Abstract Algebra

Course Description

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,

Learning Outcomes

• 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.

Prerequisites

• MTH416