Course Description

Examines the algebra of various mathematical structures with the goal of gaining a broader and more sophisticated understanding of algebraic structures. Topics include groups, rings, fields and other main algebraic structures.

Learning Outcomes

Construct and evaluate finite and infinite fields.
Apply main properties of vector spaces for construction of extension fields, elaborate algebraic extensions.
Elaborate main properties of rings, subrings, ideals and quotient rings, rings of polynomials and formal power series, division in rings.
Extend group structure to finite permutation groups (Cayley’s Theorem).
Prove Sylow’s Theorems for finite groups.
Generate groups given specific conditions.
Elaborate the Fundamental Theorem of Galois Theory.

Prerequisites

Recommended Preparation

Four-Week Classes

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Study when and where it’s convenient for you with evening, weekend, and 100% online classes.

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College of Letters and Sciences