Date  Chapter  Description 

Jan 12  2.12.2  Introduction, Group defintion and examples 
Jan 14  2.32.4  Basic facts, subgroups 
Jan 16  2.4  Subgroups and cosets 

Jan 19   Martin Luther King day! (no class) 
Jan 21   Counting, normal subgroups 
  HW 1 due 
Jan 23   Homomorphisms, isomorphisms, and automorphisms 

Jan 26   Kernels and the Isomorphism Theorem 
Jan 28   The Isomorphism Theorem and Sylow sgs 
  HW 2 due 
Jan 30   The Correspondence Theorem 

Feb 2   The Diamond Theorem; automorphisms 
Feb 4   Group actions and Cayley's Theorem 
  HW 3 due 
Feb 6   Group actions, normal subgroups, and orbits 

Feb 9   Group actions and counting 
Feb 11   S_{n}: cycle decomposition and conjugacy 
  HW 4 due 
Feb 13   S_{n}: transpositions and sign 

Feb 16   A_{n}; The Sylow E Theorem 
Feb 18  In class midterm #1 
Feb 20   The Sylow C and D Theorems 
  HW 5 due 

Feb 23   Sylow subgroups > normal subgroups; Direct products 
Feb 25   Introducing rings 
Feb 27   Ideals and quotients 

Mar 2   Isomorphism Theorems and maximal ideals 
Mar 4   Maximal ideals, Zorn's Lemma, and fraction fields 
Mar 6   Euclidean domains 

Mar 9   Spring Break! (no class) 
Mar 11   Spring Break! (no class) 
Mar 13   Spring Break! (no class) 

Mar 16   More Euclidean domains 
Mar 18   Polynomial rings 
Mar 20   UFDs and polynomial rings 

Mar 23   More UFDs and polynomial rings 
Mar 25   Face rings; the Eisenstein criterion 
Mar 27   Fields extensions: degree and dimension 

Mar 30   Degree of algebraic field extensions 
Apr 1  In class midterm #2 
Apr 3   Algebraic over algebraic extensions 

Apr 6   More algebraic over algebraic extensions 
Apr 8   Algebraic extensions and roots 
Apr 10   Splitting extensions and splitting fields 

Apr 13   Splitting fields are unique up to isomorphism 
Apr 15   Ruler and compass constructions 
Apr 17   Matrix groups (with Raj Mehta) 

Apr 20   Galois groups and the Galois correspondence 
Apr 22   When is the Galois correspondence a bijection? 
Apr 24   Galois answers; Conclusion 

May 6  Final exam (10:30 am  12:30 pm) 