Welcome to the Home Page of Gregory McColm

Deptartment of Mathematics & Statistics
College of Arts & Sciences
University of South Florida
4202 E. Fowler Ave., CMC342, Tampa, FL 33620
Office in CMC342(338)
Hours (effective August 21 - December 1): M 1 - 1:50, T 2 - 2:50, R 11:00 - 11:50, F 10 - 10:50. Note. Friday office hours may be subject to change, especially in October.
phone (813) 974-9550
email 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 85362), which is open to graduate students for three hours credit (see below for details).

  • Each session, speakers speak about mathematical topics ranging from the theory of computation to algebraic topology, from mathematical logic to graph theory. Starting September 11 (although there will be an organizational meeting on August 21), we meet every Monday from 2:00 to 2:50 in CMC 108. If you are interested in making a presentation, feel free to contact me.
  • The Discrete Mathematics Seminar is section 001 of the Graduate Seminar (MAT 6939), a 3-hour graduate course.
    1. The Graduate Seminar course is graded S/U, and counts only towards satisfying the nine-hour requirement for graduate assistantships; it does not count towards the degree in any way. A student is expected to attend regularly and to give a seminar talk; this seminar talk is developed by the student with the advice of a faculty sponsor, who is a member of the Graduate Faculty who has agreed to assist that student with the presentation.
    2. A student may enroll in the seminar if and only if the student is at least a second-year graduate student in good standing who has secured the support of a faculty sponsor prior to enrollment.
    For further information on this course, see me.

Calculus I

This fall, I am teaching Calculus, MAC 2311-008, CRN 91252, TR 12:30 - 1:45 pm, in CHE 101A. (Students will also attend peer led sessions F 12:30 - 1:20 pm in CPR 127; there will also be some exams on Saturdays, starting at 9:30 am.) We will start the 3-semester course on rates of change and accumulation. The text is a custom version of James Stewart's Essential Calculus, published by Cengage / Thompson; students will also need to purchase a Webassign account; see the campus bookstore for details. The work of the course will consist of reading the text, taking online quizzes on the text material, attending class to work on more problems, doing online and written homework, doing quizzes and filling in activity sheets for Friday sessions, and taking exams.

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 the gory details.
  • I have other activities, and thus other websites:


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Legalities ( 1999 - 2016): 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 September 2016. This site is under perpetual reconstruction, and please pardon the dust: parenthetic asterisks indicate locations of URLs TBA.


No pending announcements.

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

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 algebra, analysis, combinatorics, the theory of computation, probability and statistics, and topology. For more information on these programs, click here.

Faculty Senate

I have been elected 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. But in this political environment, if faculty are to have a voice in their own university, they must get organized - and that means more than an advisory body like a senate.

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 elecronic newsletter, the UFF Biweekly and the web-master of the chapter website.

Here is an pdf 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 co-authored 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 solutions to 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 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.

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.