MATH432 — Rings and Polynomials

5 credits CIM Verified

Binary operations, rings and polynomials, factor rings, integral domains, fields with applications to encryption and digital communication.

Mathematics BS
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Learning Objectives & Matches

LO1 CIM

Prove results related to rings, integral domains and fields

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LO1

Analyze algebraic structures including rings, fields, and integral domains

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LO2 CIM

Factor polynomials in designated integral domains or fields

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LO2

Apply polynomial ring theory to factorization and division algorithms

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LO3 CIM

Construct extension fields

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LO3

Construct and analyze quotient rings and ideals

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LO4 CIM

Relate the concepts of prime and irreducible to prime ideals and maximal ideals to integral domains and fields

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LO4

Prove theorems in abstract algebra using rigorous methods

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LO5 CIM

Compare and contrast Euclidean Domains, Unique Factorization Domains and Principle Ideal Domains

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LO5

Apply algebraic structures to cryptography and coding theory

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LO6

Analyze field extensions and algebraic closures

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LO7

Use computational algebra systems for algebraic calculations

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Source: Official CIM from EWU · Matches via cosine similarity (all-MiniLM-L6-v2, 384-dim embeddings)