MATH 402 B: Introduction to Modern Algebra

Autumn 2021
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Meeting:
MWF 10:30am - 11:20am / OUG 141
SLN:
18168
Section Type:
Lecture
Instructor:
NO OVERLOADS CONTENT WILL INCLUDE: ELEMENTARY THEORY OF RINGS AND FIELDS: POLYNOMIAL RINGS. IDEALS, HOMOMORPHISMS, QUOTIENTS, AND FUNDAMENTAL ISOMOROPHISM THEOREMS. FIELDS AND MAXIMAL IDEALS. EUCLIDEA RINGS. FIELD EXTENSIONS. ALGEBRAIC EXTENSIONS. VECTOR SPACES AND DEGREES OF EXTENSIONS. ADJOINING ROOTS OF POLYNOMIALS. FINITE FIELDS STRAIGHT EDGE AND COMPASS CONSTRUCTIONS.
Catalog Description:
Elementary theory of rings and fields: basic number theory of the integers, congruence of integers and modular arithmetic, basic examples of commutative and non-commutative rings, an in depth discussion of polynomial rings, irreducibility of polynomials, polynomial congruence rings, ideals, quotient rings, isomorphism theorems. Additional topics including Euclidean rings, principal ideal domains and unique factorization domains may be covered. Course overlaps with: MATH 411; MATH 412; and STMATH 403. Prerequisite: either a minimum grade of 2.0 in MATH 300 and a minimum grade of 2.0 in either MATH 208 or MATH 308, a minimum grade of 2.0 in MATH 334, or a minimum grade of 2.0 in MATH 136 and a minimum grade of 2.0 in MATH 300. Offered: AWS.
GE Requirements Met:
Natural Sciences (NSc)
Credits:
3.0
Status:
Active
Last updated:
October 11, 2024 - 11:01 am