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4)
CURRENT TRENDS IN UNDERGRADUATE BIOMATHEMATICS EDUCATION
Primary
Organizer: Timothy D. Comar Associate Professor of Mathematics,
Department of Mathematics, Benedictine University
Coorganizers:
Olcay Akman, Associate Professor, Department of Mathematics,
Illinois State University, Normal
Mike Martin, Department of Mathematics, Johnson County Community
College
Summary:
New undergraduate courses and programs in mathematical biology
have recently developed in response to the Bio 2010 and Math &
Bio 2010 reports. It is important to ensure that students in these
courses are prepared for graduate programs in mathematical and
computational biology and have the opportunity to participate
in research activities as undergraduates. This minisymposium presents
a variety of courses, research experiences, and other pedagogical
activities designed to prepare and engage undergraduate students
in research in mathematical biology at wide range of institutions.
Talks will discuss new course projects and undergraduate research
activities including the use of Boolean networks, neural networks
and genetic algorithms. The presentations address activities for
a wide range of undergraduate students from students in introductory
courses to advanced undergraduate students.
Purpose:
This minisymposium is designed to discuss the issues of the
preparation of undergraduates for biomathematical research and
the implementation of undergraduate research activities at different
types of institutions. As many potential future researchers in
mathematical and computational biology attend teaching oriented
undergraduate institutions, it is important to include perspectives
from these institutions in addition to the undergraduate activities
that occur at research oriented universities. The collection of
talks promotes the discussion about preparation expectations among
faculty at all types of institutions that educate undergraduate
students and exemplifies current discussion and activity in this
area. This minisymposium nicely fits into the undergraduate mathematical
biology education strand for the conference. Additionally, as
this conference is primarily a research conference, this minisymposium
provides the opportunity for discussion between researchers and
those preparing students in the undergraduate environment.
Audience:
Mathematicians and biologists interested in undergraduate
mathematical biology education, involving undergraduates in research,
and designing courses to support current and future undergraduate
student research; researchers interested in participating in the
discussion about appropriate undergraduate training for future
graduate students in mathematical and computational biology
Speakers:
1. Raina Robeva, Department of Mathematical Sciences, Sweet
Briar College, with Terrell Hodge and Reinhard Laubenbacher
Topdown
and bottomup models of the lac operon network dynamics
The lac operon allows E coli bacteria to utilize extracellular
lactose as a nutrient source by transporting it into the cell
and metabolizing it into glucose. As the first gene network,
its discovery in 1961 resulted in a Nobel Prize for F. Jacob
and J. Monod in 1965. Since then, many mathematical models have
been constructed for this network, which remains an object of
active research. This system is particularly attractive for
pedagogical purposes because the variety of different models
that have been constructed cover broad areas such as systems
of nonlinear differential equations, Boolean networks, and stochastic
methods. While modeling with differential equations is now routinely
taught in conventional courses in mathematics in mathematical
biology, the Bollean networks approach has not achieved equal
popularity even though the mathematical concepts it are fully
accessible to undergraduates with the proper use of specialized
software. The talk will focus on describing, comparing, and
contrasting the Boolean networks and the differential equations
models of the lac operon.
2.
John R. Jungck, Department of Biology, Beloit College,
Linking
A Life to Life
Reasoning about spatial, temporal, and phylogenetic patterns
are crucial to many areas in biology. Recent advances in computer
graphics involving computational geometry and graph theory have
revolutionized our ability to visualize complex patterns in
nature. How can biologists take advantage of these revolutions
in helping them not only comprehend causal forces generating
these patterns as well as rigorously testing hypotheses about
these causal mechanisms? We have developed two such software
packages: "3D FractaL Tree" and "Kame': Voronoi
Image Analyzer" (see <http://www.bioquest.org/BQLibrary/>)
that enable users to analyze two diverse sets of threedimensional
and twodimensional natural patterns. The "3D FractaL Tree"
package encourages users to take explicit measurements on actual
trees such as branching angles, phyllotactic angles, relative
lengths and diameters of successive branches, and the number
of iterative bifurcations along a branch. Realistic three dimensional
trees are generated from these measures and graph rewriting
grammars (Lindenmeyer systems) that can be rotated, translated,
and zoomed on a computer screen. Users can easily see the power
of simple fractal generation rules in the development of complex,
realistic images as well as investigate selfshading, relationships
of canopy area to trunk area, and stochasticity due to environmental
variation. The "Kame': Voronoi Image Analyzer" package
enable users to test whether such diverse biological patterns
as fish nests on a sandy lake bottom, canopy gaps between trees
in mature rain forests, packing of coral colonies, and cell
membranes of epithelial cell tessellations result from nearest
neighbor, local or longrange, global interactions. A specific
case of analyzing the difference between cancerous and noncancerous
tissue patterns will be presented as an example of what has
been termed "cellular sociology" in order to illustrate
the diagnostic power of using such mathematical abstractions
in a specific biological context. General conclusions about
enabling user communities to develop new languages and iconography
for interpreting visual data will be shared.
3. Mike Martin, Department of Mathematics, Johnson County
Community College,
Quantitative
& Computational Literacy: Observations & Implementations
for Mathematical Biology
A characteristic for STEM initiatives is often an integrated,
interdisciplinary curriculum. This talk will feature resources
and observations for models, modules, and media aimed at increasing
the quantitative and computational literacy of undergraduate
students early in their study of both the mathematical and the
life sciences. The aim is to attract mathematicallytalented
students through exposure to rich learning materials and to
enrich awareness for those pursuing careers in the life sciences.
Topics range mathematically from college algebra through differentials
equations and statistics and are scattered throughout the life
sciences. In addition to existing resources, project outcomes
from recent MAAPREP biomath workshops and the CALC for BIO
TRUST will be exhibited.
4.
Glenn Ledder, Department of Mathematics, University of Nebraska
A
Terminal PostCalculus I Mathematics Course for Biology Students
BIO2010 lays out an ambitious mathematics agenda for future
research biologists. To see most of these topics in math courses,
a student would need to take three semesters of calculus and
one each of probability/statistics, differential equations,
and linear algebra. Omission of any one of the latter three
would significantly decrease the value of the whole. However,
only the most dedicated biology major can find room for six
mathematics courses in the crowded biology curriculum. The problem
is worse than it needs to be because of all the topics in those
six courses that are not high priority for biology. At the University
of Nebraska, we set out to follow calculus I with a single course
that includes the most important topics in probability/statistics,
differential equations, and linear algebra, each geared specifically
to the needs of biologists. Students who have room for a third
course can then take a more advanced mathematical biology course.
The challenges have, of course, been to make a wise choice of
topics and to learn how to present them at a lower pedagogical
level than customary. In this talk, we will focus our attention
on the list of topics in our course and the methods we use to
teach these topics.
5.
Timothy D. Comar, Department of Mathematics, Benedictine
University
Activities
Designed to Prepare Undergraduates for Research in Mathematical
Biology
The second semester biocalculus course at Benedictine University
serves as a hybrid between a second semester calculus course
and course designed to prepare students to partake in undergraduate
research activities in mathematical biology or other quantitatively
oriented areas of the biological sciences. Project activities
in this course are designed to integrate mathematics, biology,
and the use of computational software to investigate biological
models. This presentation will highlight several of the weekly
computer laboratory projects and one extended project. The extended
project requires students to read original literature, implement
a biological mathematical model in a computational platform,
prepare a written summary of the mathematics and biology surrounding
the particular model, and give an oral presentation of their
work. This particular project enables students delve more deeply
into a particular model than they can do through a weekly assignment
and also develop skills that will be useful in an interdisciplinary
research environment.
6.
Olcay Akman, Department of Mathematics, Illinois State
University
Mathematics
and Biology Student Engagement on Biomathematics Research Projects
We started implementing student research by teaming graduate
and undergraduate students of biology and mathematics respectively
about two years ago. The hope was that the biology graduate
students get the mathematical and computingintensive methods
based research help while they gain mentoring experience. On
the other hand the undergraduate mathematics students gain valuable
insight on biological research problems while they get involved
in active research with an almostpeer advisor. In this talk
we will report the outcomes of recent research teams and offer
comparison with prior research activities.

