Math 464 Homework Assignments

Assignment 1, due Tuesday, January 22:
Do the following problems from Artin's Algebra, chapter 10, starting from page 379:
1.5,1.6,1.8,1.13,2.6,3.2,3.6,3.9,3.19,3.24,3.30
Show that a=Ö2+Ö5 is integral over Z.

Assignment 2, due January 28:
Do the following problems from Artin, chapter 10:
4.2,4.5,4.6,4.7,5.2,5.5,5.6,5.12,5.14,5.15

Assignment 3, due February 4:
Do the following problems from Artin, chapter 10:
6.2,6.5,6.6,7.4,7.6,7.11,7.12,8.5,8.8,8.11 Misc. Ex. 6,8

Assignment 4 , due February 11:
Do the following problems from Artin, chapter 11:
1.10,1.15,2.1,2.2,2.7,2.13,2.14,3.2,3.4,3.8,4.1,4.3

Assignment 5 , due February 18:
Do the following problems from Artin, chapter 11:
4.8,4.10,4.11,5.6,5.8,6.2,6.5,6.6

Assignment 6, due February 25:
Postscript or Acrobat

Assignment 7, due March 11:
Do the following problems from Artin, chapter 12:
1.5,1.6,1.7,1.8,1.9,1.10,1.12,2.1,2.3,2.4,2.6,3.4
Find the syzygies between the polynomials x²-1 and x³-1 over R=Q[x].

Assignment 8, due March 18:
Do the following problems from Artin, chapter 12:
4.3, 4.4, 4.5, 4.7, 4.11, 5.2, 5.5, 5.6, 5.7, 6.1, 6.7
Let A and B be diagonal 2x2 matrices. Give necessary
and sufficient criteria for when the abelian groups
presented by A and B are isomorphic.

Assignment 9, due March 25:
Do the following problems from Artin, chapter 12:
7.5, 7.7, 7.9, 7.11, 7.14, 7.17, 7.21, 7.23, 7.26
Do the following problems from Artin, chapter 13:
1.3, 2.3, 2.5

Assignment 10, due April 1:
Do the following problems from Artin, chapter 13:
3.1, 3.7, 3.8, 3.10, 3.11, 3.14, 4.2, 4.4, 4.5, 4.8, 4.11, Misc. Ex. 1

Assignment 11, due April 8:
Do the following problems from Artin, chapter 13:
5.2, 6.4, 6.7, 6.10, 6.11, 6.12, 6.14, 6.15, Misc. Ex. 2, 3, 5

Assignment 12, due April 15:
Do the following problem from Artin, chapter 13: 9.2
Do the following problem from Artin, chapter 14:
1.6, 1.7, 1.8, 1.9, 1.10, 1.13, 2.2, 2.3, 2.4, 2.6, 5.2

Assignment 13, due April 22:
Do the following problems from Artin, chapter 14:
2.9, 4.2, 4.4, 4.5, 5.8, 5.9, 5.10, 5.12, 6.3, 6.12, 6.15, 6.16