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