MA 407, Topology
Topology is the study of the structure of space and is one of the major theoretical areas in modern mathematics. The course serves as both a rigorous foundation for advanced study in the field and as a survey of important techniques established since its inception. After building the necessary framework of point-set topology, the course will move on to selected topics such as the classification of surfaces, knot theory, and algebraic topology. Prerequisites: MA 221 and MA 225, both passed with a grade of “c-” or higher.
MA 410, Modern Algebra
Beginning with the natural numbers, the integers and rational numbers are developed. Complex numbers and roots of unity are followed by groups, rings, and polynomials. Prerequisites: MA 221, and either MA 314 or MA 317 or MA 318 or MA 407, passed with a grade of “C-” or higher.
MA 411, Group Theory
Group Theory is the study of symmetry and is one of the core branches of abstract algebra. The course will explore the theory and applications of groups, course topics will include subgroups, group homomorphisms and isomorphisms, permutations, quotient groups, Sylow Theorems, and the structure of finitely generated abelian groups. Prerequisites: MA 221 and either MA 314 or MA 317 or MA 318 or MA 407, both passed with a grade of “C-” or higher.
MA 413, Complex Analysis
Complex numbers and plane, functions, derivatives, line integrals, Cauchy integral theorem. Cauchy’s formula, series, and applications. Prerequisite: MA 225 and either MA 314 or MA 317 or MA 318 or MA 407, both passed with a grade of “C-” or higher.
MA 415, Real Analysis
Metric spaces, real number system, limits, functions, continuity, differentiation and integration, and counter-examples. Prerequisites: MA 225 and either MA 314 or MA 317 or MA 318 or MA 407, all passed with a grade of “C-” or higher; and EN 101 or EN 102 or permission of the instructor.
MA 419, Introduction to Mathematical Modeling
Introduction to mathematical modeling, which is a process in which a real-world situation is studied, simplified, and abstracted to the point that mathematical tools can be applied to gain understanding. Introduction to the process, first via a text and mini-projects, then in teams investigating problems from local industries or organizations. Prerequisites: Junior or Senior standing; MA 220, MA 221, and MA 311, all passed with a grade of “C-” or higher, and EN 101 and EN 102 or permission of the instructor.
MA 421, Design of Experiments and ANOVA
Provides a working knowledge of multivariate regression and ANOVA methods balanced with the theory underlying these techniques. Intended for students considering a career in statistics, including but not limited to biostatistics, financial mathematics, and theoretical statistics. Topics include: an introduction to experimental design, power, and effect size calculations, data screening and transformation to meet assumptions of the analyses, multivariate regression, multinomial logistic regression, multivariate survival analysis, ANOVA/ANCOVA/MANOVA/MANCOVA, and time permitting, an introduction to time-series analysis. Extensive use is made of real-world case data from business/finance, health/biology, and education/psychology. Prerequisite: MA 116 or MA 118 or MA 126, passed with a grade of “C-” or higher, and either MA 15, MA 220 or BE 251, passed with a grade of “c-” or higher.
MA 440, Regression and Time Series Analysis
Covers topics related to multiple regression techniques, including testing the assumptions required for each to be valid. This includes applications to yield curve smoothing, pricing, and investment models, and the use of principal component analysis. Also covered are techniques for the analysis and modeling of time-series data and forecasting. Prerequisite: MA 116 or MA 118 or MA 126, passed with a grade of “C-” or higher and MA 151 or MA 220 or BE 251, passed with a grade of “C-” or higher.
MA 460, Multivariate and Categorical Statistics
This advanced statistics course provides students with skills in advanced multivariate analysis and its applications. Students will learn the material through projects using data from business, finance, and biology. Topics include MANOVA, discriminant analysis, cluster analysis, multidimensional scaling, and factor analysis. Topics may also include conjoint analysis, canonical correlation, and structural equation modeling. Prerequisite: MA 116 or MA 118 or MA 126, passed with a grade of C- or higher, and MA 151 or MA 220 or BE 251, passed with a grade of “c-” or higher.