Abstract Algebra with Applications

Catalog description

This course covers methods of mathematical reasoning and proof. It also covers elementary number theory including divisibility, primes, congruence and modular arithmetic, and Euler’s formula. It includes introduction to group theory including subgroups, symmetry and permutation groups, homomorphism and isomorphism, direct products, structure of cyclic and abelian groups, and group actions. Applications to cryptography are addressed. Other possible topics include rings and fields, solvability of polynomials, impossibility of compass and straight edge constructions, or primality testing.