This is the basic graduate algebra course, the second course in a sequence of two courses.
The courses are designed to cover the basic topics in algebra which would be needed
for a student who intends to pursue research not only in algebra but in various other areas.
For example, elements of commutative algebra which are needed for algebraic geometry
are covered in the second course.

The topics to be covered are:
Fields: Algebraic extensions, Galois theory, transcendental extensions
               Chapters 13-14

Commutatve Algebra: Hilbert's Nullstellensatz, primary decompositions
                  ;                 integral extensions
              Chapters 15-16

Grading: There will be homework assignments every week, as well as a final exam.
 
 

p. 499: 1, 6

p. 509: 3, 8, 9, 14, 16

HOMEWORK 2. Due Wednesday 1/29/03

p. 509: 18, 21, 22

p. 525: 1, 3; P. 531: 3, 5, 6, 8, 9, 10

HOMEWORK 3, Due 2/5/03

p. 535: 2, 4, 5, 7, 10, 13

p. 515: 1, 2, 4

p. 547: 4, 7, 8, 10

HOMEWORK 4, Due 2/12/03

p. 561: 1, 3, 7, 14, 15, 18, 21, 23, 24, 26, 29

HOMEWORK 5. Due 2/26/03

   P. 583: 8, 10, 13

  : p. 598: 2, 3, 5, 8, 10

HOMEWORK 6. Due 3/5/03

  : P, 598: 13, 16, 18, 22, 27, 28, 29, 32, 34, 50, 51

HOMEWORK 7. Due 3/12/03

P. 601: 31, 33, 41 P. 618: 11, 13, 15, 19, 20

HOMEWORK 8, Due 3/26/03 P.625: 3, 6 p. 634: 2, 7, 12, 14, 19

HOMEWORK 9. Due 4/2/03 P.646 : 1, 3, 5, 8, 9, 10, 11, 24, 26, 33, 35

HOMEWORK 10. Due 4/9/03 p.661: 2, 8, 19, 37 p.675: 1, 8, 16, p. 693: 1, 6, 12, 15, 16

HOMEWORK 11. Due 4/16/03 P. 712: 2, 4, 15, 16 p.818: 5, 7, 9, 10, 18, 19, 20