in discussion Homework and Discussions / Assignments » Homework Assignment 7 - Due Friday, December 11

Section 13: 1, 2, 4, 5, 8, 18, 20, 23, 36, 43, 50, 52

Section 14: 1, 5, 17,; 31

Section 15: 37 (Extra Credit)

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profedgar 03 Dec 2009 21:09

in discussion Homework and Discussions / Assignments » Homework Assignment 7 - Due Friday, December 11

in discussion Homework and Discussions / Assignments » Homework Assignment 7 - Due Friday, December 11

Section 13: 1, 2, 4, 5, 8, 18, 20, 23, 36, 43, 50, 52

Section 14: 1, 5, 17,; 31

Section 15: 37 (Extra Credit)

profedgar 18 Nov 2009 06:17

in discussion Homework and Discussions / Assignments » Homework Assignment 6 - Due Wednesday, November 25

in discussion Homework and Discussions / Assignments » Homework Assignment 6 - Due Wednesday, November 25

Section 10: 3, 4, 6, 15, 19abcde, 20, 21, 22, 23, 28, 29

Wiki:

1. Find a subgroup of your adopted group.

2. Write out some (or all) of the cosets of your subgroup from 1.

profedgar 26 Oct 2009 21:41

in discussion Homework and Discussions / Assignments » Homework Assignment 5 - Due Wednesday, November 4

in discussion Homework and Discussions / Assignments » Homework Assignment 5 - Due Wednesday, November 4

Section 8: 1, 2, 5, 6, 9, 11, 12, 16, 30, 33, 35cefgh, 40, 46, 48.

**Extra Problem:**

Let $G$ be a group, and let $H$ be a subgroup. We define a relation $\sim_H$ on the group in the following way. For any two elements $a,b\in G$, we let $a\sim_H b$ if and only if $ab^{-1}\in H$. Prove that $\sim_H$ is an equivalence relation.

profedgar 13 Oct 2009 00:35

in discussion Homework and Discussions / Assignments » Homework Assignment 4 - Due Monday, October 19

in discussion Homework and Discussions / Assignments » Homework Assignment 4 - Due Monday, October 19

Section 5: 2, 3, 6, 9, 21, 41, 43, 52, 54

Section 6: 1, 4, 7, 12, 17, 22, 32ab, 33, 46, 52, 55

profedgar 01 Oct 2009 05:29

in discussion Homework and Discussions / Assignments » Adopt A Group Project

in discussion Homework and Discussions / Assignments » Adopt A Group Project

Josh,

Yes, it is the number of even permutations inside of S5. The only question remaining is what even permutation of S5 means formally. The book may define it, but I am not sure what it says. This group may require you to understand S5 first, and then understand A5 as a subgroup.

J_Dearth 01 Oct 2009 04:46

in discussion Homework and Discussions / Assignments » Adopt A Group Project

in discussion Homework and Discussions / Assignments » Adopt A Group Project

So just to get a little bit clearer of a picture (but yes will be coming to see you tomorrow afternoon) the order of the alternating group on the set {1,2,3,4,5} is the number of even permutations on A5? Thanks again. See you tomorrow.

profedgar 01 Oct 2009 04:33

in discussion Homework and Discussions / Assignments » Adopt A Group Project

in discussion Homework and Discussions / Assignments » Adopt A Group Project

Josh,

Come by sometime to talk about this. Essentially, a permutation is a function mapping the set {1,2,3,4,5} 1-1 and onto itself. Any function will do, and is a permutation. An alternating permutation is one that "swaps an even number of things." For instance the function that swaps 1 and 2 and fixes 3, 4, and 5 is not an even permutation, but the function that swaps 1 and 2; and 3 and 4; and fixes 5, will be an even permutation. This may take a while before we get to it in class, so you might be better off coming to discuss it with me.

J_Dearth 01 Oct 2009 03:55

in discussion Homework and Discussions / Assignments » Adopt A Group Project

in discussion Homework and Discussions / Assignments » Adopt A Group Project

Dr. Edgar,

So what exactly is a permutation group. I am trying to figure out what an alternating group is but I have yet to even figure out what my operation is? I know what my set is but I don't know my operation and I think it has to do something with the fact that everywhere I look it says it is a permutation group. Is the permutations the number of times a number can be "alternated" with another number in the set? ie. swapped? Also, is there a set number of permutations allowed in the A5 set? Sorry for all the questions but this is burning me up right now. Thanks.

Josh

profedgar 26 Sep 2009 23:35

in discussion Homework and Discussions / Assignments » Homework Assignment 3 - Due October 2

in discussion Homework and Discussions / Assignments » Homework Assignment 3 - Due October 2

Section 3: 2, 3, 4, 8, 21, 26, 30

Section 4: 41

Section 3: 11, 12, 17, 27

and Prove: The inverse property is a structural property.

in other words, Let $(S,*)\cong (T,\star)$ be isomorphic binary structures via the bijection $\varphi:S\to T$. If $a\in S$ has an inverse, $a'$, then $\varphi(a)$ also has an inverse and $\varphi(a)'=\varphi(a')$ as expected.

profedgar 16 Sep 2009 21:35

in discussion Homework and Discussions / Assignments » Homework Assignment 2 - Due Friday, September 25

in discussion Homework and Discussions / Assignments » Homework Assignment 2 - Due Friday, September 25

Section 1: 22, 23, 31, 33, 34

Section 2: 1, 2, 4, 7, 8, 17, 23, 24adgj, 26, 27, 29, 36.

Section 4: Pick four from (1, 2, 3, 5, 6, 7, 8); Do 10a, 12, 19, 29, 32, (33 or 35), 36.

profedgar 11 Sep 2009 21:20

in discussion Homework and Discussions / Assignments » Homework Assignment 1 - Due Friday, September 18.

in discussion Homework and Discussions / Assignments » Homework Assignment 1 - Due Friday, September 18.

The homework due on Friday is as below. Please check this regularly as I will add to it after Monday, September 14.

Section 0: 1, 3, 4, 6, 8, 9, 12af, 14a, 15, 25, 30, 31, 34, 35c, 36a.

Bonus Problem: Section 0 #18

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