Author: Chris Aldrich

I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, IndieWeb, theoretical mathematics, and big history. I'm also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.

Paul Halmos on Prerequisites

Definitely the quote of the day:

…[the reader] should not be discouraged, if on first reading of section 0, he finds that he does not have the prerequisites for reading the prerequisites.

Paul Halmos (1916 – 2006, Hungarian-born American mathematician
in Measure Theory (1950)

 

This is essentially the mathematician’s equivalent of the adage “Fake it ’til you make it.”

Riemann’s On the Hypotheses Which Lie at the Foundations of Geometry

One must be truly enamored of the internet that it allows one to find and read a copy of Bernhard Riemann’s doctoral thesis Habilitation Lecture (in English translation) at the University of Göttingen from 1854!

His brief paper has created a tsunami of mathematical work and research in the ensuing 156 years. It has ultimately become one of the seminal works in the development of the algebra and calculus of n-dimensional manifolds.

Nicholas Bourbaki and Serge Lang

Replied to Scientific Fiction – The Bourbaki Mystery by Sue Vazakas (The Sheridan Libraries Blog)

In the 1930s, a French mathematician began writing journal articles and books. His name was Nicolas Bourbaki. He didn’t exist.

Bourbaki was and is actually a group of brilliant and influential mathematicians, mostly French but not all, whose membership changes but whose collective purpose remains the same: to write about mathematical topics they deem important. Between 1939 and 1967 “he” wrote a series of influential books about these selected topics, collectively called Elements of Mathematics.

A mysterious, mostly anonymous group of writers publishing momentous things under a single name is just really cool. But don’t try to read any of his stuff unless you are an expert mathematician.

Instead, read a wonderful story by novelist and award-winning chemist Carl Djerassi, called The Bourbaki Gambit. What do you think happens when a group of scientists, being discriminated against for various reasons, team up and use the “Bourbaki” approach to try to get their latest discovery taken seriously?

There’s an old mathematicians’ joke that goes like this:

Q: When did Nicholas Bourbaki quit writing books about mathematics?

A: When (t)he(y) realized that Serge Lang was only one person!

Brief Thoughts on the Google/Verizon Compromise and Net Neutrality in the Mobile Space

This last week there’s been a lot of interesting discussion about net neutrality as it relates particularly to the mobile space.  Though there has been some generally good discussion and interesting debate on the topic, I’ve found the best spirited discussion to be that held by Leo Laporte, Gina Trapani, Jeff Jarvis, and guest Stacey Higginbotham on this week’s episode of This Week in Google.

[youtube http://www.youtube.com/watch?v=jJQy2R6UT5U?wmode=transparent]

What I’ve found most interesting in many of these debates, including this one, is that though there is occasional discussion of building out additional infrastructure to provide additional capacity, there is generally never discussion of utilizing information theory to improve bandwidth either mathematically or from an engineering perspective.  Claude Shannon is rolling in his grave.

Apparently, despite last year’s great “digital switch” in television frequencies from analog to provide additional television capacity and the subsequent auction of the 700MHz spectrum, everyone forgets that engineering additional capacity is often cheaper and easier than just physically building more.  Shannon’s original limit is far from a reality, so we know there’s much room for improvement here, particularly because most of the improvement on reaching his limit in the past two decades has come about particularly because of the research in and growth of the mobile communications industry.

Perhaps our leaders could borrow a page from JFK in launching the space race in the 60’s, but instead of focusing on space, they might look at science and mathematics in making our communications infrastructure more robust and guaranteeing free and open internet access to all Americans?

Global classical solutions of the Boltzmann equation with long-range interactions

Bookmarked Global classical solutions of the Boltzmann equation with long-range interactions (pnas.org)
Finally, after 140 years, Robert Strain and Philip Gressman at the University of Pennsylvania have found a mathematical proof of Boltzmann’s equation, which predicts the motion of gas molecules.

Abstract

This is a brief announcement of our recent proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation without any angular cutoff, that is, for long-range interactions. We consider perturbations of the Maxwellian equilibrium states and include the physical cross-sections arising from an inverse-power intermolecular potential r-(p-1) with p > 2, and more generally. We present here a mathematical framework for unique global in time solutions for all of these potentials. We consider it remarkable that this equation, derived by Boltzmann (1) in 1872 and Maxwell (2) in 1867, grants a basic example where a range of geometric fractional derivatives occur in a physical model of the natural world. Our methods provide a new understanding of the effects due to grazing collisions.

via pnas.org

 

Terence Tao Teaching Real Analysis at UCLA this Fall

Holy cow! I discovered on Friday that Terence Tao, a Fields Medal winner, will be teaching a graduate level Real Analysis class this fall at UCLA.

Surprisingly, to me, it ony has 4 students currently enrolled!! Having won a Fields Medal in August 2006, this is a true shock, for who wouldn’t want to learn analysis from such a distinguished professor? Are there so few graduate students at UCLA who need a course in advanced analysis? I would imagine that there would be graduate students in engineering and even physics who might take such a course, but perhaps I’m wrong?

Most of his ratings on RateMyProfessors are actually fairly glowing; the one generally negative review was given for a topology class and generally seems to be an outlier.

On his own website in a section about the class and related announcements we seem to find the answer to the mystery about enrollment.  There he says:

 I intend this to be a serious course, focused on teaching the material in the course description.  As such, students who are taking or auditing the course out of idle curiosity or mathematical “sightseeing”, rather than to learn the basics of measure theory and integration theory, may be disappointed.  I would therefore prefer that frivolous enrollments in the class be kept to a minimum.

This is generally sound advice, but would even the most serious mathematical tourists really bother to make an attempt at such an advanced course? Why bother if you’re not going to do the work?!

Fans of the Mathematical Genealogy Project will be interested to notice that Dr. Tao is requiring his Ph.D. advisor’s text Real Analysis: Measure Theory, Integration, and Hilbert Spaces. He’s also recommending Folland‘s often used text as well, though if he really wanted to scare off the lookie-loos he could just say he’ll be using Rudin‘s text.

A lovely bit of satire on Evolution vs. Creationism… what will they come up with next?

Watched Christian Groups: Biblical Armageddon Must Be Taught Alongside Global Warming from The Onion
Constitutional debate continues over whether public schools should include biblical Armageddon alongside global warming in end-of-world curriculum. http://v.theonion.com/onionstudios/video/1368/640.mp4

In Law Schools, Grades Go Up, Just Like That

Bookmarked In Law Schools, Grades Go Up, Just Like That (New York Times)
In the last two years, at least 10 law schools have made their grading systems more lenient to give their students a better chance in a soft job market.

Is GPA tampering and grade inflation going too far with changes like this?

Baum’s Point Set Topology

Commenting only after reading to page 11, but having skimmed some other parts/sections, it’s a nice and condensed volume with most of the standard material on point set topology. It reads somewhat breezily, is well laid out, and isn’t bogged down with all the technicalities which those who haven’t seen any of this material before might have interest in. It seems better for those with some experience in axiomatic mathematics (I’ve always enjoyed Robert Ash’s A Primer of Abstract Mathematics for much of this material), but in my mind isn’t as clear or as thorough as James Munkres’ Topology, which I find in general to be a much better book, particularly for the self-learning crowd. The early problems and exercises are quite easy.

Given it’s 1964 publication date, most of the notation is fairly standard from a modern perspective and it was probably a bit ahead of it’s time from a pedagogical viewpoint.