Abstract Algebra
Spring 2007
There will be a midterm examination on March 27.
Student Presentation Schedule
April 17, April 18: Elizabeth Million: Knot Theory
April 20, April 23: Jean Gibb: (Axiomatic?) Origami
April 24, April 25: Alex Twist: Topology (applications to economics?)
April 27, April 30: Emily Paine: Constructive Mathematics
(Intuitionism)
May 1, May 2: Aimee Schulte: Three Dimensional Symmetries
Topics planned for the semester are:
- Application: The fundamental group of a topological space.
- Application: Rubik's Cube
- Application: Topspin Game
- More on Sylow related material
- The generalized Cayley theorem
- Use of Normalizers
- Burnside's Theorem
- The group isomorphism theorems
- Classification of Finite Abelian Groups (possibly extended to
classification of all abelian groups)
- 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
- Galois Theory
- Ruler and Compass