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
The second midterm will be held on Wednesday Nov 18 and will be based on
sections 14.2, 14.3, 12.1, 12.2, and 12.3. In section 14.2, the proof of
Theorem 9 that I gave is different from the one in the book -- you need
not know the ingredients of the proof in the book (e.g., Theorem 7, the two
definitions before the theorem, and Corollary 8). In section 14.3, you
need not know anything after Proposition 15. In section 12.1,
you only need to know the statements of Theorems 5, 6, and 9. Finally, in
section 12.2, you do not need to know anything after Proposition 20, and
in section 12.3, you need not know anything after Corollary 25.
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 25)