TWO-DAY SHORT COURSE
Short Courses are organized around relevant themes and are held the two-days preceding MAA national meetings.
The MAA MathFest Short Courses is presented in honor of William F. Lucas.
IMPLEMENTING BIOLOGY ACROSS THE MATHEMATICS CURRICULUM
John R. Jungck, Beloit College
Part 1: Wednesday, August 1, 9:00 am - 5:00 pm
Part 2: Thursday, August 2, 9:00 am - 5:00 pm
Many mathematics educators are faced with the challenge that the majority of students enrolled in their classes are from the life sciences writ broadly (biology, allied health, environmental sciences, agriculture, etc.), while most mathematicians have very little background in the life sciences themselves. Therefore, the MAA has chosen to meet this year in combination with the joint meeting of the Society for Mathematical Biology and the Japanese Society for Mathematical Biology. This short course, while preceding MathFest, is concurrent with those joint meetings and has the advantage that participants will not only be able to be involved in the short course, they will also be able to attend the plenary lectures of those societies during those days as guests of those societies at no additional cost. Besides the Society for Mathematical Biology and the SIGMAA on Mathematical Biology, the individual lecturers in the short course also represent several organizations committed to the inclusion of much more mathematics in biology education and much more biology in mathematics education: the BioQUEST Curriculum Consortium (in particular, several of its projects: NUMBERS COUNT! (Numerical Undergraduate Mathematical Biology Education: exploRing with Statistics, Computation, mOdeling, and qUaNtitative daTa); the Biological ESTEEM Project (Excel® Simulations and Tools for Exploratory, Experiential Mathematics); the BEDROCK Project (Bioinformatics Education Dissemination: Reaching Out, Connecting, and Knitting-together) http://www.bioquest.org); and CoMBiNe: (the Computational and Mathematical Biology Network http://muweb.marymount.edu/~eschaefe/combine/welcome.htm). Biological subjects will include evolution, ecology, epidemiology, biometrics, genetics, bioinformatics, microbiology, and biochemistry. Mathematical subjects will include probability and statistics, linear algebra, differential equations, combinatorics, number theory, graph theory, and geometry. The examples employed will be appropriate for inclusion in courses aimed at the first two years of the undergraduate curriculum and will serve as an entrè for introducing mathematicians to many current avenues of research in mathematical biology as well.
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LECTURE 1
Probability & Statistics-based Models
Raina Robeva, Sweet Briar College
This part of the course will focus on biological and medical models that utilize methods from the fields of probability or statistics. We will begin with examples from genetics to illustrate the Binomial, Normal, and Poisson distributions and discuss the underlying biological mechanisms and mathematical connections. More specifically, we will outline the experiments of Nilsson - Ehle and discuss the emergence of quantitative traits based on the Central Limit Theorem. We will examine the Luria-Delbrück experiments and show how using a Poisson distribution to describe the count of resistant bacterial variants allows for statistically distinguishing between the hypothesis of mutation to immunity and the hypothesis of acquired immunity. Next, we will examine some medical models for risk assessment such as assessing the risk for hypoglycemia in diabetes, quantified from self-monitoring blood glucose data, or the risk for neonatal sepsis, quantified from electrocardiographic (EKG) data.
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LECTURE 2
Biological Esteem: Linear Algebra, Population Genetics, and Microsoft Excel
Anton E. Weisstein, Truman State University
Population geneticists apply a wide range of mathematical techniques in seeking to understand and predict changes in the genetic make-up of real-world populations. In this session, we will: (1) review the recursion equations for calculating allele frequencies under the assumptions of Hardy-Weinberg Equilibrium, (2) mathematically model the effects of specific evolutionary forces such as selection and migration, and (3) apply linear algebra to understand why natural selection disfavors a specific genetic variant that provides the best known resistance to malarial infection. These investigations will introduce some of the Excel tools from the BioQUEST Consortium's Biological ESTEEM collection.
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LECTURE 3
Bioinformatics from an Applied Combinatorics Perspective
Jennifer R. Galovich, St. John's University and the College of St. Benedict
RNA folding, Smith-Waterman Sequence Alignment, and other topics will be presented in the context of a new bioinformatics course taught in an undergraduate institution's mathematics department by an applied combinatorist who spent her sabbatical last year at the Mathematical Biosciences Institute at Ohio State University and with the BEDROCK Project (Bioinformatics Education Dissemination: the BioQUEST Curriculum Consortium at Beloit College.
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LECTURE 4
The Basics of Infectious Disease Modeling
Holly D. Gaff, University of Maryland School of Medicine
A wide variety of mathematical models have been used to study an equally wide variety of infectious diseases. We will discuss the basic of infectious disease epidemiology, the building blocks for models, the types of mathematical approaches and the history of epidemiology models. We will walk the examples of disease models including measles and tick-borne diseases.
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LECTURE 5
Teaching Mathematics to Biologists and Biology to Mathematicians
Gretchen A. Koch, Goucher College
When using mathematics to model biology, one must decide the level at which to present the material. In this session, I will present several modules from the BioQUEST Consortium's Biological ESTEEM collection and demonstrate to the audience how each module can be used at varying levels of mathematical and biological ability. The modules will include a logistic growth model, a competing species model, and a SIR epidemiological model. Time permitting, an additional application based in MATLAB will be demonstrated to compare and contrast the ESTEEM competing species model.
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LECTURE 6
Biographer: Graph Theory Applied to the Breadth of Biology
John R. Jungck, Beloit College
Graph Theory is generally applicable to many areas of biology such as: pedigrees and multiple allele genetic graphs in genetics, fate maps in developmental biology, phylogenetic trees in evolution and systematics, metabolic pathways and RNA folding in biochemistry, interactomes in genomics-molecular biology, restriction maps in biotechnology, food webs in ecology, infection contact maps in epidemiology, and, Delaunay triangulations in image analysis. Despite this breadth of utility, there has been a lack of easy-to-use tools for entering biological data into graph visualization packages with tools for graph theoretical analysis. BioGrapher is an Excel® and open source graph visualization package for importing, illustrating, and analyzing biological data. Interval graphs, planar graphs, trees, de Bruijn graphs (Euler paths), n-cubes (Hamiltonian paths), and Voronoi tessellations-Delaunay triangulations will be illustrated through biological examples.
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LECTURE 7
Number Theory and Genomics
Julius H. Jackson, Michigan State University
Number Theory is used in a study of bacterial and archaeal genomes as information systems that determine the physiological states of an organism. The larger goal is to model the dynamics of information evolution and exchange in prokaryotes, and to derive the theory base to explain the origin, evolution and function of genes and chromosomes. Our goal is to discover and model gene-specific and genome-specific information that defines metabolic properties and physiological behavior of prokaryotes in adaptive response to their environment(s). The limits of coding space, protein mobility, and variation space are explored to understand the physiological consequences of such limits. This work utilizes experimental methods for genetic, molecular biological, biochemical and microbiological studies in combination with mathematical and computational methods for modeling and simulating the function of natural systems. My teaching approach is to prepare students to view organisms and their environments as biological systems, to ask critical questions about how these systems work and interact, and to design experiments that yield quantitative assessments of systems behavior that will lead to construction of mathematical models for simulation.
