Mathematics 6823-001
Name (please print)
Final Examination
May 13, 2009
Instructions: Insofar as possible, give brief, clear answers. Use major theorems when possible. Assume that
homology and cohomology are with Z coecients unless otherwise indicated.
I.
Mathematics 6823-001
Name (please print)
Midterm Examination
March 12, 2009
Instructions: Insofar as possible, give brief, clear answers. Use major theorems when possible.
f
g
I.
(6)
Let 0 A B C 0 be an exact sequence of abelian groups, and let G be an ab
Mathematics 6823-001
Name (please print)
Final Examination
May 13, 2009
Instructions: Insofar as possible, give brief, clear answers. Use major theorems when possible. Assume that
homology and cohomology are with Z coecients unless otherwise indicated.
I.
Math 6823 homework
1. (due 2/3) 2.1 # 28, 29
2. (2/3) 2.1 # 31
3. (2/3) 2.2 # 4
4. (2/12) 2.2 # 3, 5 (the reection in a hyperplane H with 0 H sends x to x 2 x, u u
where u is a unit normal to H), 6
5. (2/12) 2.2 # 12, 13 (to prove X
S 2 , one can apply Pr
Mathematics 6823-001
Name (please print)
Midterm Examination
March 12, 2009
Instructions: Insofar as possible, give brief, clear answers. Use major theorems when possible.
I.
(6)
f
g
Let 0 A B C 0 be an exact sequence of abelian groups, and let G be an ab