Forum category: general discussion / announcements

Forum thread: Group Project ]]>

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.

Forum category: general discussion / announcements

Forum thread: Take-home portion of Exam 3 ]]>

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.

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Forum thread: Google Docs & LaTeX ]]>

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Forum thread: Examples of "good" group projects ]]>

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Forum thread: Math distraction ]]>

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Forum thread: Math distraction ]]>

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Forum thread: Math distraction ]]>

Forum category: technical questions / typesetting mathematics

Forum thread: LaTeX Help for Beginners ]]>

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Forum thread: normal symbol ]]>

Forum category: general discussion / help!

Forum thread: Chap. 9 Summaries ]]>

Forum category: general discussion / help!

Forum thread: Chap. 9 Summaries ]]>

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Forum thread: Discussion of draft project write-up with instructor (due Friday, May 7) ]]>

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Forum thread: NY Times Opinion article on group theory ]]>

Forum category: general discussion / help!

Forum thread: 8.32 ]]>

Thanks for pointing these out.

Forum category: general discussion / help!

Forum thread: HW 19 Hints ]]>

Forum category: general discussion / help!

Forum thread: 8.32 ]]>

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.

Forum category: general discussion / help!

Forum thread: HW 19 Hints ]]>

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Forum thread: Cayley diagrams ]]>

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Forum thread: 5.12 ]]>

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Forum thread: HELP DANA!!! ]]>

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Forum thread: 5.12 ]]>

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Forum thread: HELP DANA!!! ]]>

Forum category: general discussion / help!

Forum thread: HELP DANA!!! ]]>

Forum category: general discussion / help!

Forum thread: HELP DANA!!! ]]>

Forum category: general discussion / help!

Forum thread: chapter 4 summary ]]>

**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?

Forum category: general discussion / help!

Forum thread: chapter 4 summary ]]>

Forum category: general discussion / announcements

Forum thread: Cayley diagrams ]]>

i actually made my own pic and am going to try to input it into the chapter summaries. i will let you know if i have a problem though.

thanks

Forum category: general discussion / announcements

Forum thread: Cayley diagrams ]]>

Forum category: general discussion / announcements

Forum thread: Cayley diagrams ]]>

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

Forum category: general discussion / announcements

Forum thread: Take-home portion of Exam 2 ]]>

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Forum thread: Review Session ]]>

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Forum thread: Sarah & Leal & Dana ]]>

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Forum thread: Hudson River undergrad math conference ]]>

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Forum thread: Review Session ]]>

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Forum thread: Review Session ]]>

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Forum thread: 5.5.d ]]>

Forum category: general discussion / help!

Forum thread: 5.5.d ]]>

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.

Forum category: general discussion / announcements

Forum thread: group project wiki pages ]]>

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Forum thread: Alice In Wonderland ]]>

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

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Forum thread: Alice In Wonderland ]]>

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Forum thread: Sage Lab 3 is graded ]]>

Question 1: In $A_4$, does $(01)(23) = (01)(23)$?

I think you'll have to try again on that. I'm not sure what you meant to ask. However, note that in this class, we would use the numbers 1, 2, 3, 4 to make permutations in $S_4$ and $A_4$, rather than 0, 1, 2, 3. I'm guessing that you got this notation from Group Explorer. It doesn't really matter what we use, but we should try to be consistent and be sure that we can translate back and forth if we are going to start changing formats.

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

Well, I guess you could, but the point is to understand how to compute them by hand. If you are confident that you know how to compute them, then using Group Explorer to speed up the process is fine. Of course, you can use Group Explorer to check your work. However, in the case of $A_4$ in $S_4$, I'm way too lazy to write them all out by hand. Instead, it pays to be clever. Remember, the cosets partition the big group. Since $A_4$ is exactly half of the elements in $S_4$ and all of the cosets turn out to be the same size (we haven't officially proved this yet, but in each specific case, it is easy to convince yourself that it has to be true), there can only be one other coset, namely the set of odd permutations. We can represent this coset using any odd permutation. For example, since $(12)$ is odd, $(12)A_4$ (this is of the form $gH$) is one of the many ways to name this second coset. In summary, there are precisely two left cosets (and hence right cosets since there isn't any "wiggle" room): $A_4$ and $(12)A_4$.

Forum category: general discussion / help!

Forum thread: 5.5.d ]]>

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

Forum category: general discussion / help!

Forum thread: 5.5.d ]]>

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Forum thread: cycle product help ]]>

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Forum thread: cycle product help ]]>

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Forum thread: cycle product help ]]>

$g_1H=g_2H$ iff $g_1H\subseteq g_2H$.

I hope that helps. If not, ask again.

Forum category: general discussion / help!

Forum thread: hw 16 clarification ]]>

Forum category: general discussion / help!

Forum thread: hw 16 clarification ]]>

Forum category: general discussion / announcements

Forum thread: Chapter 5 summary is ready for entries ]]>

- 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.

Forum category: general discussion / announcements

Forum thread: Topic selection for group project and other reminders ]]>

I have done the activities of dividing a circle and rearranging the pieces to make a parallelogram, using string to measure different circumferences and their respective diameters (and then graph the result - a line that is $\pi$), and actually doing Archimedes' method of exhaustion to approximate $\pi$ when teaching about circle area in middle school. At the time I wasn't thinking about limits or calculus… but now I will.

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Forum thread: NY Times opinion article on limits and pi ]]>

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Forum thread: Sage Lab 4 ]]>

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Forum thread: NY Times opinion article on limits and pi ]]>

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Forum thread: Sage Lab 3 & group selection for project due today ]]>

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Forum thread: Typo in Sage Lab 3 ]]>

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Forum thread: Testing for Sarah ]]>

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Forum thread: Testing for Sarah ]]>

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Forum thread: Testing for Sarah ]]>

Forum category: general discussion / help!

Forum thread: HInt for Exercises 4.26a and 4.26b has been fixed ]]>