## Past MAA Short Courses

MathFest 1997 (Atlanta)

**Epidemiology Modeling **
Herb Hethcote, University of Iowa

1998 Joint Mathematics Meetings (Baltimore)

**Mathematical Imaging and Image Processing**
Akram Aldroubi, Vanderbilt University

Dennis Healy, DARPA/Dartmouth College

MathFest 1998 (Toronto)

**Calculated Deceptions **
Arthur Benjamin, Harvey Mudd College

A. Brent Morris, National Security Agency

1999 Joint Mathematics Meetings (San Antonio)

**Mathematics in Finance **
Robert Almgren, University of Chicago

MathFest 1999 (Providence)

**Recent Developments in the Teaching of Differential Equations **
Paul Blanchard, Boston College

2000 Joint Mathematics Meetings (Washington, D.C.)

**Fuzzy Mathematics **
Kiran Bhutani, Catholic University

MathFest 2000 (Los Angeles)

**Introduction to Error Correcting Codes**
Vera Pless and W. Cary Huffman

2001 Joint Mathematics Meetings (New Orleans)

**Knots in Science**
De Witt Sumner

MathFest 2001 (Madison)

**The Life and Legacy of Ramanujan**
Kenneth Ono

2002 Joint Mathematics Meetings (San Diego)

**A Sampler of Applications of Graph Theory**
Fred Roberts

MathFest 2002 (Burlington)

**The Mathematics of Cryptology**
Carl Pomerance

2003 Joint Mathematics Meetings (Baltimore)

Mathematics in the Ancient World
Frederick Rickey

MathFest 2003 (Boulder)

Reading the Book of Life: How Bioinformatics Makes
Sense Molecular Messages
John R. Jungck

Joint Mathematics Meetings 2004 (Phoenix)

The History of Mathematical Technologies:
Exploring the Material
Culture of Mathematics
Amy Shell-Gellasch and Glen Van Brummelen

MathFest 2004 (Providence)

Random Matrix Theory
Alan Edelman

Joint Mathematics Meetings 2005 (Atlanta)

Eight Lectures on Random Graphs
Alan M. Frieze

MathFest 2005 (Albuquerque)

Recreational Mathematics: A Short Course in Honor
of the 300th Birthday
of Benjamin Franklin
Paul Pasles

2006 Joint Mathematics Meetings (San Antonio)

Trends in Experimental Mathematics
Organized by Jonathan M. Borwein, Dalhousie University

MathFest 2006 (Knoxville)

Environmental Modeling
Ben Fusaro, Florida State University

Joint Mathematics Meetings 2007 (New Orleans)

Leonhard Euler - Looking Back After 300 Years
Edward Sandifer and Robert Bradley

MathFest 2007 (San Jose)

Implementing Biology Across the Mathematics
Curriculum
(in cooperation with the joint meetings of the Society for Mathematical
Biology the Japanese Society for Mathematical Biology)

John R. Jungck

Joint Mathematics Meetings 2008 (San Diego)

Combinatorics: Past, Present, and Future
Robin Wilson

MathFest 2008 (Madison)

Game-theoretic Modeling: Techniques and
Applications
Michael A. Jones

Joint Mathematics Meetings 2009 (Washington D.C.)

Data Mining and New Trends in Teaching Statistics
Richard D. De Veaux

### Mathematics in the Ancient World

Frederick Rickey

Nearly everyone who has taken an interest in the history of mathematics
becomes fascinated with some facet of ancient mathematics. But only a
few have the mathematical preparation, historical sensitivities, and
linguistic skills to do original work. The speakers at this short
course will give an expository survey

of their special area of ancient mathematics. They will discuss some
areas of current research, point out open questions, and provide
guidelines to help you delve into the expository and research
literature. Those of you who have taught history of mathematics will
undoubtedly learn that some of what you read in older literature has
been superseded by modern scholarship. Thus you will have much to carry
back to your classroom. Speakers and their talks include:

- Eleanor
Robson, The Oriental Institute, All Souls College, Oxford University,
Mesopotamian Mathematics
- Will Noel, The Walters Art Museum, The
Archimedes Palimpsest and Its Restoration
- Reviel Netz, Department of
Classics, Stanford University, Archimedes
- Kim Plofker, Department of
the History of Mathematics, Brown University, Mathematics in India
- Joseph W. Dauben, Herbert H Lehman College (CUNY), Mathematics in
China
- Len Berggren, Simon Fraser University, Islamic Mathematics

### Reading the Book of Life: How Bioinformatics Makes Sense Molecular
Messages

John R. Jungck

Bioinformatics is an emerging area that combines extensive
mathematical and computer applications in molecular biology.
This course will introduce how genetic sequences can be
analyzed with coding and information theory, computational
linguistics, dynamic programming of multiple sequence comparison,
and phylogenetic trees. Other topics include: molecular
surface calculations as well as X-ray crystallographic approaches
to structure determination, knot theory for studying
the topological changes involved in replication, recombination,
and repair of DNA, RNA folding, and analysis of DNA chips
to study expression of genes. The level of mathematics will be
at the undergraduate level and often is accessible to biology
students.
#### Genetic Codes as Codes: Towards a Theoretical Basis for
Bioinformatics

John R. Jungck, Beloit College
#### DNA Motif Lexicon and Moving Research to the Classroom: Linking
Courses in Biology and Computer Science

Mark D. Leblanc, Wheaton College
#### Topological Toys, Tinkering Thinking: Knot Theory and DNA

John R. Jungck, Beloit College
#### RNA Folding and Combinatorics

Asamoah Nkwanta, Morgan State University
#### Microarray Data Analysis: From Tiny Pixels to the Big Picture

Laurie J. Heyer, Davidson College
#### The Middle Level Problem of Genomics: Interactive Assembly of
Restriction Fragments Using Interval Graphs and Extending This Approach
to Metabolonomics

John R. Jungck, Beloit College
#### X-ray Crystallography and Protein Structure

Stephen Everse, University of Vermont
#### Escherian Esthetics of Voronoi Polygons and Polyhedra: How to Fold
a Protein and Scale Independence in Irregular Biological Patterns

John R. Jungck, Beloit College
### The History of Mathematical Technologies: Exploring the Material
Culture of Mathematics

Amy Shell-Gellasch and Glen Van Brummelen

This short course will explore the history, development, use,
and significance of various mathematical devices throughout
history. Devices investigated will include sun dials, linkages,
navigational and surveying devices, early computing devices,
and early computers. Presenters will bring in actual historical
devices when possible. The sessions will be a mix of traditional
presentations, followed by a hands-on demonstration and
question period. Topics will cover calculations and Mensuration
devices from various eras, from ancient to modern times. Our
finale will be a presentation on mathematical devices at world’s
fairs.

Presenters include:

- Lennart Berggren, Simon Fraser
University; and James Evans, University of Puget Sound,
Instruments of the ancient
astronomers: Mathematics and
history
- Ed Sandifer, Western Connecticut State University,
Fourier without the formula: How
harmonic analyzers work
- Daina Tainima, Cornell University, What linkages have to do
with mathematics
- David Weil, Computer Museum of America,
Early computing devices
- Peggy Aldrich Kidwell, National
Museum of American History, Mathematical
instruments at
the fairs

### Random Matrix Theory

Alan Edelman

Random matrix theory: It is mathematics; it is statistics; it is
physics; it is engineering. It is stochastic equation solving in its
most glorious form. There have been applications for decades,
yet the subject is not sufficiently well-known or wellunderstood
for all of the applications to have been realized.
One-by-one the word has to spread. This is a start.
In this course we will review the theory from the finite to the
infinite. We will consider Gaussian ensembles and Wishart
matrices. There will be Riemann zeta and Painleve for the
mathematicians. There will be zonal polynomials and
hypergeometrics of matrix argument for the statisticians. We
will emphasize applications to wireless communication not
only for its own sake but as a case study for other applications
to follow.
#### Lecture 1: MOPs ’ Multivariate Orthogonal Polynomials
(symbolically) or A Maple Library to Clean Up Messy Integrals

Ioana Dumitriu (UC Berkeley)

Many statistical, physical, and engineering problems require
the use of random matrix theory, and with it, the computation
of a certain messy multivariate integral (sometimes parameterdependent)
over a subset of the real line. Using multivariate
orthogonal polynomial theory, we have written and
implemented in Maple a set of codes which provide a unified
way of dealing with such computations, for certain classical
types of random matrices. These codes are fast (in a relative
sense, as the complexity of the problem is super-polynomial)
and have the advantage of working both symbolically and
numerically. We will discuss a few problems, the computations
they involve, and demonstrate the performance of MOPs in
each case.
#### Lecture 2: How Eigenvalues of Random Matrices Can Be Used to Solve
Problems in Wireless Communications

Moe Win (MIT) and Marco Chiani (University of Bologna)

You are a medieval knight and you want to send an important
message to the king in another country. Unfortunately, the
messages that you send may become stained or soaked with
water! Furthermore, some routes may be closed due to natural
and unnatural events such as fire, floods, banditry, (and stray
dragons). Your astrologer comes up with a brilliant idea: send
multiple couriers along different routes in hopes that the
received letters can be combined to make a coherent message.
We consider a class of problems arising in wireless
communications where we are given the statistical behavior of
possible routes, and how we can use ’route diversityâ? to improve
the reliability of a wireless communication system. Finally, we
will show why it is better to have more antennas on your Wi-
Fi, or in medieval terms, more horses in your stables. We will
show how the beautiful theory of random matrices and
eigenvalues can be used to model this class of problems and
give insights into the design of future communication systems.
#### Lecture 3: Random Matrix Manipulations and Free Probability (or
Would you probably be free for a course in free probability?)

Raj Rao (MIT)

In traditional probability theory, independence of random
variables allows one to easily compute the distribution of the
sums or products of these variables. For random matrices,
freeness is the analogous concept that allows us to compute
the distribution of the eigenvalues of the sums or products or
other functions of random matrices. Freeness turns out to be
important and quite powerful because unlike scalar random
variables, the order in which the random matrices are
multiplied matters. Free probability is the theory that tells us
what it means to be ’freeâ? and what we can or cannot do when
the variables in question are ’freeâ?. We will discuss free
probability and demonstrate how it can be used to compute
the distribution of seemingly intractable functions of random
matrices. This is joint work (more accurately, joint fun) with
Alan Edelman (MIT)
### Eight Lectures on Random Graphs

Alan M. Frieze

The subject began properly with a sequence of seminal papers
in the 1960’s by Paul ErdÃ¶s and Alfred RÃ©nyi. ErdÃ¶s
had already
used randomly generated graphs as a tool for showing the
existence of various structures, but these papers began the study
of random graphs as objects in their own right. Since that time
there has been much research establishing the likely structure
of various models of random graph and finding uses for this
knowledge. In this course we provide some of the basic results
and tools used in the area.

Presenters include:

- Thomas A.
Bohman, Carnegie Mellon University, Evolution
of Gn,m
- Oleg
Pikhurko, Carnegie Mellon University, Thresholds
for some basic
properties
- Benny Sudakov, Princeton University, Probabilistic
Method
- Andrzej Rucinski, Adam Mickiewicz University, Small
subgraphs
- Nick Wormald, University of Waterloo, Random
regular graphs
- Dimitris Achlioptas, Microsoft Research, Graph
coloring and random k-SAT
- Michael Molloy, University of
Toronto
- Alan M. Frieze, Carnegie
Mellon University, Web graphs

### Recreational Mathematics: A Short Course in Honor of the 300th
Birthday of Benjamin Franklin

Paul Pasles

Despite his limited formal education, Franklin was dedicated
to learning and to facilitating the learning of others. As he famously
opined, mathematical exercises with no direct application
could still be valuable simply because they hone one’s reasoning
skills. This short course will focus on ways to use ’funâ?
problems at all levels for the purpose of developing students’
mathematical abilities. Paul C. Pasles will begin the course with
a few opening remarks.
#### Lecture 1: Magic Square Magic

Art Benjamin, Harvey Mudd College

The mathemagician invites a member of the audience to join
him onstage and to give him any number (typically a number
between 50 and 100). The mathemagician then draws a blank
4-by-4 grid, and asks the volunteer to point to the 16 cells in
any order. As each cell is pointed to, the mathemagician immediately
writes a number in the cell. When the grid is full, the
rows, columns, diagonals, and many other groups of 4, will
sum to the spectator’s number. This impressive feat of mathematical
magic is very easy to do, as you will learn. Did you
notice that my title is palindromic? All 3-by-3 magic squares
have a beautiful, little-known property called ’squarepalindromicity.â?
To illustrate, using the 3-by-3 magic square
4 9 2
3 5 7
8 1 6
you can verify that the sum of the squares of the 3-digit numbers
given by the rows satisfy
(492)2 + (357)2 + (816)2 = (294)2 + (753)2 + (618)2. The same
phenomenon occurs with the columns, and the (wrapped) diagonals.
In fact, this property holds when the numbers are
written in any base! Essentially this property holds for every 3-
by-3 magic square (of any sum), and for a large class of n-by-n
magic squares as well. These properties can be derived using
elementary linear algebra. The proof was discovered with an
undergraduate, Kan Yasuda, and was eventually published in
the American Mathematical Monthly. Time permitting, I will
also demonstrate and explain magical ways to ’squareâ? numbers.
#### Lecture 2: DÃ¼rer’s Magic Squares, Cardano’s Rings, Prince
Rupert’s Cubes, and Other Neat Things

Professor V. Frederick Rickey
United States Military Academy

Recreational mathematics is as old as mathematics itself, so a
survey of its history is out of the question. Instead we discuss a
few neat things, setting each in its historical context and explaining
their significance. As a benchmark for looking forward
and back we shall take Charles Hutton’s Recreations in
Mathematics, which in turn is based on works of Ozanam and
Montucla on recreational mathematics.
#### Lecture 4: Problem Solving Through Recreational Mathematics

Orin Chein, Temple University

My part of the program will be divided into two sessions. During
the first session, at the end of Day 1, I will describe a course
in recreational mathematics that we offer at Temple University,
and introduce a variety of problems from the text. I will
also perform some mathematical card and number tricks for
participants to think about. On day two, we will discuss solutions
to some of the problems as well as the mathematics behind
some of the tricks.
#### Lecture 5: Over Thirty Years of Alphametics in the Journal of
Recreational Mathematics

Charles Ashbacher, Editor, Journal of Recreational Mathematics

The alphametic, an arithmetic problem where letters represent
digits and the letters also create a message, has been a staple
problem in the Journal of Recreational Mathematics since the
first issue was published. The messages are simple, such as the
classic SEND+ MORE = MONEY. Solving them is usually an
exercise in algebra in combination with trial and error. Solving
an alphametic also makes an excellent programming assignment
in beginning programming classes, in that they can be
solved in a brute force manner by creating a set of nested loops.
This presentation will be a demonstration of the various forms
of the alphametic and how they are solved. The messages of
the alphametics that have been published in the JRM over the
years have covered a wide area. Everything from political statements
to congratulations and condolences has been published
as math problems. Some of the more interesting examples of
this area of mathematics will also be given.
#### Lecture 6: How to Change Coins, M&M’s, or Chicken Nuggets: The
Linear Diophantine Problem of Frobenius

Matthias Beck, San Francisco State University

How many ways are there to change 42 cents? How many ways
will there be when all the pennies are gone? How about if nickels
were worth four cents? More generally, suppose we have
coins of denominations a1, a2, ..., ad. Can one find a formula for
the number c(n) of ways to change n cents? A seemingly easier
question is: can you change n cents, using only our coins? Depending
on the culinary preference of the audience, we may
state these questions in terms of bags of M&M’s or boxes of
Chicken Nuggets (’Can you buy Chicken Nuggets so that our
34 friends get exactly one each?â?). We will see that if a1, a2, ..., ad
do not have any common factors then we can be certain that
we can change n, provided n is large enough. A natural task
then is to find the largest integer that cannot be changed. This
problem, often called the linear Diophantine problem of
Frobenius, is solved in closed form for d = 2, in generatingfunction
form for d=3, and wide open for d > 3. We will outline
several elementary approaches to the d=2 case of this classical
problem, including one that generalizes to d=3. These
proofs are well suited for undergraduate classes in discrete
mathematics, number theory, abstract algebra, combinatorics,
or geometry. Going a step further, we will use the above counting
function c(n) to recover and extend some well-known results
on the Frobenius problem. En route we will discuss some
basic number theory and discrete geometry connected to c(n).
We will mention several open problems, some which are well
suited for original undergraduate research projects.
#### Lecture 7: Magic Squares in the Twenty-First Century

Maya Mohsin Ahmed, University of California - Davis

The problem of constructing magic squares is of classical interest.
Enumerating magic squares is a relatively new problem.
I will describe how to construct and enumerate magic squares
as lattice points inside polyhedral cones using techniques from
algebraic combinatorics. I will also look at the correspondence
of magic labelings of graphs and symmetric magic squares.
### Trends in Experimental Mathematics

Organized by Jonathan M. Borwein, Dalhousie University

The last twenty years have been witness to a fundamental shift
in the way mathematics is practiced. With the continued advance
of computing power and accessibility, the view that ’real
mathematicians don’t computeâ? no longer has any traction for
a newer generation of mathematicians that can really take advantage
of computer aided research, especially given the modern
computational packages such as Maple, Mathematica, and
Matlab. While a working knowledge of some mathematical
computing package is an advantage, it is certainly not a prerequisite.
Additionally, the course will be ’hands onâ? for those
who wish to follow along using their laptops, via a wireless
Internet connection.
The goal of this course is to present a coherent variety of accessible
examples of modern mathematics where intelligent
computing plays a significant role and in doing so to highlight
some of the key algorithms and to teach some of the key experimental
approaches. The program includes the following
lectures:

- What is experimental
mathematics?, Jonathan M.
Borwein
- Case Study I: Integrals and
series using mathematica,
Victor H. Moll, Tulane University
- Algorithms for experimental
mathematics, I, David H. Bailey, Lawrence Berkeley National
Laboratory
- Case Study II: Discrete math
and number theory in
Maple and C++, Neil J. Calkin, Clemson University
- Case Study
III: Inverse scattering on Matlab, D. Russell Luke, University
of
Delaware
- Case Study IV: Analysis and
probability on the computer,
Roland Girgensohn, Bundeswehr Medical Office
- Algorithms
for experimental mathematics, II, David H. Bailey
- Concluding
examples. Putting everything together, Jonathan M.
Borwein.

### Environmental Modeling

Ben Fusaro, Florida State University

The goal of this two-day course is to introduce college teachers
to a variety of topics in environmental mathematics and to the
opportunities that this emerging field provides to interact with
the larger society. Ben Fusaro has been active in lecturing, writing,
and organizing activities in environmental mathematics
since 1984. He will do the introduction and wrap-up.
#### Lecture 1: Measuring Pollution

Fred S. Roberts, DIMACS Center Rutgers University

Finding simple ways to measure the amount of pollution in
the air we breathe, the water we drink, or the sounds we hear,
has long been a goal of environmental scientists. We will discuss
pollution indices in the context of a more general discussion
of the theory of meaningful and meaningless statements
and scales of measurement. A statement involving scales of
measurement is called meaningless if its truth or falsity can
depend on the particular versions of scales which are used in
the statement. We will develop the theory and apply it to measurement
of air, water, and noise pollution. We will discuss the
possibility of averaging different measures of pollution in a
meaningful way, or of combining different measures of pollution
to get a consensus measure. We will also describe the use
of expert judgments to assess pollution levels and describe ways
to combine these judgments in the context of mathematical
models of the level of air pollution and energy use in cities.
#### Lecture 2: Optimal Control of Environmental Models

Suzanne Lenhart, University of Tennessee ’ Knoxville

This is an introduction to optimal control of systems of ordinary
differential equations that model environmental processes.
Examples will be taken from population, disease and the bacterial
control of pollutants.
#### Lecture 3: Modeling Oil Reserves

Catherine A. Roberts, College of the Holy Cross

The challenge of modeling oil supply and production is
interdisciplinary,
calling upon geology and environmental science,
as well as mathematics. The issue is also laced with political
and philosophical perspectives on the nature of our relationship
with the planet. This talk will introduce this topic at a
level suitable for a liberal arts course in mathematical modeling
or environmental science. Models that provide insight into
how oil production schemes impact this natural resource will
be developed and discussed. As a specific example, the speaker
will describe a model tied to oil drilling in the Arctic National
Wildlife Refuge.
#### Lecture 2: A Mathematical Look at Extinction

Roland H. Lamberson, Humboldt State University

We will explore some mathematical models in ecology with
particular interest in the probability of extinction. We will look
at measures of vulnerability, risky management strategies and
how reliably models can predict the viability of a species. Species
of interest will include blue whales, northern spotted owls
and Pacific salmon.
#### Lecture 5: Clutching for Survival: The California Condor
Restoration Project

Thomas O’Neil,California Polytechnic State University - San Luis Obispo

Since 1999, several Cal Poly students and I have been providing
support to the Ventana Wilderness Society in their effort to
establish a flock of California condors in the Big Sur area. A
good recovery strategy requires an accurate population projection
program. Unfortunately, there are several condor traits
that make construction of such a program difficult. We will
discuss these traits and how we have overcome many of the
problems. Additionally, there is a lack of data. Critical to any
population projection program is the survival rate data. There
are estimates that can be used for first approximations but these
data are based on observations of small populations of wild
condors. Little was known of how the captive bred and reared
birds will fare in the wild. To help in this area, we created a
database of every California condor in captivity or in the wild,
living or dead since 1987, the year the last wild condor was
brought into captivity. We will discuss the problems encountered
in creating this database and getting it into a format that
has made it a useful tool for the biologists in the condor recovery
project.
#### Lecture 6: From Mathematics to Environmental Consulting

Charles Hadlock, Bentley College

Environmental consulting includes the use of modeling and
encompasses a considerable range of activities depending on
both the nature of the client organization and the objective of
the investigation. For example, regulatory and legal cases might
be conducted very differently from scientific and engineering
investigations. The speaker will discuss his experience in a wide
range of consulting assignments and will also suggest ways that
mathematicians can involve themselves in this kind of work.
### Leonhard Euler - Looking Back After 300 Years

Edward Sandifer and Robert Bradley

In 2007 we celebrate the 300th anniversary of Euler’s birth. As
the preparation and publication of more than 70 volumes of his
works and correspondence in the Opera Omnia begins to wind
down, this is a fitting occasion to take an in-depth look at what
Euler did and how it fit in the context of his own times. Seven
historians of mathematics will describe their recent work on
Euler, his life, times, science and mathematics.

The program includes the following lectures:

- A mathematical
life in the enlightenment, Ronald S. Calinger, Catholic
University
of America
- Leonhard Euler and the function
concept,
Ruediger Thiele, University of Leipzig
- D’Alembert, Clairaut
and Lagrange: Euler and the French mathematical community,
Robert E. Bradley
- Enter, stage center: The early
drama of hyperbolic
functions in the age of Euler, Janet Barnett, Colorado
State University at Pueblo
- Euler and classical physics,
Stacy G.
Langton, University of San Diego
- Elliptic integrals, mechanics
and differential equations, Lawrence A. D’Antonio, Ramapo
College
- Euler’s great theorems,
Edward Sandifer

### Implementing Biology Across the Mathematics Curriculum.

(in cooperation with the joint meetings of the Society for Mathematical
Biology the Japanese Society for Mathematical Biology)

John R. Jungck

Many mathematics educators are faced with the challenge that
the majority of students enrolled in their classes are from the
broader life sciences (e.g., 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, but will
also be able to attend the plenary lectures of those societies as
guests of the 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 Knittingtogether]
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 to introduce mathematicians to many current avenues of
research in mathematical biology, as well.
#### Lecture 1: Probability and 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 and
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-DelbrÃ¼ck 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, and the
risk for neonatal sepsis, quantified from electrocardiographic
(EKG) data.
#### 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 makeup 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.
#### 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 Reaching Out, Connecting With,
and Knitting Together BioQUEST Curriculum Consortium at
Beloit College).
#### 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 basics 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.
Register Online at www.maa.org
#### 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 an SIR epidemiological
model. Time permitting, an additional application based in
MATLAB will be demonstrated to compare and contrast the
ESTEEM competing species model.
#### 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,
including 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.
#### 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.
#### Lecture 8: Beyond Calculus: Integrating Mathematics, Statistics,
and Computation into Biology Courses

Claudia Neuhauser, University of Minnesota

’Today, most undergraduate biology majors take quite a bit
of basic quantitative coursework early on, but then they never
see it again,â? says Neuhauser. ’A few years later, when they’re
graduate students, they encounter the new world of biology,
full of massive amounts of data and analysis’and they’re not
prepared. We’ve got to change that.â? Neuhauser will emphasize
the need to train faculty in quantitative techniques and teaching.
She envisions adding mathematically themed guest lectures to
classes and possibly holding teaching workshops for faculty,
as well as working with faculty one-on-one. She believes that
this calls for a ’logical stepâ? in incorporating quantitative
techniques across the curriculum. ’For several years, my goal
has been to develop at least two solid years of undergraduate
quantitative training for our biology majors â?¦. ’Now, we can
do so much more.â?
### Combinatorics: Past, Present, and Future

Robin Wilson

Attend this short course to learn more about the development
of a wide range of combinatorial topics, from earliest times
up to the present day and beyond. The topics presented will
include early combinatorics from non-Western traditions, European
combinatorics during the Renaissance, the combinatiorial
work of Leonhard Euler, and various topics from the
modern era.
Early Combinatorics (up to the 17th century):
Andrea Breard, China
Victor Katz, Combinatorics in the Islamic
and Hebrew traditions
Europe Before and After Euler:
Eberhard Knobloch, European combinatorics, 1200’1700
Robin Wilson, Early graph theory and Cayley’s work on trees,
to the early attempts to solve map-coloring problems
George Andrews, Euler’s ’De Partitio Numerorumâ?
Lars Andersen, Latin squares
Robin Wilson, Triple systems, schoolgirls, and designs
Combinatorics Comes of Age:
Lowell Beineke, 20th-century graph theory
Herb Wilf and Lily Yen, Sister Celine as I knew her
Bjarne Toft, The game of Hex: History, results and problems
Toward the Future:
Ronald L. Graham, Combinatorics: The future and beyond
### Game-theoretic Modeling: Techniques and Applications

Michael A. Jones

The object of this short course is to learn about both the mathematical
techniques that collectively can be called game theory
and the range of applications that can be modeled using these
techniques. Techniques will include simultaneous and sequential
move games under different information assumptions,
cooperative games, mechanism design, theory of moves ’ a
dynamic extension of game theory, and a qualitative approach
to evolutionary game theory. Applications will be drawn from
biology, economics, environmental science, literature, political
science, and popular culture.

#### From decision Theory to Game Theory: An Introduction
and Overview to the Short Course

Michael A. Jones, Montclair State University

Anytime one person’s decision can affect another person’s
outcome is a situation that can be modeled by game theory.
This cocktail party description hints at how game theory can
rightfully be considered a collection of tools and techniques for
modeling diverse applications. For two-person, simultaneous
move games, I will discuss how Nash’s equilibrium solution
generalizes optimization in decision theory and Von Neumann’s
Minimax Theorem for zero-sum games. I will conclude with an
overview of the short course to demonstrate how game theory
has evolved from these historic roots.
non-cooperative

#### Game Theory with Applications to
Popular Culture

Paul Coe, Dominican University

Besides sharing an adjective, what do game shows have to do
with game theory? I will introduce concepts and well-known
games (e.g., the Prisoner’s Dilemma) from non-cooperative
game theory by using actual games from television game shows
including The Price is Right and Friend or Foe, among other
sources. Optimal behavior for these games will demonstrate
different solution concepts for both simultaneous and sequential
move games.

#### Extensive-Form Games

D. Marc Kilgour, Wilfrid Laurier University

I will highlight the difference between Nash and subgame-perfect
equilibria for games in which players move sequentially and
explain how subgame-perfect equilibria use a stronger criterion
of rationality to refine Nash equilibria to a more compelling (or
demanding) solution. I will extend subgame-perfect equilibria
to games of imperfect information and incomplete information.
Applications will include models of deterrence and truels (3-
person duels).

#### Cooperative Game Theory

Jennifer Wilson, New School University

Cooperative game theory models situations in which players
form coalitions whose value is greater than the sum of their
parts. In this talk, I will discuss several well-known methods,
including the core and Shapley value, which assign player’s
values based on the coalitions that they can join. Applications
include sharing the cost of building an airport runway and
cleaning up a polluted river, as well as determining power in
voting games. I will discuss recent extensions of these ideas
to multi-choice and fuzzy games.

#### Modeling Auctions: Game Theory and Beyond

Michael Rothkopf, Penn State University

Auctions are a particularly structured form of competition that
invites formal analysis. This talk will review briefly the results
from the game theoretic literature on single, isolated auctions.
It will then raise issues related to modeling auctions and argue
that improved models produce significantly, and sometimes
radically, different results. Some of these results can be obtained
using game theory, but some come from disciplines that are less
demanding mathematically.

#### Game Theory and Emotions

Steven J. Brams, New York University

Emotions such as anger, jealousy, and love would seem to be
spontaneous feelings that overtake us suddenly and hence not
the product of careful means-ends analysis that we normally
associate with rational choice. On the contrary, I argue that the
passionate pursuit of certain ends may be eminently rational in
expressing strong commitment, extreme frustration, and the
like, which in turn affect the responses of others in gamelike
situations. I will use ’theory of moves,â? a dynamic extension of
game theory, to illustrate this thesis, focusing on frustration and
its most common manifestation in anger. My principal sources
will be literary, from the Bible to Shakespeare to such modern
authors as William Faulkner and Joseph Heller.

#### A Qualitative Approach to Evolutionary Game Theory

Donald G. Saari, University of California, Irvine

Evolutionary game theory has proved to be popular in explaining
different social and biological behavior. Unfortunately the
approach is too difficult for most to use and it is very difficult
to accept the ’behavioral dynamics.â? A new, easily understood
approach is introduced to avoid these problems.
Panel discussion: Game Theory In and Out of
the Classroom
Not only has game theory been successfully taught in economics
and political science departments, game theory has been an
integral part of non-major, general education math courses and
has been a popular, yet infrequent math major elective. We
will discuss how game theory can also be introduced in math
major courses like calculus, combinatorics, probability, and
differential equations. Further, we will discuss areas of open
research that would be suitable for faculty and for faculty/student
collaborations.
### Data Mining and New Trends in Teaching Statistics

Richard D. De Veaux

There are two main themes. It will serve as a practical introduction
to and an overview of data mining. It will also highlight
some of the ways that technology has changed the way we
practice and teach statistics.
Forty years ago the emphasis in introductory statistics was on
formulas and their calculation. For example students were taught
the formula for standard deviation and learned alternatives
for avoiding rounding errors and short cuts for grouped data.
Technology has made much of that subject matter irrelevant and
obsolete. Today, we have been freed by technology to focus on
the concepts of data analysis and inference. Where is this trend
taking us? Computational methods in statistics are rendering
some of our methods obsolete as well. How much should be
introduced in the introductory statistics course?
Data mining is the exploration and analysis of large data sets
by automatic or semiautomatic means with the purpose of
discovering meaningful patterns. The knowledge learned from
theses patterns can then be used for decision making via a process
known as ’knowledge discovery.â? Much of exploratory
data analysis and inferential statistics concern the same type
of problems, so what is different about data mining? What is
similar? In the course I will attempt to answer these questions
by providing a broad survey of the problems that motivate data
mining and the approaches that are used to solve them.
The course will start with an overview of how the introductory
statistics course is taught today and what the main concepts
are. Examples of how technology enables us to get to the heart
of the subject early will be given. Some elementary modeling
concepts will be reviewed before we embark on an introduction
to data mining. Then, we will use case studies and real data sets
to illustrate many of the algorithms used in data mining. The
applications will come from a wide variety of industries and include
applications from my personal experiences as a consultant
for companies that deal with such topics as financial services,
chemical processing, pharmaceuticals, and insurance.