Also, don't forget to add an entry to the chapter summaries. Like last time, for this round, each individual only needs to do one.

]]>Google Docs already had the ability to insert math symbols, but this is pretty limited. With LaTeX Lab, you have the full power of LaTeX and all of the cool collaboration tools of Google Docs.

]]>I think that the last sentence for hint for 8.31 should refer to "symmetric (blah), reflexive (blah), and transitive (not symmetric as it is now) ( blah). "

And the hint for 8.7 should say "prove" instead of "proof" in the first sentence or so.

]]>**Product of Cycles:**

If $\alpha = (1352)$ and $\delta = (256)$ then $\alpha \centerdot \delta = (1652)(34)$.

Can someone explain this to me. I don't see a 4 in $\alpha$ or $\beta$, so how can it be in the product of the two?

]]>Also, don't forget to add an entry to the chapter summaries. For this round, each individual only needs to do one.

]]>The first thing you will do is use these pages to create your outline (due by 5PM on Friday, April 16). So that you don't have to do any unnecessary work, you should write your outline in a way that it will be easy to turn it into the write-up for your project. So, don't do any formatting that you'll have to undo later. Your outline does not need to be written in any particular way.

]]>[ http://www.maa.org/devlin/devlin_03_10.html] ]]>

Question 2: Can we copy the cosets for a group from Group Explorer, as I did for 5.5.d for $A_4$?

]]>- Don't forget that each group needs to discuss the topic for their group project with me before 5PM on Friday, April 9. A few groups have already fulfilled this obligation. I'll be happy to discuss topics with groups that are having trouble selecting a topic. If you haven't already, please read the group project guidelines and let me know if you have any questions.
- Don't forget to add at least one entry to the chapter summaries prior to the next exam.
- The next exam is on Tuesday, April 20 and the take-home portion of the exam is due Friday, April 23 by 5PM.

Also, as some of you realized, there were some errors in the chapter summaries for the last exam. Eventually, these should be fixed. For the next exam, you'll be getting the new summaries plus the old summaries (which will hopefully include some corrections and updates). Adding an entry to one of the old chapter summaries also counts as an entry.

]]>Also, it'll be a miracle if I finish grading the exams by tomorrow morning. However, I'll have them done sometime on Friday. I'll post a message here and send an email when they are done, so that you can come take a look if you are interested.

See you bright and early!

]]>Here are some other general comments:

- The entries in both of the Cayley tables were x0, x1, x2, x3, x4, x5. These are the names of the elements. In this case, x0 (and so on) is short for $x_0$. If you check the "
`typeset`" box at the top of the Sage worksheet and re-evaluate the cell, you'll see what I mean. - Many of you tried to appeal to the fact that these groups corresponded to $\mathbb{Z}_6$ and $D_3$, which I told you. However, this information is completely unnecessary. You can answer all of the questions by just looking at the tables.
- Saying that these two groups are different by saying that their tables look different is not sufficient. It's possible that the entries in the table for $H$ are just the elements for $G$ that have been relabeled and rearranged. Here's an analogy. Imagine a team of 6 people standing in a line each wearing a jersey with a number on it. Now, have the team swap the jerseys around and stand in a different order. It's the same team, right? The answers to the questions I asked you could all be used to argue that $G$ and $H$ are really different. For example, one group is abelian and the other is not. Another reason is that one group has more elements than the other that are their own inverses.

http://opinionator.blogs.nytimes.com/2010/03/07/finding-your-roots/?ref=opinion&ref=opinion

It's a worthy read and if you look closely the author is discussing group theory (look for the pictures involving 90 degree rotation).

]]>I'll be around all day on Monday if people have questions for me.

Dana

]]>The next film is “The Proof” and will be shown this Thursday, March 4. Refreshments will be provided beginning at 3:45 in Hyde 318.

“Follow a fascinating tale of obsession, secrecy, brilliance and the camaradarie of kindred souls. For Princeton math whiz, Andrew Wiles, tackling an equation is like groping around in a dark mansion, finding the light switch and suddenly seeing, with utter clarity, where you are. But in Wiles case, proving Fermat’s Last Theorem would take eight years of seclusion.” NOVA

Futures film dates are scheduled for March 10, March 18, April 1, April 7, April 15, April 22. May dates TBA. Mark you calendars and join us!

]]>(4) Which elements commute with every other element? ]]>

14: Given the groups $\mathbb{R}*$ and $\mathbb{Z}$. Let $G=\mathbb{R}^* \times \mathbb{Z}$. Define a binary operation $\circ$ on $G$ by $(a,m) \circ (b,n) = (ab, m+n)$. Show that $G$ is a group under this operation.

]]>Thanks a billion.

My username is: asewell.

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