Labs and Faculty Pages

Gregory L. McColm

Associate Professor

CONTACT

Office: CMC 338
Phone: (813) 974-9550
Email

About Me

I lecture a bit, but I also have students work on problems in class and on a lot of homework problems; if you check my course evaluations (see the Eval Mart), you will see that students are usually okay with it except sometimes in lower division courses, where students are not used to working on a few hard problems (as opposed to many little ones); see Rate My Professors for the gory details.

I have other activities, and thus other websites:

RESEARCH Areas

I was trained as a mathematical logician, with an emphasis on theoretical computer science. My specialty was Finite Model Theory, but I found myself working in combinatorial games and random structures as well. During the past few years, I have been working on geometry and its applications to materials science and what is often called nanoscience. ("Nanoscience" is probably a misnomer, since it refers to the "meso-scale" of microscopic physics -- from many Angstroms to about a micron -- in which quantum effects are usually minor.) Here are the areas ordered by my current level of attention.

Reticular Geometry, Mathematical Crystallography, & the Crystal Turtlebug

Reticular geometry is the geometry concerned with the articulation of geometric structures into more complicated structures. In the large scale, it is the geometry of architecture; on the small scale, it is the geometry of materials and nanostructure design. My primary interest in reticular geometry is the mathematics of crystal design. 

I am a member of the International Union of Crystallography's Commission on Mathematical and Theoretical Crystallography, and I maintain the Crystal Mathematician weblog on mathematical crystallography.

My primary project in reticular geometry is the Crystal Turtlebug crystal design program posted on Sourceforge.

As part of my involvement with reticular geometry, I am:

I have the attention span of a gerbil, so I am also active in:

Philosophy of Mathematics, Science & Education

In addition to my website on taking college classes I have looked into the philosophy of these subjects, especially the problem of reality.

Physics, chemistry, and engineering entail statistical mechanics and other probabilistic concerns, so I am still involved in probability and combinatorics. I got interested in probability originally because of "zero-one" laws of logic. I still keep a weather eye on my original research topic.

Old Stuff

  • A stochastic (or random) process may consist of many tiny processes; if they are independent, then dealing with the entire process is easy. But if all the tiny processes are coupled in some way, one has a more complicated ensemble of coupled Processes.
  • Combinatorics is concerned with finite or finitary structures, often with counting them, but also with describing them. One uses enumerative combinatorics to count structures of given kinds to compute probabilities (or vice versa in what is often called the probabilistic method). One uses graph theory, poset theory, or some other structural theory to describe some complex finitary object, and whenever the word "describe" appears, logic is never far away.
  • Logic is traditionally divided into model theory (describing things), recursion theory (computing things), proof theory (proving things -- or being unable to prove things), and set theory (the foundations of mathematics -- or cloud nine, take your pick). Computational queries can be expressed in model theory, just as algorithms can be expressed in various formalisms. Finite model theory is that branch of model theory concerning predicate calculus (and variants) applied to finite models, and has its most compelling applications to computational complexity theory and database theory. 
  • More of this research

Apprenticeship

Part of the college experience is apprenticeship, when a student completes a project under the direction of someone more experienced in the field. Here are the theses and dissertations completed under my direction.

Miscellany

Sites I maintain as part of my mathematical activities:

  • The International Union of Crystallography gave me a place to run a blog dedicated to mathematical crystallography, the Crystal Mathematician.
  • I also have a lot of pages about Taking College Courses; the primary audience are calculus students, but it should be useful to undergraduates in general.

Then there is a site I maintain for the United Faculty of Florida and the University of South Florida Community: the USF Chapter of the UFF.

And I also maintain two sites on my own:

  • I am an amateur writer, so I have a site dedicated to the craft of writing.
  • I am also a political junkie, and I maintain a sort of map of the political spectrum with commentary on top, called Liberal Moonbat.

Mathematics Clubs

There are several major organizations in the U.S.A. concerned with mathematics. One of these, the Mathematical Association of America has a chapter here at USF, which meets weekly. Members get subscriptions to mathematics journals, plus other goodies, and student memberships are inexpensive. (It also looks good on resumes.) Students interested in joining the USF MAA are encouraged to contact Fernando Burgos.

Other major mathematical organizations include:

And there are more specialized organizations, such as the Association for Symbolic Logic and the European Association for Theoretical Computer Science. 

Mathematics Awards

There are several awards in mathematics research. Here are some of the most important.

  • Probably the most important award in mathematics is the Abel Prize, the closest thing to a Nobel in mathematics, and clearly set up by the Norwegians with an eye towards Stockholm, which had had its chance. This prize is relatively new, so many people aren't used to it, instead they are aware of...
  • The Fields Prize, a junior achievement award. It is awarded to researchers under 40 whose stellar work shows the greatest potential, and is often misleadingly called the mathematical equivalent to the Nobel.
  • Computer scientists have their own awards, the most important probably being the Turing Award.
  • Speaking of Nobel's, the Swedish Academy has a sort of mini-Nobel for those areas (like mathematics) not covered by the Nobel, the Crafoord Prize.
  • Meanwhile, the Israelis also have a prize in some areas,including mathematics, the Wolf Prize.
  • Muddying the waters is the Clay Mathematics Institute, which is offering $ 1 million each for solutions to seven Millenium Problems.

Writing

There are several writer's groups in the Tampa Bay area, and amateur writers (like myself) can get feedback from fellow amateurs (and occasional professionals) by joining in. Groups in Tampa including the Tampa Writer's Alliance, an independent organization. And I am the editor of two newsletters:

  • The Quaternion, the annual newsletter of the USF Department of Mathematics.
  • The UFF Biweekly, the electronic fortnightly newsletter of the USF Chapter of the United Faculty of Florida. The union produces this newsletter independently of the University, and USF is not responsible for its content.