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Archive for February, 2011

Math Genealogy Project

February 14, 2011 3 comments

I traced my mathematical lineage back into the XIV century at The Mathematics Genealogy Project. Imagine my surprise when I discovered that a big branch in the tree of my scientific ancestors is composed not by mathematicians, but by big names in the fields of Physics, Chemistry, Physiology and even Anatomy.

There is some “blue blood” in my family: Garrett Birkhoff, William Burnside (both algebrists). Archibald Hill, who shared the 1922 Nobel Prize in Medicine for his elucidation of the production of mechanical work in muscles. He is regarded, along with Hermann Helmholtz, as one of the founders of Biophysics.

Thomas Huxley (a.k.a. “Darwin’s Bulldog”, biologist and paleontologist) participated in that famous debate in 1860 with the Lord Bishop of Oxford, Samuel Wilberforce. This was a key moment in the wider acceptance of Charles Darwin’s Theory of Evolution.

There are some hard-core scientists in the XVIII century, like Joseph Barth and Georg Beer (the latter is notable for inventing the flap operation for cataracts, known today as Beer’s operation).

My namesake Franciscus Sylvius, another professor in Medicine, discovered the cleft in the brain now known as Sylvius’ fissure (circa 1637). One of his advisors, Jan Baptist van Helmont, is the founder of Pneumatic Chemistry and disciple of Paracelsus, the father of Toxicology (for some reason, the Mathematics Genealogy Project does not list any of these two in my lineage—I wonder why).

There are other big names among the branches of my scientific genealogy tree, but I will postpone this discovery towards the end of the post, for a nice punch-line.

Posters with your genealogy are available for purchase from the pages of the Mathematics Genealogy Project, but they are not very flexible neither in terms of layout nor design in general. A great option is, of course, doing it yourself. With the aid of python, GraphViz and a the sage library networkx, this becomes a straightforward task. Let me show you a naïve way to accomplish it:

Categories: sage

Basic Statistics in sage

February 13, 2011 Leave a comment

No need to spend big bucks in the purchase of expensive statistical software packages (SPSS or SAS): the R programming language will do it all for you, and of course sage has a neat way to interact with it. Let me prove you its capabilities with an example taken from one of the many textbooks used to teach the practice of basic statistics to researchers of Social Sciences (sorry, no names, unless you want to pay for the publicity!)

Estimating Mean Weight Change for Anorexic Girls

The example comes from an experimental study that compared various treatments for young girls suffering from anorexia, an eating disorder. For each girl, weight was measured before and after a fixed period of treatment. The variable of interest was the change in weight; that is, weight at the end of the study minus weight at the beginning of the study. The change in weight was positive if the girl gained weight, and negative if she lost weight. The treatments were designed to aid weight gain. The weight changes for the 29 girls undergoing the cognitive behavioral treatment were

$\begin{array}{rrrrrr} 1.7&0.7&-0.1&-0.7&-3.5&14.9\\3.5&17.1&-7.6&1.6&11.7&6.1\\1.1&-4.0&20.9&-9.1&2.1&1.4\\-0.3&-3.7&-1.4&-0.8&2.4&12.6\\1.9&3.9&0.1&15.4&-0.7\end{array}$

Categories: sage, Statistics

A Homework on the Web System

February 4, 2011 Leave a comment

In the early 2000’s, frustrated with the behavior of most computer-based homework systems in the market, my advisor—Bradley Lucier—decided to take matters into his own hands, and with the help of a couple of students, developed an amazing tool: It generated a great deal of different problems in Algebra and Trigonometry. A single problem model had enough different variations so that no two students would encounter the same exercise in their sessions. It allowed students to input exact answers, rather than mere calculator approximations. It also allowed you to input your answer in any possible legal way. In case of an error, the system would occasionally indicate you where the mistake was produced.

It was solid, elegant, fast… working in this project was sheer delight. The most amazing part of it all: it only took one graduate student to write the codes for the problems and checking for validity of answer. Only two graduate students worked in the coding of this project, with the assistance of several instructors, and Brad himself. He wrote a fun article explaining how the project came to life, enumerating the details that made it so solid, and showing statistical evidence that students working with this environment benefitted more than with traditional methods of evaluation and grading. You can access that article either [here], or continue reading below.

Categories: sage