For a copy of the course syllabus, click here

Homework 1 (due Friday, Jan. 18)

• Page 8-9, #4, 8, 11.

• Page 16-17, #1,3,9.

• Page 23-24, #1,4,6,7.

• Show that if a | bc, then a | ( gcd(a,b) gcd(a,c)).

• Show that if ax == ay (mod N), then x == y (mod N/gcd(a,N)).

Homework 2 (due Friday, Feb. 1)

• Page 35-36, #1,2,6,11,14,21.

• Page 48-49, #2,3,4,5,6,12,13,15,19,38.

• *** Your first exam will be Friday, Feb. 15. ***

• I believe I said that all your problems in this last homework can be solved in ``one line''. This is not exactly true -- most will take a couple lines perhaps. Problem #38 is the only one that might pose some difficulty (as far as finding a short proof).

Homework 3 (due Friday, Feb. 15 -- before exam)

• Click here for some extra problems.

• Page 53, #1,2,4,7, 12 (assume in 12 that the group is finite). Also, show that the opposite of a group G is isomorphic to G -- Recall that G^opp = opposite of G, which is the group with operation * such that a*b in G^opp is the same as ba in G.

• Page 64 - 65, #1,3,6,8,10.

• Here are some old homework writeups from the last time I taught this course, which should be useful to study for the exam: 1. and 2.

• Click here for a note I wrote on group actions (handed out in class).

• Extra Problem for homework: Show that if phi is an isomorphism from a group A to a group B, and if x is in A, then order(phi(x)) equals order(x).

• Page 70, #1, 5.

• Click here for a copy of an old midterm.

Homework 4, due Feb. 29

• Page 75-75, #1, 5, 8.

• Page 80-81, #1, 2, 3, 11, 12, 18, 20.

• Click here for a writeup of the proof that A_5 is simple.

Homework 5, due March 14

• Page 90, #1,4,5,14.

• Page 101, #1,7,9,15.

• Click here for an old homework writeup from the last time I taught the course (some of these coincide with some of homework 4).

• Click here for a short writeup that A_n is generated by the 3-cycles.

• Page 108, #1,6,8.

• Page 115, #4,6,9.

• These are to be turned in next time: Page 116-117, #2, 4, 11, 14.

• Click here for an old homework writeup, which should coincide with some of the assigned problems.

Homework 6, due April 4.

• Page 130, #1, 3, 7, 12.

• *** Don't forget that your next midterm is on Monday, April 7. ***

• Click here for a copy of a practice midterm. Your midterm will have more material on it than this, but will still be only 5 questions.

• Click here for a study sheet for the exam.

Homework 7.

• Page 135, #3.

• Page 139-140, #1, 3.

• Page 142-143, #1, 6.

• Page 149, #1, 2, 3, 5.

• Page 152, #1, 2, 3, 4, 5, 6, 7.

Homework 8, due Friday, Apr. 25.

• Page 158, #1, 2, 3, 4, 6.

• Page 161, #1, 2, 3.

Your final exam will be Monday, Apr. 28 from 2:50 - 5:40. Check back later for a list of topics to study for the final (I will try to put it up by Saturday night.)

Click here for a copy of the final exam study sheet.

The test will have 10 questions, and you will choose 8 to work. The test is *very* challenging. I anticipate the median score to be around 40-50%, requiring a curve; and the highest will be probably around 80%, but those who have consistently worked the homeworks and attended the lectures should do OK.

Click here for a copy of the final exam.