Tuesday, May 01, 2007

Intuitive math stuff

While we are considering SIS 2K, these articles may be of interest to the entire school. The first is titled "Euler's beautiful equation" and the second " An Intuitive Explanation of Bayesian Reasoning".

4 comments:

Martin Weiss said...

I wonder if an intuitive explanation of the Shannon-Hartley theorem or the formulation of entropy might be helpful for SIS 2000 ... There is an interesting book "The Illusion of Reality" by Howard Resnikoff that gets into some of this, though it isn't what I could call "intuitive".

Prashant said...

The concept is really hard. Two of the most useful analogies I found, especially of the noisy coding theorem were something like this: Imagine a lumber plant (I don't know if this is the right term) where logs are being delivered at a certain rate. The output of the lumber plant is a conveyer belt that drops some planks if the packing is not correct. How should the lumber plant chop the logs into planks and at what rate so that the planks fit into the conveyer belt without being dropped?
The second analogy considers a water pipe and an inlet and asks how water may be fed into the pipe without spillage.

Martin Weiss said...

Appropos this topic, you might find this item of interest, especially with regard to different distribution types. Is this the level that is appropriate for SIS 20900?

Prashant said...

Thanks! Very interesting article - maybe useful to SIS 2K, but after some understanding of distributions perhaps. It does not explain the two distributions themselves to the point where a non-math oriented student can appreciate the discussion that follows. For instance, would such a student know why the average and standard deviation of the Pareto distribution are not "well-behaved"?