AA II Taking Over Math Club

This Wednesday, April 27th, Dr. Savic’s Abstract Algebra II students will host an exhibition of children’s books and mobile apps about Abstract Algebra! Come and learn from their creative endeavors!  The art exhibition will run from 6-7.  From 5:30-6 there will be officer elections for next year.

As always, there will be pizza.  Hope to see you all there!

Here are the details:

When: Wednesday, April 27, at 5:30

Where: PHSC1105

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Game about squares.

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From the Department of “I have too much time and I want to waste some”, here is a fabulous game that you can check out. The beauty of it is that you figure out the rules as you go (the silly comments when you clear each level are just a bonus), and some mathematician (Jens Massberg) just wrote a paper on the game showing it is NP-hard.

Here is the game: http://gameaboutsquares.com/

and here is the link to the article on NP-completeness:

http://arxiv.org/abs/1408.3645

What is NP-hard? Well… here you go:

http://en.wikipedia.org/wiki/NP-hard

The Rubik’s Cube celebrates 40 years.

The beloved Rubik’s Cube turns 40 this year. And a celebration is under way to celebrate its enduring appeal. Created by Erno Rubik, a Hungarian architect and designer, it was initially sold as a toy at fairs before becoming an international phenomenon. “Speed cubing” is a recognized championship sport where participants compete to solve a randomized cube in the shortest possible time. The world record: 5.5 seconds.

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The cube has inspired a lot of beautiful mathematics including the notion of a Rubik’s cube in higher dimensions (and an appropriate algorithm to solve it).

See this article for the traveling exhibit:

http://online.wsj.com/news/articles/SB10001424052702304518704579523513594900696

2048

Perhaps you have heard of the extremely addictive new game “2048” created by Gabriele Cirulli. The object is to combine numbers (powers of 2) by sliding tiles and getting to 2048. This is much harder than it appears. The game was in turn inspired by the simple (and also addictive) game “Threes” by Asher Vollmer.

2048

It is easier to play it and understand it than write a long explanation about it. The potential for mathematical explorations from this game are obvious and enormous! Go check it out and when you emerge after several days please do not curse the blog for sucking up your time!! You can find the original game here (there are already several clones):

http://ov3y.github.io/2048-AI/

and here are some variations. The first variation below generates Fibonacci numbers rather than powers of 2. The second one is based on divisibility. Enjoy!!!

http://themoreyouknow.github.io/fib/

http://themoreyouknow.github.io/div/

Here is a link to the original “Threes” by Asher Vollmer.

http://asherv.com/threes/

Tossing unfair coins.

We take a break from blog posts on REU’s, career advice and conference announcements and ruminate a bit on mathematics. Here is a question that probably comes up in a probability class (ha ha, yes pun intended).

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You are given a random coin and you have to come up with a way to determine two outcomes with equal probability. How do you do that?

“Well, OU Math Blog”, you might say, “just flip the coin!” Trouble is, most coins are biased. As a mathematician one would like to know a way to achieve a (near) perfect 50-50 outcome. Can this be done? Well, yes, and if you want to think about it, then Spoiler Alert! Stop reading now!

Let us say that whatever coin you are given has some (biased) probability of returning Heads; let us call this  α. Then assuming that the coin won’t land on its edge (a fairly safe assumption given the nature of gravity) the probability of getting Tails must be 1 – α. The following protocol will now generate a theoretically 50-50 outcome no matter the bias of the coin. Toss the coin twice and select the following two outcomes as “Heads” and “Tails”: let’s say the outcome HT is “Heads” and the outcome TH is “Tails”. If the outcome is HH or TT, then start over (i.e., toss twice more). By the independence of Bernoulli trials, the probabilities of the event HT is α(1 – α) while the probability of the event TH is (1 – α)α i.e., they are equal! The only drawback with this method is that this is not guaranteed to end in finite time. One could theoretically keep tossing HH or TT indefinitely and thus have to keep going. But, it provides an elegant solution to the problem of tossing a coin when one does not know the bias of the coin.

Question: The above solution is near perfect in that we had to discard the possibility of the coin landing on its edge. Is there a way out of this dilemma?

Field Trip to Phillips 66 offices in Houston

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Would you like to know more about career and networking opportunities at Phillips 66? They have invited a small number of students for a field trip to their corporate offices on Wednesday, March 19th, 2014 (during Spring Break). This will be a day trip and there is even some funding provided by the company to help with students’ travel expenses.

If you are interested in being selected to join this trip, then please contact Adrienne Jablonski, Director, Student Career and Leadership Development (Ellison Hall).