October 30, 2003
How Well Can Monkeys Rank Football Teams?
That is the question that Professors Mucha, Porter and undergraduate Thomas
Callaghan ask. And they find that the Monkeys do a pretty repsectable job.
This article was featured on ESPN's magazine called "The Spin."
This investigation has a short intro here,
but you really want to check out the graphics in the full article.
The inspiration comes from the odd end of season rankings that come out of the complicated
mechanism used to rank College Football, at the time of the end of season College Football
Bowl games. Part of the confusion comes from the fact that a full season of football consists of
about 11 games, with some of those games deliberately played against weaker teams. That leaves relatively few head to head games between top teams.
But does the complicated mechanisms compensate for this? Callaghan, Mucha and Porter look into it by designing a simple random mechanism to select the end of year rankings, and compare their results to the actual decisions, concentrating on a few especially interesting years.
Fun reading. Highly recommended. This might be making it's way to ESPN soon!
October 22, 2003
Quantum Computation Special Topics Courses
Professor Bellisard is offering, for the second time, a course in Quantum Computation. The description is below.
A full listing of the different special topics courses being offered, in Spring
2004 and past semesters has more information.
Math 4803 BDU Quantum Information and Quantum Computation 3-0-3
Instructor: Prof. Jean Bellissard
Description: Restricted to DMTH, MATH, CS, PHYS students.
Quantum computing and quantum information might give rise to important technological developments in the future. This course will be organized around the following topics:
Classical information theory. Clues in quantum theory.
Quantum systems used in experiments.
Quantum information: Compression, transmission, noise, entanglement cryptography, teleportation.
Quantum Complexity: introduction, algorithm, error correcting codes
This course is taught jointly with CS4803 and PHYS5106.
Prerequisites: Familiarity with matrix calculus adn finite dimensional vector spaces.
Text:
Professor Mason Porter's Mathematical Modeling Course
In the Spring 2004 Semester, Mason Porter will offer a Mathematical Modelling
course at the Undergraduate Level. Here is his description of the course:
Math 4803: Mathematical Modelling MWF 0105-0155pm
The purpose of this course is to introduce undergraduates in math,
science, and engineering (and interested graduate students) to the
rudiments of mathematical modeling with a case study approach. We will
consider both continuous and discrete systems and applications from
numerous scientific disciplines. We will also consider topics (such
as small world networks) in which many scientists are currently actively
engaged in fascinating research in applied mathematics.
There will also be some room for student input when deciding precisely
which topics are covered and students who take the course will have the
opportunity to work on a project of their own choosing.
Anybody interested in discussing this course with me is encouraged to
e-mail me at mason@math.gatech.edu or to come by my office (120 Skiles).
Arithmetic Combinatorics
Professor Ernie Croot, who has just started as tenure track professor at Georgia Tech, will offer a Special Topics course in "Arithmetic Combinatorics." This course listed as a Graduate and a Undergraduate course.
Math 4803: Arithmetic Combinatorics MWF 1105-1155am
Arithmetic combinatorics is a branch of number theory and combinatorics that aims to show that every subset of the integers with certain
prescribed properties must have a particular substructure. For example,
a classic theorem due to K. F. Roth asserts that for all sufficiently large integers X, any subset S of {1,2,...,x} having at least x/\log\log x members must contain a three-term arithmetic progression. By this we mean a must contain a three-term arithmetic progression, by which we mean a
triple of integers a,b,c, with a and b distinct, such that a+b = 2c.
The main results in this area are proved using a variety of methods and techniques taken from graph theory, probability theory, geometric
combinatorics, harmonic analysis, and analytic number theory (in particular, the circle method). Even so, no prior background, except a knowledgeof elementary number theory, basic analysis, combinatorics, and
probabilitytheory, will be necessary. The main requirement will be mathematical maturity, and an ability to read through and present proofs.
The main topics I plan to cover are as follows:
1. Schur's theorem on monochromatic solutions to $x+y=z$, basic
Ramsey Theory, and van der Waerden's theorem.
2. The classical combinatorial inequalities: Cauchy-Davenport
inequality,
Shnirel'man's theorem, Kneser's inequality, and others.
3. Basic estimates for points on varieties on ${\bf Z}/N{\bf Z}$ and
$F_q$ (where $q$ is a prime power). The methods used here will be
purely
classical, and will mostly involve Gauss and Jacobi sums.
4. The circle method and applications to Waring's problem.
5. Behrend's lower bound for the densest subsets of the integers free
of 3-term arithmetic progressions. Rankin-Laba-Lacey's result for
k-term progressions.
6. Roth's theorem on 3-term arithmetic progressions. Sarkozy's result.
7. Szemeredi's theorem, and H. Furstenberg's ergodic theory proof.
8. Szemeredi and Heath-Brown's Improvement of Roth's theorem.
9. Plunnecke's inequality, Ruzsa's finite group version of Freiman's
theorem, and the version in the integers.
10. Lower bounds for the maximum size of the product set $A \cdot A$
and sumset $A+A$: The Szemeredi-Trotter theorem, and Elekes's
application
to sums and products.
\bigskip
Depending on the amount of time it takes to get through these topics, I
may decide to remove some from the list, but I may also decide to add
a few more. In addition to my own weekly lectures, I will try to
encourage
everyone to read through some of the papers in the literature and give
in-class expositions.
October 21, 2003
Public Universities' Tuition Rises by 14 PercentBy GREG WINTER
So reads an article in the New York Times, based on a report by the
College Board.
More and more of the costs of an education are being placed on the students and their parents. The change over the last 25 years or so are very dramatic.
This author, in 1981, paid more for college tution than at any point in the previous four years: $210 for 20+ hours of credit at the University of Texas at Austin. This was during a time when the State of Texas, and the Texas endowment were paying the lion's share of the cost of education.
The NYT requires free registration. Use the login in "gtmath" and the pass "Atlanta."
Emory Grad Recruitment Program: Math Day at Emory
Fifth Annual MATH DAY AT EMORY
Saturday November 15, 11 AM - 4 PM
Department of Math and CS, Emory University, Atlanta, GA
Organized by: Department of Math & CS, Emory University.
For Whom: Any one interested in graduate studies in math leading to a PhD.
Activities:
* Informal presentations by faculty and graduate students on their
interests in mathematics and on graduate studies at Emory and in general.
* Entertaining Videos.
* Casual conversations with faculty and graduate students to learn more
about Emory.
* Free lunch.
Location: Mathematics and Science Center, 400 Dowman Drive, Atlanta.
Registration: Encouraged, but not required.
Contact and More Info: http://www.mathcs.emory.edu/News/Special
or nagy@mathcs.emory.edu, syang@mathcs.emory.edu
October 19, 2003
Georgia Tech's Graduate Recruiting Brochures
From Evans Harrell:
You can get it as
http://www.math.gatech.edu/~harrell/GP/brochure/flyer1.pdf
and
http://www.math.gatech.edu/~harrell/GP/brochure/flyer2.pdf
(A fuller brochure is at
http://www.math.gatech.edu/~harrell/GP/brochure/ )
I'll also prepare some copies to leave with Genola, which might be more
convenient than using your own color printer.
Information About Graduate Study
ASSISTANTSHIPS AND GRADUATE FELLOWSHIPS
IN THE MATHEMATICAL SCIENCES - 2003 EDITION POSTED
By the American Mathematical Society
This publication for students, mathematical sciences departments and
faculty brings together a wealth of information about resources
available for graduate study in mathematical sciences departments in the
U.S. and Canada. Information on the number of faculty, graduate
students, and degrees awarded is listed for each department when
available. Stipend amounts, number of awards available, foreign language
requirements, sources of support for graduate study, and a list of
reference publications for fellowship information are also included. See
http://www.ams.org/careers-edu/asst.pdf.
REU Recruiting for Students
REUs are Research Experiences for Undergraduates. These are programs
all over the country. The letter below is for a program at UCLA. There is much
more information about REUs at the Undergrad Math Site.
October 16, 2003
Dear Colleague, we are very excited to announce the fourth year of
an innovative summer program for undergraduates at UCLA's Institute
for Pure and Applied Mathematics. We are recruiting talented
national and international undergraduates and would be grateful for
your assistance in bringing this program to their attention. Our
program called Research in Industrial Projects for Students ("RIPS")
creates teams of 3-5 undergraduates paired with faculty mentors and
industry liaisons whose goal is to solve real-world industrial
problems. Sponsors included companies such as Pixar and national
laboratories such as Los Alamos. Last summer we completed our 3rd
program and as in the previous two years, it was very successful and
the undergraduates who participated were enthusiastic about their
experience. More information, including comments from students and
information on prior projects can be found on our website at:
http://www.ipam.ucla.edu/programs/rips2004/
Questions can be addressed to rips2004@ipam.ucla.edu
You can view and/or print out a poster for the program (and we'd be
grateful if you could post it in an area visible to undergraduates)
at this url:
http://www.ipam.ucla.edu/programs/rips2004/rips2004_poster.pdf
October 15, 2003
Kamal Jain, ACO Grad, Giving Seminar
Kamal Jain, who got his doctorate in 2000 through the Georgia Tech ACO Graduate Program, is back in town to give a Graph Theory seminar with the title"Combinatorics in Network Coding" on Thursday October 16.
Kamal Jain, who got his PhD in Computing, is now at the Theory Group at Microsoft. You can find out more about his work at his Georgia Tech home page. The ACO (Algorithms, Combinatorics, and Optimization) is a joint program between Mathematics, Computing and Industrial Systems.
Two Undergrad Courses of Interest
There will be two noteworthy undergraduate courses in the Spring 2004 Semester: Professor Porter's Introduction to Mathematical Modeling,
and Professor Croot's Arithmetic Combinatorics class.
Concerning the Mathematical Modeling, Professor Porter write:
The purpose of this course is to introduce undergraduates in math,
science, and engineering (and interested graduate students) to the
rudiments of mathematical modeling with a case study approach. We will
consider both continuous and discrete systems and applications from
numerous scientific disciplines. We will also consider topics (such
as small world networks) in which many scientists are currently actively
engaged in fascinating research in applied mathematics.
There will also be some room for student input when deciding precisely
which topics are covered and students who take the course will have the
opportunity to work on a project of their own choosing.
Anybody interested in discussing this course with me is encouraged to
e-mail me at mason@math.gatech.edu or to come by my office (120 Skiles).
October 10, 2003
Intel's Andy Grove on Job Future
The problem of job migration overseas was addressed by a Intel's legendary
Andy Grove, today. The speech was covered by several news agencies,
such as The Register.
In the speech, Grove warns that the IT industry in the US could go the way of the steel industry. (And in fact is already well down that path.) "It would be a miracle if it didn't happen in the software and services industry,'' Grove said.
The points that Grove points to fight this trend include: boost funding for research and development at universities; adopt policies that attract the best workers from around the world. This is the part of the message most relevant for GT students. You are in the very good place to gain an education in the high value work that will continue to be done in the US.
On a personal note, I was recently on a two week trip to Armenia, on the other side of the Baltic sea, sharing borders with Iran and Turkey. There, the better jobs are software programming jobs. Even the Mathematics Institute in Yerevan rents out space to such a company, a move that is described as completely normal.
It is easy to see why, as the workers are still able to get a high quality education from the university system built in the Soviet era. And the costs are very low: A watermelon costs about 11 cents. A lovely meal for 6 at a resturant as little as $20.
On my flight in, I sat next to two software execs from Silicon Valley, flying in to check up on the Armenian employees. While there, I met a woman who was a C++ programer. Oh I said, who do you program for? The answer was the Army of the Peoples Republic of China! The impact of IT outsourcing are indeed very broad.
Casey Warmbrand to go to Budapest
Casey Warmbrand, a senior in math, with very wide set of interests,
has been accepted into the Budapest Semestes in Mathematics.
He will be the second math major to participate in the program, the first is
David Eger.
David liked the atmosphere so much, that he applied for and received a Fulbright grant to study there for this academic year. The following year, he will be in graduate school in CS at Carnegie Mellon. There is another Fulbright at Budapest this year who will start graduate study in the ACO program at Georgia Tech next academic year.
The Budapest program is an outstanding intensive Semester of Mathematics. Another program is math in Moscow program at Moscow State University. Elizabeth Sanders participated in this program. It is has plenty of scholarships for the semester. Elizabeth got one, and GT students should be very competetive for these awards.
More information is availible. And we look forward to Casey's news from Budapest.
October 07, 2003
Ryan Hynd off to Conferences
Ryan Hynd, one of the undergraduates who is finishing his degree this year,
will be presenting a poster at a Sigma Xi national meeting in Los Angeles
this year. He will present work completed with Professor McCuan on
rolling curves, while both were at a Max Planck Institute in Leipzig Germany this past summer.
This meeting has a very wide set of interests and presentations. Many of them concern the promotion of mathematics and science in third world countries. The mathematicians that work in those countries can possess a quite decent talent, but they are terribly isolated, work for very little money, and have limited range of resources to offer their students.
Ryan will also participate in a Grad Student Recruitment Program at UC Berkeley in the month of October. While there, he'll likely meet up with
GT alum Andy Wand, who is studying for his PhD at Berkeley under the well known topologist Rob Kirby.
Results from the Comprehensive Exams
The first major hurdle the Graduate Students face are the comprehensive exams, one in Analysis and one in Algebra, both at the level of the first year courses in those subjects.
The exams given this past September were taken by 17 students, with three of those being students who had just started gradute school, with the remaining 13 being students who had been in the program for at least one year.
Six of those 13 passsed the exam. The six are Nate Berglund, Michael Kettner, Jean-Phillipe Lessard, Bill McClain, John Pearson, and Turkay Yolcu. These results are some what better than the results from the last couple of exams given.
Some more students passed one exam, but not both, as is currently required.
Nevertheless, grad students and faculty are concerned about the administration of the exams, and the role they are playing the PhD program. The Graduate Committee, chaired by Professor Mucha, with the graduate student Christel Hohenegger on the committee, is considering the adminstration of the exam.
The committee will likely propose some tweaks to the system. The items under discussion include (and are not limited to)
(1) permitting the passage of one exam at a time, rather than both as is currently required
(2) having the exams three times a year, Fall, Spring, and Summer
(3) placing all students on the same time limit to pass the exams, in contrast to the current system that treats those with masters differently
These changes have to make it out of the Graduate Committee, and then be voted on by the whole faculty before becoming effective.
Some students and faculty have deeper concerns about the Comprehensive Exams. Namely, the time spent on the exams is really large. And the Exams do not serve the interests of all faculty, especially those with more applied interests. But, addressing these concerns would require a significant overhaul of the current Comprehensive and Oral Exams, and will have to be addressed at some later date.
October 06, 2003
Meet The Math Majors Pics
Meet the Math majors is a free lunch, with all of the math majors in attendence, and the grad students and faculty invited as well.
A great opportunity to meet outside of classes and study groups, it is
usually very well attended, and even more so in the Fall Semester.
Undergrad Corbett and Synder Lecture to Physics Group
Tuesday, 11am on the 5th floor of Howey.
(The room is opposite the elevator.)
The venue is the Center For Nonlinear Systems group meeting,
so it's pretty informal.
Jeremy Corbett and Jessica Snyder, GT Undergrads, both did research under
Mason Porter's direction this past summer as part of the VIGRE program, so
come and provide moral support.
Jeremy will be talking about pattern formation in spatially extended
dynamical systems (like granular media and fluids) and Jessica will be
talking about mathematical models of bipolar disorder.
Also, these two short talks (we'll finish by noon) are relevant for
anybody thinking about doing research as part of the VIGRE program.