# MS in Mathematics Courses - Fall 2021

For term dates, please see https://www.una.edu/registrar/Academic%20Calendars/index.html.

MA 600. Applied Engineering Programming. (3 Credits) Use of high level programming language (Matlab) and associated application programming interfaces (API) to design and create models for manufacturing processes. Programming methods for designing, implementing and using machines used in manufacture. The approach will be practical where students will learn to develop, debug and execute scripts to achieve specific objectives. (Fall)

MA 602. Advanced Applied Engineering Mathematics. (3 Credits) Advanced Applied Engineering Mathematics: Mathematics remains the language which engineers design, modify and use machines. Topics covered will include: linear algebra, differential equations, numerical methods and approximations, use of computer algebra systems like MATLab. (Fall)

MA 627. Mathematical Thinking for the Teacher I. (3 Credits) Theoretical framework for mathematical learning, transitioning from action to process to object level thinking. Explicit method for teaching mathematical thinking using computer programming to push the learner to recognize and use connections, relationships and patterns among mathematical ideas, write general expressions, conjecture and write convincing arguments or proof. Project based applications reinforce abstract thinking about the mathematical concepts as representations are used to model and interpret physical and technical phenomena.

MA 630. Foundations of Advanced Mathematics. (3 Credits) Proof-writing techniques; logic; sets and functions; fundamental topics in analysis, abstract and linear algebra, number theory, and combinatorics. Prerequisite: Admission to MS in Mathematics Program or permission of instructor.

MA 638. Rings and Fields. (3 Credits) Theory of rings; integral domains; fields; Galois theory. Prerequisite: MA 637 with a grade of C or higher.

MA 651. Advanced Calculus. (3 Credits) Logic; basic set theory and topology; real number system; limits; functions; continuity; sequences and series. Prerequisites: MA 630 with a grade of C or higher or permission of instructor.

MA 653. Real Analysis I. (3 Credits) Real number system, Lebesque measure, Lebesque integral, convergence theorems, differentiation of monotone functions, absolute continuity and the fundamental theorem of calculus, L^p spaces, Holder and Minkowoski inequalities, and bounded linear functions on the L^p spaces. Prerequistie: MA 652 with a grade of C or higher.

MA 667. Theory of Finite Groups. (3 Credits) This course is a continuation of topics in group theory from MA 637 with a strong emphasis on the structure of finite groups. Topics include a review of introductory group theory, Sylow theory, composition series and subnormality, split extensions, solvable groups, simple groups, commutators, fusion, and the transfer homomorphism. Computational algebra software may be utilized. Prerequisite: MA 637 with a grade of C or higher.