Rings and Fields

Description

Integers, polynomials, modular arithmetic, rings, ideals, homomorphisms, quotient rings, division algorithm, greatest common divisors, Euclidean domains, unique factorization, fields, finite fields. Learning Hours: 132 (36 Lecture, 12 Tutorial, 84 Private Study) Requirements: Prerequisite MATH 110 /6.0 or MATH 111/6.0* or ( MATH 112 /3.0 and MATH 212 /3.0) or ( MATH 112 /3.0 with permission of the Department). Exclusion MATH 211/6.0*. Course Learning Outcomes: - Perform accurate and efficient computations with integers and polynomials involving quotients, remainder, divisibility, greatest common divisors, primality, irreducibility, and factorization. - Define and illustrate basic concepts in ring theory using examples and counterexamples. - Describe and demonstrate an understanding of equivalence classes, ideals, quotient rings, ring homomorphisms, and some standard isomorphisms. - Recognize and explain a hierarchy of rings that includes commutative rings, unique factorization domains, principal ideal domains, Euclidean domains, and fields. - Write rigorous solutions to problems and clear proofs of theorems. Assessment/Exam Context: Course assessment and examinations vary by course; Queen's notes that eligible exchange students whose first language is not English may receive extra final-exam time. Exchange Registration Note: Arts and Science courses are open to exchange students subject to prerequisites and space. Most courses should be in Arts and Science; other faculties may be limited. Education, Medicine, and Nursing are not open to incoming exchange enrolment.