400

An introduction to Statistical Learning with extensive applications with the R programming language. Emphasis on various types of statistical models including Linear and Nonlinear Regression, Regression Trees, Clustering, Classification Trees, and Random Forests. An exploration of advanced techniques including Regularization (Ridge and Lasso), K-Nearest Neighbor, and Principal Component Analysis. Finally, an introduction to model evaluation including Cross-Validation and the Bias-Variance Trade-Off. This course helps to prepare students for the examination "Statistics for Risk Modeling" in the Actuarial Profession. Prerequisites: MAT-322 and one of MAT-363 or MAT-204

A continuation of MAT-344 Modern Abstract Algebra. Topics include advanced group theory, theory of factorization, extension fields, Galois theory, and selected applications. Prerequisite: MAT-344.

An advanced multivariate treatment of calculus for the mature student of mathematics. This course will present derivation of the properties of continuity, differentiation, integration and convergence using the fundamental concepts and theorems of analysis. Applications in differential geometry and vector calculus will build on previous calculus experience. Prerequisite: MAT-255.

A study of metric spaces and general topological spaces. Continuity, connectedness, compactness, separation, completions, product spaces, and quotient spaces. Prerequisite: MAT-255 and MAT-282.

A theoretical study of single variable calculus. Topics include the real number system, sequences, limits, continuity, derivatives, Riemann integrals, and convergence of series. Emphasis will be placed on understanding, writing, and communicating proofs. Prerequisite: MAT-255 and MAT-282.

An introduction to functions of a single complex variable. Topics include complex numbers, analytic and harmonic functions, mappings, integration techniques and theory, series, and residues. Prerequisite: MAT-255 and MAT-282.

Individually arranged reading, problem solving, or research in higher mathematics or statistics. Prerequisite: Permission of Division Chair.

A classical historical approach to the study of the foundations of mathematics. Contributions of ancient cultures such as the Egyptians, Babylonians, Greeks, Chinese, Hindus and Arabs are considered, as well as the transmission of mathematics into Europe from antiquity through the twentieth century. A comprehensive overview of the various branches of mathematics, such as number theory, logic, geometry, analysis, probability, and statistics is given using concrete applications and high level abstract thinking. Prerequisite: MAT-282.

A mathematical/statistical work experience individually arranged with an employer or volunteer agency. Internships must be preapproved by the Mathematics Department Coordinator for suitable placement and determination of the number of credits. Requirements at the end of the experience include a presentation to the Department as well as student and employer evaluations, a journal, and a paper submitted to the Coordinator. The course may be repeated for credit; a maximum of 4 credits may be applied to a major within the Math Department. Prerequisite: Junior or senior status.

A capstone course designed to integrate Christian faith, mathematics, philosophy, and other disciplines. Emphasis will be placed on researching and presenting advanced topics in mathematics. The relationships between the world changing mission of the university, truth, and the student's mathematical career will also be explored. The Major Field Achievement Test in Mathematics will be administered. Prerequisite: Senior standing in a major offered through the Mathematics Department.

Students will engage in a research project in conjunction with a faculty member. Designed for mathematics majors who plan on graduate level work. This course may be repeated for up to 4 credits total. Prerequisite: At least sophomore standing and permission of Division Chair.