M373K ALGEBRAIC STRUCTURES I

Prerequisite and degree relevance:

Either consent of Mathematics Advisor, or two of M341, 328K, 325K (Philosophy 313K

may be substituted for M325K), with a grade of at least C.

Students who receive a grade of C in M325K or M328K are advised to take M343K

before attempting M373K.

Course description:

M373K is a rigorous course in pure mathematics. The syllabus for the course includes

topics in the theory of groups and rings. The study of group theory includes normal

subgroups, quotient groups, homomorphisms, permutation groups, the Sylow theorems,

and the structure theorem for finite abelian groups. The topics in ring theory include

ideals, quotient rings, the quotient field of an integral domain, Euclidean rings, and

polynomial rings.

This course is generally viewed (along with 365C) as the most difficult of the required

courses for a mathematics degree. Students are expected to produce logically sound

proofs and solutions to challenging problems.