Charles Frohman
Department of Mathematics
University of Iowa
Iowa City, Iowa 52242
Office: B1F MLH
Phone: (319) 335-2543
FAX: (319) 335-0627
Email: frohman@math.uiowa.edu
Charles Frohman
Department of Mathematics
|
|
Quantum Invariants of Three-manifolds
Click here for my vita. vita
The practice exams have the same format as the qualifying exam. As I am making them up quickly each particular exam may not have the balance of topics that the real exam will have.
In addition to the four posted here. Carmen will administer the first and last as three hour exams. Also I will put out a list of other practice problems, but not organized as exams. You should practice writing out formal solutions to as many problems as you can. Find a partner or partners who will read your work critically.
Your ideal should be to have the definitions so wired that when you look at a problem you are not thinking about how to solve it, just thinking about how to write the solution up.
For the material on general topology, Munkres' book is where I am taking my definitions. For the material on multivariable calculus Spivak's book is the source. Finally, for the material on smooth manifolds Boothby's book is the source, except he is not as formal as he should be when it comes to defining the tangent space. For this material my class notes should be used as the final source.
Click here for the second practice exam. typical exam 2
Click here for the third practice exam. typical exam 3
Click here for the fourth practice exam. typical exam 4
Click here for the fifth practice exam. typical exam 5