Mathematics

STEM-specific technology tools for the secondary teacher for lesson preparation and presentations. Techniques for integrating dynamic computer software and its applications in teaching. Designing technology-based activities for STEM instruction. Field work component.

Characteristics and needs of low achievers and accelerated students in mathematics, and methods of effectively teaching these two student populations. Scheduled summer semesters of even years.

Linear regression and correlation, analysis of variance and applications. Scheduled spring semesters of odd years.

This course gives a broad introduction to machine learning through basic programming and probability theory. Topics to be covered include classification, support vector machines, neural networks, clustering, feature selection, ensemble learning, and reinforcement learning. The courses will discuss applications of machine learning to various fields including computer science, data mining, and bioinformatics.

The course introduces concepts in stochastic processes and stochastic modeling in a nonmeasure theoretic manner. Topics include Poisson process, renewal theory, queueing theory, Markov chains, martingales, and Brownian motion.

An axiomatic development of Euclidean and non-Euclidean geometries. Scheduled spring semesters.

Sequences, Bolzano-Weierstrass Theorem, and foundations of functions of one real variable that include limits, continuity, Intermediate Value Theorem, differentiability, Mean Value Theorem, Riemann integral, Fundamental Theorem of Calculus. Scheduled fall semesters of even years.

Metric spaces and fundamental concepts, topological spaces, subspaces and product spaces, countability properties, separation properties, compactness, and connectedness. Scheduled fall semesters of odd years.

Linear Algebra: systems of linear equations, matrix algebra, vector spaces and linear transformations. Introduction to Group Theory: subgroups, structure of cyclic groups, direct products, group isomorphisms, cosets and Lagrange’s theorem. Scheduled fall semesters of odd years.

Normal subgroups and factor groups; rings, ideals and factor rings; polynomial rings and irreducibility; extension fields; finite fields; introduction to Galois theory. Scheduled spring semesters of even years.

Examines a general overview of social science research, a brief history of mathematics education research, and the application of experimental, descriptive, qualitative, and meta-analytical methods in the field of mathematics education. Scheduled spring semesters of even years.

Research and writing of the thesis in the area of concentration, under the direction of a mathematics department faculty member. For specific details, consult the chairperson or graduate coordinator of the department.

Current issues in mathematics education. Scheduled summer semesters of odd years.

Provides qualified students with an opportunity for independent study and careful discussion from an advanced standpoint of selected topics in mathematics.