Courses

The course offers an introduction to Algebraic Quantum Field Theory (AQFT). It starts with a review of Hamiltonian mechanics and canonical quantization. The student is then introduced to the axioms of AQFT and some of its main results, including the GNS construction and the Reeh-Schlieder theorem. The formalism allows the study of quantum fields in curved spacetime.

This course is designed to deepen your mathematics content knowledge, empowering you to teach a rich K–8 mathematics curriculum aligned with the National Council of Teachers of Mathematics’ (NCTM) Principles and Standards for Mathematics and the Alabama Numeracy Act, including the Alabama State Course of Study: Mathematics.

Student study basic structures of abstract algebra: groups, rings, and fields. groups, homomorphisms, cosets, Cayley's Theorem, symmetric groups, rings, domains. Writing enhanced.

Students study basic structures of abstract algebra: groups, rings, and fields. groups, homomorphisms, cosets, Cayley's Theorem, symmetric groups, rings, domains. Note: Students who have taken Math 4377 may not take MATH 5377.

This course examines algebraic structures in secondary and post-secondary mathematics underlying theory, along with the appropriate integration of manipulatives and technology Mathematics, will be emphasized.

Explore the interconnections between the algebraic, analytic, and geometric areas of mathematics with a focus on properties of various number systems, importance of functions, and the relationship of algebraic structures to solving analytic equations. This exploration will also include the development and sequential nature of each of these branches of mathematics and how it relates to the various levels within the algebra mathematics curriculum.

Mappings, binary operations, equivalence relations, groups and subgroups, Lagrange's theorem, homomorphisms and isomorphisms, normal subgroups and quotient groups, rings, fields, ordered integral domains, fields of quotients, error correcting codes, linear codes, and decoding.

An introduction to the concepts of homotopy and homology theories. The following surfaces, higher homotopy groups, cellular and/or simplicial homology.

Covering spaces; introduction to homotopy theory; singular homology, cohomology.

A study of the important algebraic structures of rings and fields. Topics covered include rings, ideals, modules, polynomial rings, Euclidean algorithm, finite fields, and field extensions. Topics also include an introduction to Galois Theory with an emphasis on the geometric applications.