Courses

This course emphasizes algebraic functions - including polynomial, rational, exponential, and logarithmic functions. The course also covers systems of equations and inequalities, quadratic inequalities, and the binomial theorem. Additional topics may include matrices, Cramer's Rule, and mathematical induction.

Introduction to equations of straight lines in various forms and transition between these forms; Manipulation and solution of linear equations and linear inequalities; graphing solution sets on the number line and expression of solution sets in both set and interval notation.

A graduate level introduction to group theory. Topics include quotient groups, homomorphisms, group actions, Sylow theorems, composition series, simple groups, free groups, fundamental theorem of abelian groups.

Groups, Lagrange's Theorem, normal subgroups, factor groups, Isomorphism and Correspondence Theorems. Symmetric groups, alternating groups, free groups, torsion groups. Introduction to rings, correspondence theorems.

Linear codes, Hamming and Golay codes, BCH codes, cyclic codes. Random error detection and correction. Burst-error correction. Decoding algorithms. Credit will not be given for both MATH 5150 and MATH 6150/6156.

Linear codes, Hamming and Golay codes, BCH codes, cyclic codes. Random error detection and correction. Burst-error correction. Decoding algorithms. Credit will not be given for both MATH 5150 and MATH 6150/6156.

``C” or better in Math 7320 and Math 7500. Affine and projective varieties, the Ideal-Variety Correspondence, morphisms and rational maps of varieties, Bezout's Theorem, sheaves, schemes, divisors, sheaf cohomology.

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.

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.