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

Focus on one subject at a time — one month at a time — and finish your degree faster.

75+ Degree Programs

Choose from associate, bachelor’s, and master’s degrees, plus credentials and certificates.

On Campus or Online

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

Year-Round Enrollment

Apply or transfer any time. Classes start monthly, and applications are accepted year round.

20+ Locations

Attend class and learn onsite at one of over 20 locations in California.

Military Friendly

As a Yellow Ribbon school, we offer tuition discounts to servicemembers and dependents.

“Our faculty are established scholars and creators in their own fields. They are dedicated to making your entry into their disciplines a successful one, preparing you for your career as well as graduate study.”
— Dr. Carol RichardsonDean, College of Letters and Sciences

College of Letters and Sciences