About Me

I am a Professor at the Department of Mathematics at the University of Arizona, where I have taught undergraduate and graduate mathematics courses and pursued a diverse, interdisciplinary research program. In recent past I worked in private industry developing software and leading R&D of a data compression company.SantaMonica

Lectures on Applied Combinatorics

In the Spring of 2015 I taught a course on Applied Combinatorics, using a superb book by Alan Tucker.
You will find the outline of the course by following this link:

Combinatorial Mathematics

Website 2.0

Over the past few years, I neglected the content of this website somewhat. So many things to do, so little time. But in part this was due to the hard time that the chosen CMS, Drupal, was giving me. Yesterday I moved the Website to Drupal 7, and things appear to work better. For a math website, it is a must to have formulas. The package DruTeX has become obsolete, and the current rendering is done using MathJAX, which is both more secure (rendering of TeX happens in user's browser) and more reliable way to render random formulas, such as this one:

A new efficient implementation of Ukkonen's algorithm in C++

I  implemented a suffix tree library. There is a Wikipedia article on suffix trees here:


The new library is really neat! It can also generate nice images from real inputs. Here are some images of suffix trees generated by the library:

Petaflop computing

The BlueGene project at IBM is aimed at making int possible to reach a petaflop speed in numerical calculations.

A petaflop = 1000 teraflops = 1 million gigaflops. A typical PC of today is able to achieve speeds of several gigaflops. One gigaflop roughly means one billion multiplications of 14-digits digit numbers per second.

Maxima Grobner package back on line

My Groebner basis and Comprehensive Groebner packages needed a little dusting. I have authored two software packages in this area:

  • An extension to the Computer Algebra System Maxima, which provides for Grobner basis calculations. The package contains a demo file which illustrates its usage.
  • A standalone package for calculating Comprehensive Groebner Systems, called CGBLisp. Comprehensive Groebner bases allow one to answer questions about systems of parametric equations with parameters.

The packages will be available at my development site at:

Site Launched

In recent days I grappled with the issue of choosing the CMS. This amounts to the "Joomla vs. Drupal" contest, it appears. These are the two most popular CMS of today.

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