Basic Problems: Don't hand these problems in. You should do them before the Core Problems in the same section, to help your understanding.
Core Problems: Everyone must turn these problems in. Always justify your answer, even if the question does not explicitly say so.
Challenge Problems: MATH 6010 students must turn at least one of these per week. They are extra credit for MATH 4010 students. Please hand these in stapled separately from the other problems.
Basic Problems: Section 6.1 # 0, 2
Core Problems: Section 6.1 # 4, 10, 12, 13, 17a
Challenge Problems: Section 6.1 # 17b, 22, 23, 24
Core Problems: Section 6.2 # 5 abd, 6a, 11, 13ab, 15ab
Challenge Problems: Section 6.2 # 15c, 16
Hints: For simplicity let R = rho and F = psi. For 15a, what you have to show is that you can write the inverse of R^i F^j and the product (R^i F^j)(R^k F^l) in the form R^m F^n (that is, with the R's first).
Core Problems: Sec. 6.3 # 6, 7, 10, 16, 18, 19, 21
Challenge Problems: Sec. 6.3 # 17, 31
Core Problems: Sec. 6.3 # 15, 23, 26 ; Sec. 6.4 # 2, 6, 10
Challenge Problems: Sec. 6.3 # 32, 33 ; Sec. 6.4 # 21
Note: A fixed point of a permutation sigma is an integer i such that sigma(i) = i.
Core Problems: Sec. 6.4 # 8, 9, 12, 14, 16
Challenge Problems: Sec. 6.3 # 35 ; 6.4 # 18
Core Problems: Sec. 7.1 # 6, 7, 11, 14, 19
Challenge Problems: Sec. 7.1 # 15, 16, 17
Core Problems: Sec. 7.2 # 1, 4a, 6 (see Prop. 2.1 of this section), 8, 9. (For 8e, you can work with the dodecahedron -- see the picture of this in its Wikipedia entry.)
Challenge Problem: Sec. 7.2 # 12 (you may use computer algebra software such as Maple or Mathematica to help with the matrix computations nif you like; also, remember that for a group acting on itself by conjugation, the stabilizer G_a of a consists of the elements g satisfying ga = ag).
Core Problems: Sec. 7.3 # 2, 5, 6b, 8, 9
There are no challenge problems this week. Have a good break!
This assignment is available here: Assignment 9
Although we just started Section 7.5 today (3/29), I have decided to assign some problems which depend on the material in the first few pages of that section (Propositions 5.2 and 5.3, and Example 2). I'll go over this on Tuesday. Note: Problem 11 does not depend on this material.
Core Problems: Section 7.5 # 2, 4, 5, 6, 7 abc, 11, 13.
(Remember, Test 2 is Thursday 4/12/12!)
Core Problems: Section 7.5 # 14, 16, 17, 19, 23 (add part (c): Deduce that G is abelian).
This assignment is available here: Assignment 12
Remember: Final Exam is Thursday, May 3, 12-3 pm.