Math 600 Homework
- Homework #1: (Due Friday, September 12)
- p. 61: 2.20, 2.23, 2.24, 2.25, 2.26
- p. 72: 2.31, 2.33, 2.37
- Homework #2: (Due Friday, September 19)
- p. 80: 2.41, 2.43, 2.44, 2.47, 2.51, 2.53
- p. 94: 2.69, 2.70 (Q=quaternion group), 2.71
- Homework #3: (Due Wednesday, October 1)
- p. 112: 2.78, 2.79, 2.82, 2.86, 2.89, 2.90, 2.94, 2.96
- Homework #5: (Due Wednesday, October 15)
- p. 277: 5.17, 5.19, 5.24, 5.25, 5.28
Midterm #1: Wednesday, October 22
- Homework #6: (Due Friday, October 31)
- p. 124: 3.3, 3.6, 3.16, 3.18
- P. 130: 3.26(iii). 3.27
- p. 149: 3.41, 3.51, 3.54
- Homework #8: (Due Wednesday, November 19)
- p. 324: 6.1, 6.3, 6.4(ii), 6.5, 6.6, 6.8, 6.9, 6.13
I. Let C[X,Y] be the ring of polynomials in X, Y with complex coefficients.
Let R be the set of polynomials in C[X,Y] of the form a+Yg(X,Y) where a is a complex number and g is
in C[X,Y] (so X is not in R but 3+XY is in R).
(a) Show that R is not a unique factorization domain.
(b) Show that R is not Noetherian.
Midterm #2: Monday, December 8
Sample Exam
- Homework #10 (Due Tuesday, Dec. 16)
- p. 440: 7.5, 7.9
- p. 681: 9.40, 9.43
- I. Find all abelian groups of order 200.
- II. If the characteristic polynomial of a matrix is X^2 (X-1)^3,
find all possible Jordan forms for the matrix.
- III. Let B be a module (over some commutative ring) and let A be
a submodule. Show that B is Noetherian if and only if both A and B/A are Noetherian.
- Don't forget to fill out the online evaluations at www.courses.umd.edu/online_evaluation
The dealine is Wednesday, Dec. 10, 11:55pm.
- Solutions to some homework problems (written by Sean Lawton)