Math 446/546 SPRING 2012, List of lectures

  • On this page I will post content of all lectures. All handouts also will be posted here.
  • Monday, April 2: Ideals and Factor Rings. Fraleigh, Section 26.
  • Wednesday, April 4: Prime and maximal ideals; ideals in the ring of polynomials. Fraleigh, Section 27. Please find your homework.
  • Friday, April 6: Extensions of fields. Fraleigh, Section 29.
  • Monday, April 9: Simple, finite, algebraic and finitely generated extensions. Fraleigh, Section 31.
  • Wednesday, April 11: Algebraically closed fields and algebraic closure. Fraleigh, Section 31. New homework.
  • Friday, April 13: Existence of algebraic closure. Finite fields. Fraleigh, Sections 31 and 33.
  • Monday, April 16: Geometric constructions and constructible numbers. Fraleigh, Section 32.
  • Wednesday, April 18: Isomorphism theorems. Subnormal and normal series. Fraleigh, Sections 34-35. New homework.
  • Friday, April 20: Jordan-Holder theorem. Solvable and nilpotent groups. Fraleigh, Section 35.
  • Monday, April 23: Actions of p-groups. Cauchy's theorem. Fraleigh, Section 36. We will have MIDTERM on Friday!!! Please find practice problems!
  • Wednesday, April 25: The Sylow theorems. Fraleigh, Section 36. Please find solutions for the practice problems. New homework.
  • Friday, April 27: MIDTERM. The solutions are here.
  • Monday, April 30: Applications of Sylow theory. Fraleigh, Section 37.
  • Wednesday, May 2: Conjugacy classes. p-groups are nilpotent. Alternating groups are simple. Fraleigh, Section 37. New homework.
  • Friday, May 4: Free abelian groups. Fraleigh, Section 38.
  • Monday, May 7: Smith normal form. Free groups. Fraleigh, Sections 38-39.
  • Wednesday, May 9: Generators and relations for groups. Semi-direct product. Fraleigh, Section 40. New homework.
  • Friday, May 11: Automorphisms of fields and extensions of homomorphisms. Fraleigh, Sections 48-49.
  • Monday, May 14: Splitting fields. Fraleigh, Section 50.
  • Wednesday, May 16: Index of extension. Separable extensions and perfect fields. Fraleigh, Sections 49 and 51. New homework.
  • Friday, May 18: Primitive element theorem. Galois extensions. Fraleigh, Sections 51 and 53.
  • Monday, May 21: Main theorem of Galois theory. Fraleigh, Section 53. We will have MIDTERM on Friday!!! Please find practice problems!
  • Wednesday, May 23: Galois theory examples. Fraleigh, Sections 53-54. Please find solutions for the practice problems. New homework.
  • Friday, May 25: MIDTERM. The solutions are here.
  • Monday, May 28: Memorial Day.
  • Wednesday, May 30: Galois groups for finite fields. Discriminant and low degree polynomials. Fraleigh, Sections 53 and 54. Last homework.
  • Friday, June 1: Fundamental theorem of algebra via Galois theory. Cyclotomic extensions. Fraleigh, Section 55.
  • Monday, June 4: Radical extensions and solvable Galois groups Fraleigh, Section 56.
  • Wednesday, June 6: Kummer's theory. Solvable extensions are radical.
  • Friday, June 8: Dedekind theory. Please find practice problems for the final! Please find solutions for the practice problems.
  • THE END.