A Mathematician Goes on Vacation 3

As I said the first week it rained...a lot. That wasn't all bad. I did get a chance to read a bit. I brought along On Aggression by Konrad Lorenz. I'm not much of a biologist so a lot of the animal behavior descriptions flew over my head. But, I felt right at home with the above diagram. How nice to find a Caley table in the middle of a ten page meditation on the nuances of the duck and drake mating ceremony! Remember your multiplication tables? This is a binary operation. A binary of operation of what? Lorenz call the above diagram a motivational analysis Each picture on the diagram is a combination of the dog's fight or flight instincts. If you go down the left most column, you are seeing the progression of the flight instinct. Going across the top most row, you are getting the progression of the fight instinct. Any other image is some combination of the two instincts. All part of the math of mother nature. Quite interesting!

Using xtimeline in class

Here is an interesting project my math for liberal arts class started. They used xtimeline to start a history of math timeline. We're a small class so there are only around 10 posts right now. I hope to grow this over the semesters. It was my first project like this. I waffled between using xtimeline and TimeToast. I liked TimeToast better visually, but it doesn't accept BC dates. That's fatal for a history of math timeline. xtimeline also allows multiple editors. The down sides are the appearance and the embed code is slow to load and akward. I'd like to hear in the comments of experience with similar net apps. I'm planning on doing my course schedule on one of these next semester.

Below is Jim R's Tunxis timeline. He tipped me off on this nice set of web tools. Thanks, Jim!

Using Selectricity

I'm entering a unit on elections in my Math for Liberal Arts class. There are a lot of slick tools out there to run online polls like PollDaddy. I was having trouble finding any tool that allowed user's to fully order their preferences... until Selectricity. It's a really great tool, particularly if you are studying elections. Check out this poll, it allows you to see current results, and the current winner under a number of common election systems: Borda, Condorcet, etc. Anyone can create an election without registering. For more extensive security measures, register for a full account. All free!

pic by Enrico Fuente

Understanding Instant Runoff

I've been crawling the web, gearing up to teach voting systems in my Math for Liberal Arts course. I want to pass on this interesting site.

The voting that we do in the US is a modified plurality vote. One problem with our system is that often the winning canidate has not garnered a majority. One popular alternative used frequently in other countries is run-off voting, or what we call the Hare method in class. I found a video (below) and a great site, Choiceranker to explain how run-off voting works. Choiceranker even gives you the chance to participate in opinion polls that use the run-off method. Check them out.

Really Cool Visual Algorithm for Multiplication

One of my students in math for Liberal Arts dug this up on YouTube. I had never seen this technique for multiplication before. I love it--completely visual. Thanks, Rachael!

Twitter's Rising Popularity < Twitter's Rising Cost ?

I picked this up on a data mining feed. A really interesting discussion is brewing on how much it costs twitter to maintain it's network. The worry is that users getting SMS messages are going to eat the network out of house and home as the network gets larger. Here is a really simple demonstration of where the worries come from. Say it costs twitter $100 a year to maintain a the correspondence between any two users.



One can see adding a third user increases the overall cost of the network by $200. Adding the fourth will increase the cost by $300. You see where this is going. The fifth member will increase the cost by $400...and the nth member will increase the cost by (n-1)*100.

Now Twitter's actual case is much more complicated. First, each new member doesn't connect with every single old member. Second, some links cost more than others. Third, the more members, the greater twitter's add revenue (I assume they are add-based). This helps offset the greater costs.

Curious? Here is Paul Botin's post that started the discussion.

I came a cross the discussion reading Mathew Hurst's critique of Botin describing the growth of costs as "exponential". The math snark in me also laments the imprecision with which this word is often used.

Project Euler

Great problems are really hard to come by. Great problem sets are even harder. I just ran into Project Euler online. I'm really blown away. I would love to use this in one of my courses.

Project Euler is a sequence of 220 problems. The problems are designed to be an "inductive chain learning" experience for the solver. This is from the PE website:

The problems range in difficulty and for many the experience is inductive chain learning. That is, by solving one problem it will expose you to a new concept that allows you to undertake a previously inaccessible problem. So the determined participant will slowly but surely work his/her way through every problem.

Let me know if any of you are working your way through the problem set at the moment.