The project, due Wednesday, May 7, in class: Project assignment. Homework #11 is due Wednesday(!), April 30. 4.3 6,22 4.4 1,2 (these are the facts I used in class today) 4.4 8 Also think about the question I asked in class. If I change 0 to any other number in the evaluation mapping from the polynomials to the real numbers, would that mapping still be a homomorphism? (Yes.) What will be the kernel? Solutions to Test #5. Extra Credit problem solution. About the test on Friday: There will be 4 problems on the material from Chapter 3 that we covered, similar to homework problems, and the sections 4.1 to 4.3 up to and including the last homework. Homework #10 is due Monday, April 21. 4.1 1,2,3,21 4.2 1,2 4.3 1,2,3,4,5 Homework #9 is due Monday, April 14. 3.1 1,2,4 3.2 2,3 3.3 1,2,3 This is the complete homework assignment. A solution of question 2 from Test #4. Homework #8, due March 31 (there is no HW due Monday after the break): Read Theorem 2.5.6 on page 72 and its proof that is given BEFORE the theorem on pp. 71-72. Do the problem I stated in class: the notion of an isomorphism between two groups is defined on page 68, and there is a brief discussion on that page afterward. My problem is related to problem #2 in the book. I want you to check the inverse to an isomorphism is also a homomorphism. Then do #2 on page 73. In this problem you check that being isomorphic is an equivalence relation on the set of all groups. 2.6 #7,8,9 2.7 #2,3,4 One more problem for Monday: illustrate the homomorphism theorems by relating the lattices of subgroups for Z_16 and Z_8, where Z_16 is being mapped to Z_8 by reduction modulo 8. This is the same kind of computation that I did in class for Z_12 and Z_6. Solutions to Test #3. Homework #7: 2.5 #12,15,16,17,18 #24,26,27 2.6 #3,4,5,6 This is the complete homework assignment for Monday, March 10. Homework #6: 2.5 #1,6,7,14,22 This is the complete homework assignment for Monday, March 3. Solutions to Test #2. Homework #5: 2.3 #12,14,26,27 (last two are "hard" but think about them before I discuss them in class) 2.4 #5,9,10,11 This is the complete homework for Monday, February 24. Homework #4: 2.2 #1,2 2.3 #1,2,4,5,6,7,19 2.3 #3 This is the complete homework for Monday, February 17. Here is the final detail for the proof that the rule given in #1(d) on page 46 is indeed a group operation. Solutions to Test #1. Homework #3: 2.1 #14,15,16,17,25 This is the complete homework to turn in on Monday, February 10. Homework #2: 1.3 6,7,9,24,28 (this is the quesion I mentioned in class),30 (this is fun but not easy) 1.4 2,5,8,9,15 2.1 1,8,9,26 This is the complete homework for Monday, February 3. Related to the project announced in class, here is a link to the number of groups of order N. Also, I want to announce the first test that will be in class on Friday, February 7. Homework assignments start here. This is for week 1. These problems are due in class on Monday, January 27. 1.2 Make sure you are familiar with the material in 1.2 before the definition of the Cartesian product of sets on page 5. Do problems ## 14,15,20 on page 7. Also do the problem I suggested in class: verify at least 4 different places in the multiplication table for the symmetries of the square. What you really need to do is see what the composition you are looking at does, then check what it does to the corners, then match that action with the action of one of the 8 symmetries. 1.3 3,8,16,17,18 on pages 13-14 This is it for this week.