Mathematics and Computer Science at Western Carolina University

Revised: November 2006

Topics from theory of equations, linear algebra and modern algebra. Three semester hours.

To expose the student to some relatively deep algebraic theorems.
To make the student aware that algebra is a rapidly developing area of knowledge.

Maxfield, J. and Maxfield, M. Abstract Algebra and Solution by Radicals, Dover Inc.

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Chapter 1. Groups (3 days)
Group properties, examples of groups.
Chapter 2. Other Abstract Algebras (5 days)
Rings, fields, examples, countable, equivalence relations, isomorphism.
Chapter 3. More About Groups (5 days)
Permutations, subgroups, congruence, cosets, quotient groups.
Chapter 4. Mappings that Preserve Relations (3 days)
Homomorphisms of groups and rings.
Chapter 5. Groups of Prime Order; Two Alternating Groups (4 days)
Cauchy's theorem, simple groups.
Chapter 6. Polynomials (4 days)
Division algorithm, Euclidean algorithm, Eisenstein's irreducibility theorem.
Chapter 7. Algebraic Field Extensions (4 days)
Algebraic numbers, transcendental numbers, splitting fields
Chapter 8. Galois Theory (4 days)
Galois group, fundamental theorem
Chapter 9. Radicals and Roots of Unity (3 days)
Primitive nth root of unity
Chapter 10. Solution by Radicals (3 days)
Abel's theorem, solvable group