# HW6, due Monday March 13 (revised date), 2017

• DF 4.3 #5, #8, #33
• DF 4.4 #6, #18
• DF 4.5 #3, #40

Recall that the deadline for completing a bonus problem in Friday March 3.  (It is not necessary to write up the solution.  It is enough to notify the instructor by Friday.  It is not necessary to have a complete solution by that date.)

# Exam Feb 22, 2017

The exam will cover up to and including Section 4.2.

The bonus problems (not to be presented during the exam) are as follows:

• Given the category of finite abelian groups, can you determine which object is which group (up to isomorphism)?
• Determine the group generated by two adjacent faces of the Rubik’s cube.

# HW5, due Wed Feb 15, 2017

• DF 3.2 #8, #11,
• DF 3.3 #4, #7,
• DF 3.4 #5, #7, #11, #12

# HW 4, due Wed Feb 8, 2017

• DF Section 2.4 #9 #17 (Zorn’s lemma appears in Appendix 1), #18
• DF Section 3.1 #1, #12.
• Let F be any field.  Show that there is a 1-1 homormophism from $S_n$ to $GL(n,F)$ given by the action of $S_n$ on the indices i in the standard basis $e_1,\ldots,e_n$.  Combine this with Cayley’s theorem (page 120) to show that for every finite group G, there exists n, such that G is isomorphic to a subgroup of $GL(n,F)$.
• Show algebraically that every isometry T of $R^2$ is a glide reflection provided it has the form $\latex T=T_\lambda A$, where $A\in O(2,R)$, $A\not\in SO(2,R)$, $\latex \lambda\ne 0$.
• Solve the following problems without submitting a solution
• DF Section 2.4 #15, #19

# Midterm Exam

The midterm exam will be held on Wednesday, February 22, 2017.