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MATH 210 Rings and Fields Units: 3.00
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*.
Offering Faculty: Faculty of Arts and Science
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.