Welcome to the Lair of Gregory McColm

[ME]
Dept. of Mathematics
College of Arts & Sciences
University of South Florida
4202 E. Fowler Ave., PHY114, Tampa, FL 33620
Office: PHY342(338); hours MW 11:30 - 12:30 (warning: the door of PHY342 is locked at 12 noon, so if you are arriving later, call me up so I can let you in), F 9 - 9:50 in CPR 471 (for a problem session)
phone (813) 974-9550
mccolm@usf.edu

Teaching &c.:

  • Each semester, I am the organizer for the Discrete Mathematics Seminar, which is also a section of the Graduate Seminar (MAT 6939) open to graduate students for three hours credit (see me for details). Each session, speakers speak about mathematical topics ranging from the theory of computation to algebraic topology, from mathematical logic to graph theory; for a sample, see the announcement page for fall 2011. Starting January 23, we meet every Monday from 3:05 to 3:55 in PHY 108.
  • This spring, I am teaching Engineering Calculus I, MAC 2281-002, CRN 16261, MW 9:40 - 11:30 am in CHE 102.
    • This course is part of the Engineering Calculus sequence, for engineering and some natural science majors; mathematics majors should consider taking the regular Calculus sequence.
    • The overpriced text is Essential Calculus: Early Transcendentals by James Stewart. While the list price is $ 174.95, new copies are available for $ 80 - $ 120 from major on-line retailers, and there are used copies available for as little as $ 45. Additional stuff -- study guides, solutions manuals, software, etc. -- is not required or even desired, but you will need a good calculator with exponential, trigonometric, and similar functions. You will also need to purchase access to WebAssign, and then send me an email so I can send you the course code.

Taking College Courses

I have written some pages, for math students (and teachers) in general, on homework, texts, grading, etc. (Some of these pages may be of interest to people in other fields as well.) To go to these pages, start at my main page on taking college classes.

Destinations

Back to the USF Department of Mathematics Home Page
Back to the USF College of Arts and Sciences Home Page
Back to the USF Home page

Legalities (© 1999 - 2011): All material on this web-site is protected by U.S. copyright laws. It may be used (and reproduced electronically, or as hardcopy copies) for educational or charitable or other non-profit purposes as long as pages are reproduced in toto and properly attributed. However, please do not post copies of this material: put in links to it instead (although external links to images in this site are okay, as long as attributed). For permissions, contact me.

This page last updated August 2011. This site is under reconstruction, and please pardon the dust: parenthetic asterisks indicate locations of URLs TBA.

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

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.

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

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

Old stuff includes:
  • 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. <\ul>

Miscellany

Math Programs

The Mathematics Department offers a mathematics major for bachelor's students and a M.A./B.A. program that allows one to get both degrees in about five years. In addition, we offer a Ph.D. Our primary research areas are in various areas in analysis, probability and statistics, and various areas of discrete mathematics. For more information on these programs, click here.

The Mathematics Department is also a partner in the new Master's Program in bioinformatics, which involves the design and analysis of very large molecules, especially pharmaceuticals, proteins, and DNA.

United Faculty

The faculty of a university is the university. Alas, many universities are controlled by an administration which often behaves like the shortsighted management of a business concern. So faculty have must organize to protect their interests and the long-term interests of the university.

Florida State University System faculty are represented by the United Faculty of Florida, which, via the Florida Education Association, is a merged affiliate of the National Education Association and the American Federation of Teachers (the latter being an affiliate of the American Federation of Labor / Congress of Industrial Organizations). USF faculty are represented by the local chapter of the UFF, which also has an off-campus site.

I am the editor of the USF Chapter newsletter Uncommon Sense and the web-master of the chapter website.

Here is an MS Word file for a membership application to join UFF.

As the Chapter's webmaster, I maintained, and still maintain (at a lower level), UFF's website on the Al-Arian controversy. I also wrote an article on A University's Dilemma in the Age of National Security with Sherman Dorn in the NEA journal Thought and Action.

USF Faculty Senate

I am a member of the USF Faculty Senate, serving a 3-year term from 2009 to 2012. Any faculty members with concerns that they believe the Senate should or could address can contact me at mccolm@chuma1.cas.usf.edu.

The Senate is currently addressing several issues, most notably academic governance at USF and faculty salaries. For more on such issues, see the Faculty Senate website.

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 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 three newsletters:

  • The Quaternion, the annual newsletter of the USF Department of Mathematics.
  • The Uncommon Sense, the periodic hardcopy newsletter of the USF Chapter of the United Faculty of Florida.
  • The UFF Biweekly (scroll to the bottom of the page), the electronic fortnightly newsletter of the USF Chapter of the United Faculty of Florida.

Lecture Series

The Mathematics Department presents the R. Kent Nagle Memorial Lecture Series, in which we bring eminent scholars to USF to speak to the public about subjects mathematical. For more information, click here.

This series is one of many series that this and other departments are supporting to reach out to the community. For other programs of this kind, click here.