Abstract Algebra
Spring 2011
There will be a midterm examination on March 10.
Student Presentation Schedule
Topics planned for the semester are:
- Abstract Symmetry and Group Actions
- Sylow Theorems
- Application : The fundamental group of a topological space.
- Application: Rubik's Cube
- Introduction to Ring Theory
- Integers from the Peano axioms.
- Introduction to Polynomials
- Ring homomorphisms and ideals
- Quotient rings
- Adjunction of elements to a ring
- Fraction fields
- Maximal ideals
- Factoring integers and polynomials
- Unique factorization in R[x]
- Gauss's Lemma
- Explicit factorization of polynomials
- Gaussian primes
- Basics of Fields
- Degree of a field extension
- Finite Fields
- Galois Theory
- Ruler and Compass Constructions