Welcome to the Home Page of Gregory McColm

GMAIL WARNING

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.:

I am engaged in research this summer. 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 15306) 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 2013. Starting August 26, we meet every Monday from 3:05 to 3:55 in a room TBA. If you are interested in making a presentation, feel free to contact me.

Upper Division Undergraduate Course on Modern Geometry

This fall, I am teaching Modern Geometry, MTG 4214-001, CRN 93254, TR 12:30 pm - 1:45 pm in CMC 118. The text is Geometry (2nd ed.), by David Brannan, Matthew Esplen, and Jeremy Gray, and published by Cambridge University Bookstore. We will also use selected sections from Thomas Sibley's The Geometric Viewpoint, available free (thank you, Professor Sibley).

• This course will focus on ``analytic geometry'', and thus be more readily applicable to analysis, algebra, and topology, as well as to mathematical and computational fields in natural science and engineering. All sufficiently prepared students are welcome.
• The USF and state catalogues are sort of confused, so here are the prerequisites for this semester. In order to take this course, you must already have taken Engineering Calculus III (MAC 2283) or Calculus III (MAC 2313) or equivalent, and also have taken Linear Algebra (MAS 3105) or equivalent. There will be group theory in this course, but we will introduce the group theory that we will need (in this day and age, natural scientists and engineers really need to know their group theory!).
• The course will consist of a study of 2- and 3-dimensional space, mostly Euclidean from a vector-ish point of view. We will look at the vector-and-matrix operations (mostly ``affine geometry'') and at figures on planes and in space. We will conclude with a look at 2-dimensional examples of elliptic and hyperbolic geometry.
• Will there be proofs in this course? Well, a proof is merely a verification that something is correct. In 2002, a study commissioned by the U. S. Chamber of Commerce concluded that software bugs alone cost the U. S. economy 0.6 % of the total Gross National Product. Extending that to design errors in cars, planes, bridges, electrical systems, chemical plants, etc., etc., it's a safe bet that errors cost us hundreds of billions a year -- not counting human misery, injuries, and lives lost. So yes, under the heading of ``how not to get fired,'' we will talk about verification techniques, and practice a few.

Teaching Seminar -- for Faculty, and for Students Interested in Education

I am continuing the monthly seminar on teaching mathematics in college. All faculty and students interested in pedagogical issues are welcome. For more information, contact me.

Legalities (© 1999 - 2012): 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 May 2013. This site is under reconstruction, and please pardon the dust: parenthetic asterisks indicate locations of URLs TBA.

• 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>

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.

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:

• The American Mathematical Society.
• The European Mathematical Society.
• The National Council of Teachers of Mathematics.
• The Society for Industrial and Applied Mathematics.

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 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.