Math 373K Syllabus

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.

Text: Herstein, Topics in Algebra

Material to be covered: Chapters 1, 2, 3 and if time permits some topics in Chapters 4 and 5. This includes: properties of the .integers, including divisibility and prime factorization; properties of groups, including subgroups, homomorphisms, permutation groups, the Sylow theorems; properties of rings, including subrings and ideals, homomorphisms, domains, especially Euclidcan, principal ideal and unique factorization domains, polynomialsrings. If time permits: Fields, elementary properties of vector spaces including concept of dimension, field extensions.

We will be glad to discuss any questions or listen to any comments which you may have now or during the term on the course, the text, or the syllabus.

The Undergraduate Curriculum Committee