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Terms & Conditions

By checking this box as my electronic signature and submitting this form by clicking the Request Info button below, I provide my express written consent to representatives of National University and National University System affiliates (City University of Seattle, John F. Kennedy University, and Northcentral University) to contact me about educational opportunities, and to send phone calls, and/or SMS/Text Messages – using automated technology, including automatic dialing system and pre-recorded and artificial voice messages – to the phone numbers (including cellular) and e-mail address(es) I have provided. I confirm that the information provided on this form is accurate and complete. I also understand that certain degree programs may not be available in all states. Message and data rates may apply. I understand that consent is not a condition to purchase any goods, services or property, and that I may withdraw my consent at any time by sending an email to optout@nu.edu.

I understand that if I am submitting my personal data from outside of the United States, I am consenting to the transfer of my personal data to, and its storage in, the United States, and I understand that my personal data will be subject to processing in accordance with U.S. laws, unless stated otherwise in our privacy policy. Please review our privacy policy for more details or contact us at dataprotection@nu.edu.
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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.

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

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

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Attend class onsite at one of over 20 campus locations across California or in Nevada.

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“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