Max-Plus Algebras

Jul 13, 2009 by

Someone asked for a copy of my Master’s Thesis Max-Plus Algebra: Properties and Applications (written in 2002 when I was finishing my Masters in Mathematics at the University of Wyoming). I thought I would just make it generally available in case anyone else is interested.

The thesis explains what max-plus algebras are, relevant theorems and definitions, and illustrates examples of how max-plus algebras could be used.  For example, you could use Max-Plus algebras to calculate the quickest traffic route or finding the bottlenecks in a production line.

maxplus1

maxplus2

For the record, not one character of LaTeX was typed to write this thesis.  I typset the whole thesis using MathType and Word.

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Mathematical Algorithms and the AlloSphere

Apr 20, 2009 by

What is “The AlloSphere” ?

Watch the 7-minute TED video to see.  What you all might be interested in is what they do with the Allosphere.

Ann Kuchera-Morin: We map complex mathematical algorithms that unfold in time and space visually and sonically. Our scientist colleagues are finding new patterns in the information and our engineering colleagues are making one of the largest dynamically varying computers in the world for this kind of data exploration.

This reminded me of the city of Auroville , which I visited in India.  Both involve large spheres.  Both involve a strange collection of collaborators.  Only the AlloSphere is lot more high tech and focused on science instead of the human spirit.

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Claymation Topology

Apr 17, 2009 by

These claymation videos (posted over on Division by Zero) by Dave Richeson are absolutely fantastic!

First, Tying the Knot.

Second, Through one hole or two?

Whether you teach topology or not, you (and your students) should be able to appreciate these demonstrations. I hope there will be more coming!

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Math of the Brown Sharpie

Apr 1, 2009 by

Before the world-wide-web, I doubt that math cartoons could seriously have been a popular or widely read endeavor.  Today, geeky cartoons have their own fan followings curtesy of the long tail.  Probably you’ve heard of xkcd and Indexed.  If you haven’t seen Brown Sharpie, you should check it out.  Here’s a couple of my favorites (since many of you are on Spring Break).

Euler’s Formula on Spring Break

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Matrix Algebra Demos

Jun 20, 2008 by

Here’s a little collection of nice Matrix Algebra / Linear Algebra Demos that I found today:
1. From the Demos with Positive Impact site, a collection of Matrix Algebra Demos with voiceovers. These could be very nice lesson material for supplementing a hybrid/online course or for helping students who missed a day of class.

2. From Wolfram Demonstrations (remember you will need to download the Mathematica Player AND the demonstration in order to use and manipulate it)

3. Guess what? Gaming programmers need math. Amongst other things, they need to understand linear transformations! Want to prove it? Here is a website of “essential math” for programmers. Scroll down the page and you will find a powerpoint presentation on linear transformations and matrices.

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