH 2270
This is the second in a two-course sequence. Topics in this course include the determination of eigenvalues and eigenvectors of matrices; method of least squares, and curve fitting; numerical solutions of ordinary and partial differential equations. Three hours per week.
MATH 4901 Operations Research I
Credit: 3 hours
Prerequisite: At least a "C" in MATH 4150
This course is an introduction to the mathematical aspects and applications of operations research. Topics are selected from linear programming (mainly), integer programming, and dynamic programming. Three hours per week.
MATH 4902 Operations Research II
Credit: 3 hours
Prerequisite: At least a "C" in MATH 4621
This course is an introduction to stochastic operations research. Topics are selected from stochastic modeling and optimization, probability models, queuing theory, and Monte Carlo simulation. Note that MATH 4901 is not a prerequisite for this course. Three hours per week.
MATH 4905 Optimization
Credit: 3 hours
Prerequisites: At least a "C" in MATH 2252
Topics in this course include Lagrange multipliers, gradient methods, search techniques, variational methods and control problems dynamic programming, and nonlinear programming. Three hours per week.
MATH 4910 Mathematical Models
Credit: 3 hours
Prerequisite: At least a "C" in both MATH 2253 and MATH 3600
This course is an introduction to basic principles and applications of classical mathematical models, optimization models, and probabilistic models. Three hours per week.
MATH 4920 Senior Seminar
Prerequisites: Student must have completed 90 or more hours.
This seminar course is intended for mathematics majors in the last year of their program. Through lectures, scientific literature, and class discussions, students will be introduced to particular areas of active research. Students will be expected to undertake individual projects which may include oral and/or written presentations and preparation of mini-grant applications. Two hours per week.