## M373K ALGEBRAIC STRUCTURES I

**Prerequisite and degree relevance:** Consent of the faculty undergraduate adviser, or two of the following courses with a grade of at least C- in each: Mathematics 325K or Philosophy 313K, Mathematics 328K, Mathematics 341. Students who receive a grade of C- in one of the prerequisite courses are advised to take Mathematics 343K before attempting 373K. Students planning to take Mathematics 365C and 373K concurrently should consult a mathematics adviser.

**Course description: **A study of groups, rings, and fields, including structure theory of finite groups, isomorphism theorems, polynomial rings, and principal ideal domains.

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.