Welcome to the Home Page of Gregory McColm

Dept. of Mathematics
College of Arts & Sciences
University of South Florida
4202 E. Fowler Ave., CMC342, Tampa, FL 33620
Office in CMC342(338), hours: M 11 - 12; W 2 - 3; F 5 - 6
phone (813) 974-9550
email mccolm@usf.edu


It seems that USF created a gmail account for a lot of faculty -- without even telling us. I have just discovered that I had this spurious account, and that people had been sending stuff to me at that account ever since 2008. I apologize for not responding to messages sent to that account; no one even told me it existed. I am working to get this account deleted, but meanwhile it is haunting Blackboard. Please send email to me at my regular USF account, mccolm@usf.edu.

Teaching &c.:

Here are my primary activities this coming fall:

Discrete Mathematics Seminar

Each semester, I am the organizer for the Discrete Mathematics Seminar, which is also a section of the Graduate Seminar (MAT 6939-001, CRN 85843) 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 Spring 2014. Starting September 8, we meet every Monday from 2:00 to 2:50 in CMC 109; contrary to the Registar's posting on OASIS, we do not meet on Wednesdays. If you are interested in making a presentation, feel free to contact me.

Upper Division Undergraduate Course on Symbolic Computation

This fall, I am teaching Symbolic Computations in Mathematics, COP 4313-002, CRN 93749, TR 9:30 - 10:45 am in CMC 209. Students will learn to program using the language Maple. There will be no text; instead, information for purchasing Maple will be posted on Canvas before classes start, and students will be provided with (free) Maple "worksheet" files via Canvas. The work of the course will consist of reading the worksheets, doing the homework on the worksheets, and completing the two exams.

Spring Semester

Next spring I will continue to run the Discrete Mathematics Seminar (MAT 6939-001, CRN 15716), which will be meeting on Mondays at 2 pm in CMC 108. In addition, I will be teaching Mathematical Logic and Foundations II (MHF 6307-001, CRN 14557), meeting MW 12:30 - 1:45 in CMC 13. Because Mathematical Logic and Foundations I was not taught last semester, and because of popular demand for that course, I will be covering the material in that course instead: and introduction to first order logic, semantics and Model Theory, Completeness, some basics of computability and recursion theory, decidability and Incompleteness.

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.

About me:

  • Here is my Curriculum Vita, and here is departmental website.
  • 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 details.
  • I have other activities, and thus other websites:


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Legalities ( 1999 - 2013): 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. Note: everything posted here is my responsibility, and I am not representing USF in any official way - other than as one of USF's pointy-headed professors.

This page last updated August 2013. This site is under perpetual reconstruction, and please pardon the dust: parenthetic asterisks indicate locations of URLs TBA.


2014 is the Year of Crystallography

The United Nations General Assembly has decided that 2014 is the International Year of Crystallography. This would be a good year to look at the mathematical foundations of crystallography, and to look forward to how mathematics may be used in crystal design as well as crystal analysis. For more news, see the International Union of Crystallography.

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 consultant for 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

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>


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.


Other Pages

Here are links to 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:

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.

Faculty Senate

I have been elected to a 2-year term (for 2014 - 2016) to the USF Tampa Faculty Senate. I have an agenda: faculty morale and retention. If you have any thoughts on these two issues, please feel free to contact me. Meanwhile, here is the link to the Senate's Website.

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.

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.


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 UFF Biweekly (scroll to the bottom of the page), 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.
  • I have launched a personal website on the craft of writing. I run this site independently of the university, and USF is not responsible for its content.

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.