"Mathematics is biology's next microscope, only better; Biology is mathematics' next physics, only better." --Joel E. Cohen

**Algebra & Discrete Math**: Enumerative combinatorics,
graph theory, group actions and Weyl groups.

**Analysis**: Singularity analysis, differential
equations for generating functions.

**Computation**: Algorithm design, thermodynamic models for RNA
pseudoknot structures.

**Operations Research**: Maximum weighted matching algorithms,
dynamic programming.

**Probability & Statistics** Branching processes,
central limit theorems for arcs in k-noncrossing structures.

We will take advantage of the diversity of the mathematical background
and strengths of the students taking this class. *This course is not
intended to be one faculty member teaching eleven graduate students,
but rather, a dozen mathematicians with various backgrounds coming
together to learn a new area of research.* As with any young
field, there are surely many unexplored areas, loose ends, and good
future research problems that we can discover, and one of our goals is
to find and propose these problems. In this class we will write a
self-contained *research proposal* as a final project, and give a
series of short presentations about what we've been studying and our
new ideas for future research. Everyone will contribute by either
writing a section in the proposal, or giving a presentation. These
presentations will be given in a *research symposium* that we
hold during our 2 1/2 hour final exam period. We will invite other
graduate students and faculty members from our department, and outside
our department, to learn about what we've been doing all semester. In
addition, there will be a few in-class quizzes and (reasonable)
homework assignments, because at this point in our careers, we all
understand that it is simply not possible to truly learn mathematics
by just watching and not doing.

This course is suitable for students who have a basic foundation at the undergraduate level in abstract algebra, complex analysis, differential equations, and probability theory (though a deficiency in one of these is not a problem). After successfully completing this course, a student will have knowledge of how discrete mathematical techniques have been applied to the field of biology, the challenges that still exist, and areas of active research. Students are encouraged to pursue any research problems they find interesting as an ongoing project after the semester ends.

- Course Flyer
- Course Syllabus
- Homework
- In-class quizzes: 1 | 2 | 3 | 4 | 5 | 6 | 7.
- Midterm | Solutions.
- Tutorial & Research Symposium (final project)
- Blackboard
- Slides from talks on combinatorics of RNA at the Clemson discrete math mini-conference: Christine Heitsch (2008), and Debra Knisley (2010).
- The first comprehensive book (and freely available online!) on the new field of Analytic Combinatorics, by Philippe Flajolet and Robert Sedgewick.
- What is a neutral network?
- The Pfold web server.
- The mfold and UNAFold web servers at the RNA Institute, at SUNY Albany.
- The RNA Tree Graph Subproject at Tamar Schlick's research group in computational biology, chemistry, and biomathematics, at NYU.
- EteRNA, an RNA folding game. See this article on it from the New York Times.

- Peter Clote, Boston College (Biology, CS. Formerly Math/CS.)
- Jennifer R. Galovich
, St. John's U. and College of St. Benedict
(Math).
*Phylogenetics, combinatorics of RNA*. - Daniela
Genova, U. North Florida (Math).
*Formal languages and DNA sequences*. - Christine Heitsch, Georgia Tech (Math)
- Debra Knisley, Eastern Tennessee State (Math/stats)
- Asamoah Nkwanta, Morgan State (Math. Sci. / CS)
- Svetlana Poznanovik, Clemson (Math. Sci.)
- Christian Reidys, U. Southern Denmark (Math/CS)
- Peter Stadler, U. Leipzig (Bioinformatics)
- Michael Waterman, U. Southern California (Bio Sci, Math, CS. PhD Stats)
- Michael Zuker, Rensselaer Polytechnic Institute (Math)

- Combinatorial Computational Biology of RNA. (Required course textbook.)
- Preprints on the arXiv: Christian Reidys, Christine Heitsch.
- Robert
Willenbring. RNA
secondary structure, permutations, and statistics.
*Discrete Appl. Math.***157**(2009) 1607-1614. - Trees of relations, clusters and RNA secondary structures, by Robert J. Marsh, Sibylle Schroll.
- Watson-Crick pairing, the Heisenberg group and Milnor invariants, by Siddhartha Gadgil.

- Réka
Albert, Penn State (Physics).
*Biological physics and network modeling*. - Edward Allen
, Wake Forest (Math).
*Combinatorics. Biological signaling networks from omics data*. - Elizabeth S. Allman, U. Alaska, Fairbanks
(Math/stats).
*Algebraic statistics, phylogenetics*. - David
Anderson, Wisconsin (Math).
*Biochemical reaction networks*. - Peter Clote, Boston College (Biology,
CS. Formerly Math/CS).
*Combinatorics of RNA.* - Margaret Cozzens, Rutgers (DIMACS).
*Graph theory and biology*. - Elena
Dimitrova, Clemson (Math. Sci.).
*Algebraic and systems biology*. - Mathias Drton, U. Washington (Statistics. PhD
Stats).
*Algebraic statistics*. - Jo Ellis-Monaghan, Saint Michael's College
(Math).
*Graph theory and biology*. - Andrew Francis, U. Western Sidney
(Math).
*Algebraic biology, evolutionary processes*. - Jennifer R. Galovich
, St. John's U. and College of St. Benedict
(Math).
*Phylogenetics, combinatorics of RNA*. - Luis
Garcia-Puente, Sam Houston State U. (Math/stats).
*Algebraic and computational biology*. - Daniela
Genova, U. North Florida (Math).
*Formal languages and DNA sequences*. - David Haws, IBM Genomics Lab.
*Phylogenetics and algebraic statistics*. - Monika Heiner, Brandenburg Technical U.,
Cottbus (CS. PhD CS).
*Petri nets* - Christine Heitsch, Georgia Tech (Math.)
- Franziska Hinkelmann, Ohio State (Mathematics
Biosciences Institute)
*Algebraic and systems biology*. - Terrell Hodge, Western
Michigan (Math).
*Phylogenetics, metabolic pathways* - Valerie
Hower, U. Miami (Math).
*Computational biology*. - Abdul
Jarrah, American University of Sharjah (Math).
*Algebraic and computational biology*. - Natasha Jonoska, U. South Florida
(Math/stats).
*Biomolecular computations*. - John Jungck, U. Delaware (Interdisciplinary Science
Instruction, PhD biology).
*Mathematical molecular evolution*. - Winfried
Just, Ohio U. (Math).
*Systems biology, dynamical systems, neuronal networks*. - Debra
Knisley, Eastern Tennessee State
(Math/stats).
*Combinatorics of RNA.* - Jeff
Knisley, Eastern Tennessee State
(Math/stats).
*Computational biology*. - Reinhard Laubenbacher, University of Connecticut (Center for Quantitative Medicine).
*Algebraic biology, cancer systems biology*. - Matthew Macauley, Clemson
(Math. Sci.).
*Discrete dynamical systems, Boolean networks*. - Henning S. Mortveit, Virginia Tech (Virginia
Bioinformatics Institute).
*Discrete dynamical systems*. - Asamoah Nkwanta, Morgan State (Math. Sci. /
CS).
*Combinatorics of RNA.* - Megan
Owen, Waterloo.
*Phylogenetic trees and networks*. - Lior
Pachter, Berkeley (Math, Molecular Biology, EE&CE.).
*Algebraic statistics, computational biology.* - Sonja
Petrovic, Illinois Instutute of Technology (Applied mathematics).
*Algebraic statistics*. - Svetlana Poznanovik, Clemson
(Math. Sci.).
*Combinatorics of RNA.* - Christian Reidys, U. Southern Denmark
(Math/CS).
*Combinatorics of RNA.* - John
Rhodes, U. Alaska, Fairbanks (Math/stats).
*Algebraic statistics, phylogenetics*. - Manda
Riehl, U. Wisconsin, Eau Claire (Math).
*Combinatorics of genome mutations*. - Raina Robeva, Sweet Briar College.
*Systems biology*. - Joseph Rusinko, Winthrop (Math).
*Algebraic geometry and phylogenetics*. - Anne
Shiu, Texas A & M (Math).
*Biochemical reaction networks, genomics, algebraic statistics*. - Ilya Shmulevich, U. Washington. (Institute for Systems
Biology. PhD EE).
*Boolean networks*. - Peter Stadler, U. Leipzig
(Bioinformatics).
*Combinatorics of RNA.* - Brandilyn Stigler, SMU (Math).
*Algebraic and computational biology*. - Bernd
Sturmfels, Berkeley (Math, Statistics, CS).
*Algebraic statistics, computational biology*. - Seth
Sullivant, NC State (Math).
*Algebraic statistics*. - Jeremy Sumner, U. Tasmania (Math).
*Group theory and phylogenetics*. - Glenn Tesler, UCSD (Math).
*Bioinformatics, genome assembly*. - Alan Veliz-Cuba, Houston (Biochemistry and
Cell Biology).
*Algebraic and systems biology*. - Michael Waterman, U. Southern California (Bio Sci,
Math, CS. PhD Stats).
*Combinatorics of RNA.* - Ruriko Yoshida,
U. Kentucky (Statistics).
*Algebraic statistics, phylogenetics*. - Mingfu Zhu, Duke (Center for Human Genome
Variation).
*Computational genomics*. - Michael Zuker, Rensselaer Polytechnic Institute
(Math).
*Combinatorics of RNA.*

- Virginia Bioinformatics Institute (VBI), Virginia Tech. (NDSSL, and Applied Discrete Math Group)
- Institute for Systems Biology (ISB), Seattle, WA. (Shmulevich Lab)
- Mathematical Biosciences Institute (MBI), Ohio State U.
- National Institute for Mathematical and Biological Synthesis (NIMBioS), U. Tennessee.
- Duke Center for Systems Biology (DCSB), Duke University.
- Center for Combinatorics, Nankai University.