In the last decade, methods from modern discrete mathematics have been used with great success for solving a wide range of biological problems. Graph theory, Boolean networks, polynomial dynamical systems (including many agent-based models), Petri nets, Groebner bases and other elements from algebraic geometry and modern algebra have rapidly gained popularity and have become essential tools for mathematical biology research. Relatively little progress has been made, however, in introducing those techniques to the mainstream undergraduate mathematical biology curriculum even though for many of them the level of mathematical sophistication and the nature of the material are often entirely appropriate. Thus, while the more traditional mathematical biology topics including ODEs, PDEs, difference equations, and continuous dynamical systems have already successfully worked their way into classes and have become standard curriculum, discrete and algebraic mathematical techniques have remained relatively invisible. There is a growing gap between research and education with regard to utilizing algebraic methods and there is pressing need in the colleges and universities across the country for: 1) identifying and developing curricular materials focusing on discrete and algebraic methods for biology, and 2) preparing faculty with research interests in mathematical biology to teach undergraduate courses that stress the importance of these methods.
The workshop has two major goals: 1) Introduce current problems from biology that utilize discrete and algebraic methods at a level appropriate for undergraduates and outline the methods, models, and software as well as existing materials with examples, exercises, and projects. 2) Produce outlines of new curricular materials based on some of the workshop talks on topics for which no materials for undergraduate courses are available. Speakers will provide introductory examples and exercises/projects and participants will work through those, provide additional ones, and compile a list of notes and solution guidelines and outlines that, together with outlines of the main biological questions and mathematical methods, will form the core of new instructional modules on those topics. Links to the existing and newly developed material, together with approved video recordings of the lectures and the presentation slides, will be posted on the MBI's site to make the materials available to anyone who wishes to introduce the respective topics in their classes.