This course continues and advances the work done in MTH 416 Algebraic Structures, discussing selected fundamental algebraic structures, the main concepts of Sylow Theory of finite groups, finite permutation groups (Cayley’s Theorem), Lattices Theory, Coding Theory and Cryptography,
- Discuss field extension, algebraic extensions.
- Extend group structure to finite permutation groups (Cayley’s Theorem).
- Discuss Sylow’s Theorems.
- Generate groups given specific conditions.
- Investigate symmetry using group theory.
- Identify plane periodic patterns (lattices).
- Understand the base of the coding theory as an application of finite fields.
- Demonstrate knowledge that the rational numbers and real numbers can be ordered and that the complex numbers cannot be ordered, but that any polynomial equation with real coefficients can be solved in the complex field.
- Discuss the three major concrete models of Boolean algebra: the algebra of sets, the algebra of electrical circuits, and the algebra of logic.
- Describe other applications of abstract algebra such as in avoiding problems of round off in computations.
Why Choose National University?
We’re proud to be a veteran-founded, San Diego-based nonprofit. Since 1971, our mission has been to provide accessible, achievable higher education to adult learners. Today, we educate students from across the U.S. and around the globe, with over 180,000 alumni worldwide.
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.
Apply or transfer any time. Classes start monthly, and applications are accepted year round.
Attend class and learn onsite at one of over 20 locations in California.
As a Yellow Ribbon school, we offer tuition discounts to servicemembers and dependents.
College of Letters and Sciences
“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.”College of Letters and Sciences