MATH 320 Abstract Algebra for Educators

This course introduces abstract algebra for future mathematics educators, emphasizing connections between advanced algebraic structures and secondary mathematics. Topics include number theory, modular arithmetic and its applications (including cryptography and check digits), groups, rings, fields, polynomial structures, cyclic and permutation groups, symmetry groups, and the real and complex number systems as algebraic structures. Students verify algebraic properties, construct proofs, and analyze how abstract structures justify K–12 procedures involving operations, factoring, equation solving, divisibility, and patterns.

The course culminates in a capstone project in which students design secondary-level instructional materials that surface the abstract structure underlying a school mathematics topic. Emphasis is placed on pedagogical applications and mathematical communication.