Discrete Mathematics

Discrete mathematics is a rather inclusive notion, and captures many of the most active research fields today, from theoretical computer science to probabilistic methods, from graph theory to category theory, with applications to all the natural sciences, the social sciences, the professions of business, engineering, and medicine, and even the humanities. At USF, we have faculty exploring many of these frontiers. Discrete Mathematics is rather inclusive at USF, with places for algebra, combinatorics, computing, logic, number theory, topology, and related areas.

The Discrete Mathematics Group

The faculty in our department who make up the discrete mathematics group are:

Brian Curtin, who works in algebraic graph theory.
Mohamed Elhamdadi, who works in topology and K-theory.
Natasha Jonoska, who works in biomolecular computation, symbolic dynamics, and formal languages.
Milé Krajcevski, who works in combinatorial group theory and geometric group theory.
Greg McColm, who works in combinatorics, logic and probabilistic methods.
Masahico Saito, who works in knot theory, dynamical systems and DNA computing.
Richard Stark, who works in asynchronous distributed computation and biological information processing.
Stephen Suen, who works in combinatorics and theoretical computer science.

Other members of the department, and some outside of the department, also participate.

The Discrete Mathematics Seminar

The primary formal forum for discrete mathematics discussion here is the weekly Seminar in Discrete Mathematics, which is open to everyone, and offers credit to graduate students as the seminar course MAT 6939 (which requires the approval of the Graduate Program Director for enrollment).

This Fall 2002 semester, the seminar meets weekly on Mondays, from 4 p.m. to 5 p.m., in LIF 269. For more information, contact the organizer, Gregory McColm, at mccolm@math.usf.edu.

Graduate Study in Discrete Mathematics

The Discrete Mathematics Program is designed to bring students to the frontiers of several areas in discrete mathematics.

First, there are two core sequences in this area.

MAS 5107, 5311, 5312. Algebra and Linear Algebra.
MTG 5316, 5317. Topology.

Second, there are the three elective sequences.

MAD 6206, 6207. Combinatorics. Elementary counting principles, distributions, sets, multisets, partitions of sets and integers, generating functions and recurrences, graph theory, probabilistic methods, combinatorics of finite sets: posets, hypergraphs and extremal problems, matroids, block designs, Mobius inversion for posets, Polya theory.
MHF 5306, 6307. Foundations. Recursion and computability theory, predicate calculus, incompleteness, model theory, completeness, set theory.
MHF 5306 & MAD 6616. Theory of Computing. Recursion and computability theory, predicate calculus, model theory, deterministic and non-deterministic finite automata, regular and other languages, Turing machines and related machine models, cellular automata and other network models.

Then there are three cycling topics courses:

MAD 6617. Topics in Abstract Structures. Advanced topics in combinatorial structures, logical structures and models, algebraic structures, set theory and topology, or related topics.
MAD 6510. Advanced Theory of Computation. Advanced topics in theoretical computer science, such as recursion theory, process theory, computational or descriptive complexity theory, abstract computations, or related topics.
MAD 6XXX. Topics in Combinatorics. Advanced topics in combinatorics, combinatorial analysis, combinatorial enumeration, or related fields.

There are also a few other electives in these areas.

MAD 5101. LISP: Programming with algebraic applications.
MAD 5305. Graph Theory.
MAS 5125. Number Theory.

For more information, consult the page for graduate students.

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