MthSc 985, Fall 2011

MthSc 985, Fall 2011


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

About the class

Finding good research problems is a challenge, even for the most experienced mathematicians. The course represents an introduction to a new active research area in the theory of RNA pseudoknot structures, in a non-traditional class setting. The author of our book, Christian Reidys, pioneered this subfield within the last decade and has carved a niche. In the process, he was honored as a Chang Jiang Scholar, the Chinese national research prize in mathematics. Reidys has written over fifty research articles on this topic with his collaborators (including 7 PhD students) at the Center for Combinatorics, at Nankai University. Reidys has written a book on this research, aimed at researchers and graduates students who are interested in learning about computational biology, RNA structures, and mathematics. The goal of this class is to learn about this new and exciting field. The content of this research area is truly transdisplinary, and draws from all five subfaculty research areas in the mathematical science department at Clemson. That said, no one (instructor included) will be fully prepared in terms of having a solid grasp on all of the prerequisites. However, the unique aspect is that the Clemson graduates students, who are required to take multiple courses in all five subfaculty areas, will have a more diverse and well-rounded background than any of the Clemson faculty! Examples of how various mathematical aspects of this research fall into the five subfaculty areas is given below:

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.

Resources

People involved in combinatorics of DNA/RNA

PhD listed iff it is not in mathematics, applied math, or mathematical sciences.

Literature on the combinatorics of RNA

People who work on new & novel aspects of discrete mathematical biology

PhD listed iff it is not in mathematics, applied math, or mathematical sciences.

Places