Bill Rau it the TA for the course. He is available to answer questions about homework in the MAC 10-12 Mondays and 4-5 Mondays.
In class on January 25, we went over a large number of exercises. You will not be asked to submit solutions on February 1. Instead, read all of the exercises from Sections 2.1 (17 problems), 2.2 (14 problems), and 2.3 (26 problems).
Submit a sheet of paper stating for each problem which category each problem falls into:
- (Solved) You have solved the problem.
- (Understand) You have not solved the problem, but you are convinced that you understand exactly how to solve the problem.
- (Unsolved) You are not convinced you understand how to solve the problem.
- DF Sec 1.3 #5, #8, #14
- DF Sec 1.6 #9, #17, #23,
- DF Sec 1.7 #17
- (wording updated on Jan 23.) Let F be a field. Let , viewed as an n-dimensional vector space over the field F. Show the following:
- The group G=GL(n,F) acts on V by linear transformations.
- If is the standard ordered basis of V and if , then is an ordered basis of V.
- There is a 1-1 correspondence between elements of GL(n,F) and bases of V.
- Friday, Jan 20, 2017, 3:30. Speaker: Prof. Jeremy Avigad. Title: The History of Dirichlet’s Theorem on Primes in an Arithmetic Progression.
- DF Section 1.1, problems #5, #9, #19 (do this one carefully using induction), #33a
- DF Section 1.2, problems #2, #9, #16.