MAS 5311
ABSTRACT ALGEBRA I (aka GROUPS, RINGS, AND VECTOR SPACES III)
Fall 2009,
Instructor: Amod Agashe
Office: 216 Love
Office hours: MW 1:30--2:30
Phone: 644-8704
Email: agashe@math.fsu.edu
First day handout
HW1: pdf
HW2: 13.5: 1, 5, 7(optional), 8.
HW3: 13.5: 3 (optional), 4, 6 (optional). due Sept 23.
HW4: 14.1: 1, 2, 3, 5; optional: 4, 8, 10. due Sept 30.
HW5: pdf, due Oct 14.
HW6: 14.4: 1, 14.7: Prove that a quotient of a solvable group is solvable.
due Oct 21.
HW7: 14.9: 1 (due Oct 28)
HW8: 12.2: 1, 2, 3 (optional), 4 (optional), 6, 8. (due Nov 4)
HW 9: 12.3: Prove that the Jordan block of size k with eigenvalue lambda
has minimal polynomial (x-lambda) raised to k, 31, 34. (due Nov 16)
HW 10: 10.5: Prove part 2 of Proposition 24 (the short five lemma),
Prove the first sentence of Proposition 25 (the proof in the book is
a sketch; complete it with details) (both due Nov 30)
HW 11: 5.5: In the context of the proof of Theorem 10, prove that
(1,1) is the identity, and prove the formula for the inverse of (h,k).
(due Dec 2)