Jason Underdown’s Blog

It does not surprise me that Rush Limbaugh would think that Energy Secretary Stephen Chu’s proposal to paint flat roofs white is idiotic, but I found it rather amusing that he couldn’t even figure out how reflection works on his radio talk show this morning. This is a very simple idea, light colors are brighter or lighter than dark colors because they reflect more light. The key is to understand that light is energy and light that impinges upon dark surfaces is far more likely to be absorbed and converted to kinetic energy, a.k.a. heat. Although I’m not sure, I bet the reason for only painting flat roofs white is because slanted roofs will reflect the light such that it will travel through far more of the earth’s atmosphere and therefore almost certainly be absorbed by the air, whereas a flat roof will reflect the light nearly vertically and thus the photons will be far more likely to escape our atmosphere back out to space. The solution is simple and cheap, yet elegant in its simplicity.

I feel that anybody who has completed a high school education in this country should be able to come up with the explanation that I just gave above, but the sad fact is that probably the majority of American’s could not give such an explanation, despite the fact that the overwhelming majority of Americans have completed high school. Science has been the hallmark of the advancement of all civilizations, why is “illiteracy” in science (and innumeracy) so acceptable in our society? Although left wing extremists will jump at the opportunity to make Rush look stupid, the general public won’t care. Although it is possible that Rush was being disingenuous and really did understand the simple ideas behind the proposal, but feigned ignorance for political reasons, I am more inclined to believe that he was being honest when he said he didn’t understand how it works.

We really need to look at how we teach in this country, and start experimenting with radical new approaches because this perfectly illustrates how inadequate current methods are. I realize changes in how science is taught have been made since Mr. Limbaugh attended school, but I am quite certain that most recent graduates would respond similarly.

This post details how to make high quality, printable flash cards like I have available at my web site. I am assuming you are using Ubuntu Linux. I did this on Ubuntu 8.04 (Hardy Heron), but it might work on some previous and later versions as well.

First you want to install LaTeX, plus Andrew Budge’s flashcards package. Open a command terminal and type in the following command to install TeX and LaTeX. The flashcards package resides in the texlive-latex-extra Ubuntu package.


$ sudo apt-get install texlive texlive-latex-extra


I also recommend installing Kile which is a great program for editing TeX/LaTeX documents. You can do this with the following command. Depending on your system configuration, apt-get might require you to install several extra packages. The following is optional:


$ sudo apt-get install kile


At this point, if you try to compile a latex document that uses the flashcards package, you’ll get the following error:


! Package geometry Error: You must set \paperwidth properly.


To fix this, we need to create a small file called geometry.cfg, which tells the geometry packages which type of paper we will be using. Create the file using the following command:


$ sudo gedit /usr/share/texmf-texlive/tex/latex/geometry/geometry.cfg


Now copy and paste the following into gedit, save the file and exit from gedit.


%%
%% This is file `geometry.cfg',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% geometry.dtx (with options: `config')
%%
%% File: geometry.dtx Copyright (C) 1996-2002 Hideo Umeki
%% (hideo.umeki@toshiba.co.jp)
%%
%% This package may be distributed under the terms of the LaTeX
%% Project Public License, as described in lppl.txt in the base
%% LaTeX distribution, either version 1.2 or (at your option)
%% any later version.
%%

%% Uncomment and edit the line below to set default options.
\ExecuteOptions{letterpaper,dvips}

\endinput
%%
%% End of file `geometry.cfg'.


Now, you should be able to compile a LaTeX document that uses the flashcards package without errors, but there will be some warnings. To fix the warnings, we need to change one line in flashcards.cls.


$ sudo gedit /usr/share/texmf-texlive/tex/latex/flashcards/flashcards.cls


The following diff command shows the change you need to make:


$ diff -ru flashcards.cls.bak flashcards.cls
--- flashcards.cls.bak 2009-01-26 17:15:27.000000000 -0700
+++ flashcards.cls 2009-01-26 19:43:57.000000000 -0700
@@ -83,7 +83,7 @@
top=\topoffset,
left=\oddoffset,
right=\evenoffset,
- twosideshift=\oddevenshift,
+ twoside=true,
bottom=0.0in,
noheadfoot}
\ifthenelse{\boolean{flashcards@dvips}}{\geometry{dvips}}{}


Now you should be able to compile a LaTeX document without any errors or warnings, excepting for any errors in your own markup of course.

This code generates fractals based upon an iterated function system (IFS). Several input files and a Makefile are included. The code is written in C++, and distributed as a tarball. I did this for a class at the University of Utah, but it is based upon a homework assignment for a computer graphics class at MIT (6.837).

Below is the famous Barnsley fern which was generated by an IFS with just four transforms!

I modified my Sierpinski triangle code so that it now allows you to adjust the contraction mapping constant. Normally one uses a contraction mapping constant of 1/2 but if you invert that and instead use an expansion mapping constant of 2, then you get the following pretty picture.

The New York Times has an excellent op-ed piece today on college admissions. Read the article, and you’ll see why test prep centers like Kaplan are doing so well.

Here are the classes I’m taking this fall:

• Introduction to Complex Analysis
• Introduction to Topology
• Research Experience for Undergraduates: Metric Spaces, The Contraction Mapping Principle, Fractals and Other Applications

I added an RSS feed to update anyone interested on changes I’ve made to my Math and Physics flash cards page.

In my last post, I mentioned that I had created some flash cards for Real Analysis that had definitions on them. I recently created a set with many of the relevant theorems, and I will be updating them as the summer progresses. Thanks to Erin Chamberlain for providing the source TeX code for the theorems. You can find them at

http://www.physics.utah.edu/~jasonu/flash-cards/

Enjoy!

I’ve been busy this summer studying Real Analysis, and in the process I’ve made a set of printable flash cards in PDF format. They’re still a work in progress, but I have over 90 cards full of definitions. Cards with theorems on them will probably come some time later. The pictures below show what the typical front and back of a card look like.

Below is a very interesting video clip which explains the Mobius transformations as simple motions of a sphere. I found this on Mark Chu-Carroll’s “Good Math, Bad Math” blog.

I have an RSS feed from Boing Boing on my Google home page, and today they have a posting about University of Utah physics professor Orest Symko! The post describes his research into turning waste heat into electricity via an intermediary acoustic step.

It seems to me that the solar updraft tower might be a good match for this technology.

I’ve added a C++ class that handles gravitational potentials to my Kaliope project. Below is a picture of a binary cluster orbiting around a logarithmic potential well. A logarithmic potential is the simplest kind of potential well. It corresponds to an inverse distance radial force field.

Here is a slightly different simulation, with each body given its own color, so it is easier to see individual paths:

I’ve been a big fan of Dilbert for years now, but I recently found a great webcomic that I’ve started reading daily called XKCD. The tagline is: A webcomic of romance, sarcasm, math, and language. The drawings are simple stick figures, but it is the situations and ideas that are interesting and funny.

While googling for information on the Virial Theorem, I ran across a really cool page hosted at the Harvard ADS system. ADS stands for Astrophysics Data System, and it is primarily an abstract search engine that helps you locate journal articles mostly in the realm of Astronomy and Astrophysics, but they also have a small virtual library of books that you can freely download.

Here are the titles I found interesting:

• The Foundations of Celestial Mechanics by George W. Collins, II
  (1989, 2004).
• The Fundamentals of Stellar Astrophysics, by George W. Collins, II
  (1989, 2003).
• Fundamental Numerical Methods and Data Analysis by George W. Collins, II
  (1990, 2003).
• The Virial Theorem in Stellar Astrophysics, by George W. Collins, II
  (1978, Pachart Publishing House, Tuscon, Arizona).

If you want to concatenate all the separate PDF chapters, I recommend using the texexec method oulined in this web page by Matthew Skala.

I found this book in my local library and read it over the weekend. It is a quick read, but has some excellent advice. One thing I liked is the advice on how to read a math text or other technical material. The main idea is that if you get stuck, don’t go backwards assuming you missed something, instead keep going because often you’ll find the new or unfamiliar term defined in a short while. I only learned this myself about a year or two ago. It definitely seems counter-intuitive to keep going, but in the long run it usually works.

I’ve created a new deck of flash cards for calculus. They cover high-school and college-level Calculus I, that is functions, limits, continuity, derivatives, and differentiability.

I also updated my Abstract Algebra flash cards to cover most all of elementary group theory. You can find my PDF flash cards at my web site:

http://www.physics.utah.edu/~jasonu/flashcards/

Larry Cusick, a professor of mathematics at Cal-State Fresno has written a good introduction on how to write proofs. There are lots of great examples. I wish I had found this before I took my introductory analysis classes.

If you have ever wanted to learn some higher mathematics, but don’t want to slog through the long tedious proofs associated with calculus and analysis, then you might like this gem of a book by Edwin H. Connell. He is an emeritus mathematics professor at the University of Miami, and has graciously made his book available for download on the web.

I am currently taking a course in abstract algebra and thus not well qualified to review the book yet, but I have read the first two chapters and find that it presents the material succinctly and quite readably. It is definitely at the undergraduate level and probably accessible to ambitious high-school students as well. I also agree wholeheartedly with the following comment which comes from his web site.

The present situation with college textbooks is a national disgrace. Textbooks are too big and too expensive.

The Hertz Foundation is accepting applications for Graduate Fellowships
with preference given to seniors and first year graduate students. The
amount awarded ranges from $28,000 to $33,000 per year. The application
deadline is October 27, 2006. For more information and application
forms, go to www.hertzfoundation.org.

William Chace, a former president of Emory and Wesleyan Universities, and the author of “100 Semesters: My Adventures as Student, Professor and University President, and What I Learned Along the Way” wrote an excellent op-ed piece for the New York Times.