Teaching Discrete and Algebraic Mathematical Biology to Undergraduates

(July 29,2013 - August 2,2013 )

Organizers


Terrell Hodge
College of Arts and Sciences, Western Michigan University
Matthew Macauley
Mathematical Sciences, Clemson University
Raina Robeva
Mathematical Sciences, Sweet Briar College

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.

Accepted Speakers

Reka Albert
Department of Physics, Pennsylvania State University
Margaret Cozzens
DIMACS, Rutgers University
Kristina Crona
School of Natural Sciences, University of California, Merced
Monika Heiner
Computer Science, Brandenburgische Technische Universit""at Cottbus
John Jungck
Interdisciplinary Science and Engineering Learning Laboratories, University of Delaware
Winfried Just
Department of Mathematics, Ohio University
Reinhard Laubenbacher
Center for Quantitative Medicine, University of Connecticut Health Center
Svetlana Poznanovikj
Department of Mathematical Sciences, Clemson University
Christian Reidys
Mathematics, University of Southern Denmark
Brandilyn Stigler
Mathematics, Southern Methodist University
Alan Veliz-Cuba
Mathematics, University of Nebraska
Ruriko Yoshida
Statistics, University of Kentucky
Monday, July 29, 2013
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:00 AM

Welcome, overview of workshop, and introductions: Marty Golubitsky

09:00 AM
10:00 AM
10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM
Reinhard Laubenbacher
11:30 AM
12:30 PM
Margaret Cozzens
12:30 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
John Jungck
03:00 PM
03:30 PM

Break

03:30 PM
04:30 PM
Svetlana Poznanovikj
04:30 PM
05:30 PM
Christian Reidys
05:45 PM

Shuttle pick-up from MBI

Tuesday, July 30, 2013
Time Session
08:15 AM

Shuttle to MBI

08:30 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Monika Heiner
10:00 AM
10:30 AM

Break

10:30 AM
12:30 PM

Hands-on time and work on module development

12:30 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Kristina Crona
03:00 PM
03:30 PM

Break

03:30 PM
05:30 PM

Hands-on time and work on module development

05:30 PM
07:00 PM

Reception and Poster Session

07:15 PM

Shuttle pick-up from MBI

Wednesday, July 31, 2013
Time Session
08:15 AM

Shuttle to MBI

08:30 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM
Winfried Just
11:30 AM
12:30 PM
12:30 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Alan Veliz-Cuba - Dicrete dynamic modeling of signaling networks
Dicrete dynamic modeling of signaling networks
03:00 PM
03:30 PM

Break

03:30 PM
04:30 PM
Reka Albert
04:30 PM
05:30 PM
Brandilyn Stigler
05:45 PM

Shuttle pick-up from MBI

Thursday, August 1, 2013
Time Session
08:15 AM

Shuttle to MBI

08:30 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Ruriko Yoshida - Comboinatorics of Phylogenetics
Comboinatorics of Phylogenetics
10:00 AM
10:30 AM

Break

10:30 AM
12:30 PM

Hands-on time and work on module development

12:30 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM

Hands-on time and work on module development

03:00 PM
03:30 PM

Break

03:30 PM
05:30 PM

Hands-on time and work on module development

05:45 PM

Shuttle pick-up from MBI

06:30 PM
07:00 PM

Cash Bar

07:00 PM
09:00 PM

Banquet in the Fusion Room @ Crowne Plaza Hotel

Friday, August 2, 2013
Time Session
08:15 AM

Shuttle to MBI

08:30 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM

Hands-on time and work on module development

10:00 AM
10:30 AM

Break

10:30 AM
11:30 AM

Hands-on time and work on module development

11:30 AM
12:30 PM

Closing Discussion

12:30 PM

Shuttle pick-up from MBI (one to hotel, one to airport)

Name Email Affiliation
Albert, Reka ralbert@phys.psu.edu Department of Physics, Pennsylvania State University
Callender, Hannah Callende@up.edu Mathematics, University of Portland
Comar, Timothy tcomar@ben.edu Mathematics, Benedictine University
Cozzens, Margaret midgec@dimacs.rutgers.edu DIMACS, Rutgers University
Crona, Kristina kcrona@ucmerced.edu School of Natural Sciences, University of California, Merced
Davies, Robin davies@sbc.edu Biology, Sweet Briar College
Dawes, Adriana dawes.33@osu.edu Department of Mathematics / Department of Molecular Genetics, The Ohio State University
Dimitrova, Elena edimit@clemson.edu Mathematical Sciences, Clemson University
Dorman, David dorman@middlebury.edu Mathematics, Middlebury College
Galovich, Jennifer jgalovich@csbsju.edu Mathematics and Statistics, St. John's University
Gerald, Tonya tgerald@nccu.edu Chemistry, North Carolina Central University
Goins, Gregory gdgoins@ncat.edu Department of Biology, North Carolina A&T State University
Greene, Devin dgreene@ucmerced.edu Math, Science, and Engineering, Evergreen Valley College
Hao, Wenrui whao@nd.edu Department of Applied and Computational Mathematics and Statistics, University of Notre Dame
Heiner, Monika Monika.Heiner@informatik.tu-cottbus.de Computer Science, Brandenburgische Technische Universit""at Cottbus
Hodge, Terrell terrell.hodge@wmich.edu College of Arts and Sciences, Western Michigan University
Hrozencik, Dan dhro@att.net Mathematics and Computer Science, Chicago State University
Jarrah, Abdul Salam ajarrah@aus.edu Mathematics and Statistics, American University of Sharjah
Jungck, John jungck@udel.edu Interdisciplinary Science and Engineering Learning Laboratories, University of Delaware
Just, Winfried mathjust@gmail.com Department of Mathematics, Ohio University
Kadas, Zsuzsanna zkadas@smcvt.edu Department of Mathematics, St. Michael's College
Kheibarshekan, Leila lkheibarshekan@gmail.com pharmacy, Universite de Montreal
Kheyfits, Alexander akheyfits@gc.cuny.edu Mathematics and Comp. Science, Bronx Community College, CUNY
Khurana, Archana archana2106@gmail.com University School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University
Kondrashov, Dmitry dkon@uchicago.edu BSCD, University of Chicago
LaMar, Michael drew.lamar@gmail.com Department of Biology, College of William and Mary
Laubenbacher, Reinhard laubenbacher@uchc.edu Center for Quantitative Medicine, University of Connecticut Health Center
Macauley, Matthew macaule@clemson.edu Mathematical Sciences, Clemson University
Matache, Mihaela dmatache@unomaha.edu Mathematics, University of Nebraska
O Hara, Kathy kohara1@vbi.vt.edu Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University
Owen, Megan megan.owen@uwaterloo.ca Computer Science, University of Waterloo
Pangborn, Greta gpangborn@smcvt.edu Computer Science, Disease Pathways, LLC
Poznanovikj, Svetlana spoznan@clemson.edu Department of Mathematical Sciences, Clemson University
Reidys, Christian duck@santafe.edu Mathematics, University of Southern Denmark
Robeva, Raina robeva@sbc.edu Mathematical Sciences, Sweet Briar College
Rusinko, Joseph rusinkoj@winthrop.edu Mathematics, Winthrop University
Stigler, Brandilyn bstigler@smu.edu Mathematics, Southern Methodist University
Toporikova, Natalia toporikovan@wlu.edu Biology, Washington and Lee University
Vatter, Vince vatter@ufl.edu Mathematics, University of Florida
Veliz-Cuba, Alan aveliz-cuba2@unl.edu Mathematics, University of Nebraska
Vera-Licona, Paola paola.vera-licona@curie.fr Bioinformatics and Computational Systems Biology of Cancer, Institut Curie
Washington, Talitha talitha.washington@howard.edu Mathematics, Howard University
Wiesner, Emilie ewiesner@ithaca.edu Mathematics, Ithaca College
Yoshida, Ruriko ruriko.yoshida@uky.edu Statistics, University of Kentucky
Dicrete dynamic modeling of signaling networks
Dicrete dynamic modeling of signaling networks
Comboinatorics of Phylogenetics
Comboinatorics of Phylogenetics
  • Dynamics of Disease Transmission on Networks: Slides, Student Projects, m-files, and Sample Solutions

    These materials give a brief introduction to models of disease transmission on contact networks. Such models allow for exploration of stochastic effects and incorporation of more biological detail than the classical compartment-based ODE models. The module contains a brief introduction that outlines the scope of the module and lists a number of conceptual exercises, lecture notes, as well as simulation-based exercises and projects together with software documentation and the m-files of the companion MatLab-based software. We also provide sample solutions. The conceptual exercises mainly illustrate some of the tradeoffs inherent in choosing a mathematical model, while the simulation exercises focus on exploring how properties of the underlying contact network influence the expected dynamics. We also include a preliminary version of alternative NetLogo code for the simulation exercises and projects, as well as a stand-alone sample project based on the NetLogo code.

    A much expanded version of these materials will be published in two chapters of the forthcoming book Algebraic and Discrete Mathematical Methods in Modern Biology, R. Robeva (ed.), Academic Press.


    The materials posted here grew out of the lecture Dynamics of Disease Transmission Networks given by Winfried Just (Ohio University) at Teaching Discrete and Algebraic Mathematical Biology to Undergraduates, as well as a collaborative effort that was initiated during the workshop by Hannah Callender (University of Portland), Dmitry Kondrashov (University of Chicago), Drew LaMar (College of William and Mary) and Natalia Toporikova (Washington and Lee University).


    For most convenient working with the module, including access to the sample solutions via the embedded hotlinks, download the compressed file, be sure to unzip it, open the file DDTN.pdf in your local .pdf viewer, and follow the links.