**Title:** Teaching a Biomathematics Modeling Course with Allen's Textbook

Author: Fusun Akman

Institution: Illinois State University

**Abstract:** We will discuss the pros and cons of teaching with L.J.S. Allen's textbook "An Introduction to Mathematical Biology", including the choice of topics, mathematical rigor, and biological significance. The book is in general a good choice for an all-purpose course because of the unusual ordering and depth of topics covered (difference equations, applications, differential equations, applications, partial differential equations). But...

**Title:** *On vague predication*

Author: Jeremy Alm

Institution: Illinois College

**Abstract:** *Mathematicians are accustomed to reasoning in situations in which dichotomies are ubiquitous: an element is either a member of a set or it is not; a proposition is either true or it is false; a predicate either applies or it does not. However, if we widen the scope of our interest to include the more broad use of language, the situation becomes less clear (and more interesting). There are many vague predicates, such as "is within walking distance from", whose vagueness is essential to their application. Consideration of these predicates requires that we put on our philosopher hats and consider a three-valued logic.*

**Title:** Plane Analytic Geometry Using Complex Numbers

Author: Peter Andrews

Institution: Eastern Illinois University

**Abstract:** Thinking of the Euclidean plane as **C** rather than **R**2 , this talk shows how many of the formulas and proofs of elementary analytic geometry appear in their (often simpler!) complex versions.

**Title:** Chances of a Cruise Ship Birthday Match

Author: David Atkinson

Institution: Olivet Nazarene University

**Abstract:** What are the chances that during a cruise of k days there will be one or more matching birthdays among the n passengers? This is an interesting variation of the well known birthday problem that is accessible to undergraduate mathematics majors. A solution will be presented and for selected values of k we will note the minimum n for which the probability of a match is at least 50%.

**Title:** Linear Algebra Done Right! Back to Grassmann

Author: Rohan Attele (speaker) with Victor Akatsa and Dan Hrozencik

Institution: Chicago State University

**Abstract:** In Grassmann's enunciation of linear algebra, parallelograms, parallelepipeds (directed by handedness) etc., were treated as vectorial objects. However, its exclusion in the contemporary treatment makes basic concepts (e.g. linear independence) less intuitive, and limits the scope of its applicability. A curriculum for a second linear algebra course for math and physics majors is proposed that includes Grassmann's wedge product as a fundamental tool in bringing a **coordinate free** fusion of algebra and geometry, i.e., theorems in the geometries become identities in algebra and vice-versa. The curriculum subsumes the traditional, and the students will gain a deeper understanding fundamental concepts such as linear independence/dependence, duality, and linear transformations in a more intuitive natural setting. Vector subspaces are viewed as computational objects that can be multiplied and divided. The applications therein to physics, computer graphics, and geometries will provide an appreciation of the unifying power of mathematics. The conceptual and computational foundation that students gain will also prepare them to understand concepts in abstract algebra.

**Title:** *A 2-bedroom, Bing-style House with a Great View*

Author: Tony Bedenikovic

Institution: Bradley University

**Abstract:** *Bing's house with two rooms is a well-known example in low-dimensional topology. Bing's house is a 2-dimensional complex which demonstrates the disconnection between contractibility and collapsibility, as it has the former property but not the latter one. In this talk, I will describe a generalization of Bing's house to a higher dimension. Describing this newly-remodeled Bing-style house proves to be an interesting exercise in higher-dimensional visualization. The emphasis here will be on the visualization, though the opportunity will be taken to seek connections to deep questions in low-dimensional topology. *

**Title:** *The SATS Project*

Presenter: Marjorie E. Bond

Institution: Monmouth College

**Abstract:** *Educational research and theories suggest that students’ attitudes toward statistics help determine: course completion, course achievement, future course enrolment, and their use of statistical thinking in their lives. The Survey of Attitudes Toward Statistics (SATS©) is designed to measure six components of students’ attitudes – Affect, Cognitive Competence, Value, Difficulty, Interest, and Effort. Individual researchers and instructors have used the SATS© for many years in small projects. These projects are interesting and useful on a limited scale, but there is a need to look more broadly at students’ attitudes. The SATS Project was designed: to understand students’ attitudes toward statistics, how these attitudes impact statistical thinking in the classroom and in life, and what statistics instructors can do to improve students’ attitudes. These goals are being accomplished through web-based data collection of the SATS, instructor, and course information from statistics courses offered in post-secondary institutions located across the United States. This project yields a data warehouse that will allow statistics education researchers and instructors to explore a variety of important questions about students’ attitudes toward statistics. *

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**Title:** A "Founders of Mathematics" Project Which Requires More Than Cut & Paste

Author: Stephen Brown

Institution: Olivet Nazarene University

**Abstract:** Are you tired of students doing little more than cut & paste work on your projects? Looking for an assignment which requires reflection and maybe even positive behavior modification? This "Founding Fathers of Mathematics" project has been successfully used in both Calculus I and Mathematics For The Liberal Arts. The first three requirements ask for a description of the founder's life, education, and contributions to mathematics, the usual requirements for biographical papers. However, the fourth requirement asks the student to estimate, by their own judgment, the founder's worth to the particular field of mathematics. Then the fifth requirement pushes them to draw parallels from the founder's life to their own performance in the current course. "What will it take for you to become a famous student of mathematics in this course?" You may be surprised with the responses from some of the papers that have been submitted. A list of founders will be available.

**Title:** IMTE Discussion and Meeting

Author: Astrida Cirulis

Institution: Concordia University Chicago

**Abstract:** Illinois math teacher educators and other faculty involved in the education of future teachers are invited to come share insights from the conference sessions that they attended. We will also discuss future activities of the organization.

**Title:** *The American Mathematical Society and an Earlier New Math Movement Around 1900*

Author: M. A. Clements (speaker) and N. F. Ellerton

Institution: Illinois State University

* Abstract:In 1902 the Chicago-based President of the Mathematical Society (AMS), Dr Eliakim Hastings Moore, devoted much of his Presidential Address to advocating radical new mathematics curricula and pedagogical approaches for US schools. Moore’s address, which is regarded as one of the most poignant moments in US school mathematics, stimulated much criticism from AMS members who disagreed strenuously with the ideas that Moore put forward. These critics argued that Moore’s comments were not representative of the AMS membership and a presidential address should not be concerned with such issues. Details relating to the skirmish will be presented, and issues arising that are relevant to the 21st century will be discussed*.

**Title:** Biocalculus Courses and Computer Laboratory Projects

Author: Timothy Comar

Institution: Benedictine University

**Abstract:** Benedictine University has been offering a rigorous two-semester biocalculus course sequence since 2003. The courses emphasize the integration of biology, mathematics, and the use of computational software to analyze biological problems and models and a new textbook is being developed for the course. Achieving an appropriate balance of mathematical rigor and biological applications is an important goal for such a course sequence. In this presentation, we address the course syllabus, highlight several of the computer laboratory projects used in the courses, and discuss student success in the course sequence. We also discuss how the course sequence has evolved since its initial implementation, how biological content has been incorporated into other lower level mathematics courses, and challenges for implementing our biocalculus courses as well as other models for integrating mathematics and biology.

**Title: ***ISMAA’s Challenge to the Mathematics Education Establishment in the 1940s*

Author*: N. F. Ellerton (speaker) and M. A. Clements*

Institution*: *Illinois State University

**Abstract:**During the 1930s and 1940s US mathematicians increasingly became concerned about the effects of “progressive” trends in education especially with respect to school mathematics. In the early 1940s, ISMAA directly challenged the tenets and claims of progressive education, arguing that progressive practices were seriously affecting the extent and quality of mathematics learning in the schools. Details relating to this challenge will be presented, and the effects on mathematics in schools will be evaluated.

**Title:** An MAA Study Tour to The Galapagos Islands and Peru

Author: Herb Kasube

Institution: Bradley University

**Abstract:** In the summer of 2008 the sixth Annual MAA Study Tour traveled south. Following a side trip to the Galapagos Islands, the group traveled to Peru to study the Incas and the mathematics of quipus. This presentation chronicles our journey.

**Title:** Fractals Produced by Affine Transformations

Author: Vince Matsko

Institution: Illinois Mathematics and Science Academy

**Abstract:** Interesting fractal images may be produced by using an iterated function system with only two affine transformations. The basics of this algorithm will be presented as well as several intriguing examples. A brief review of the geometry of affine mappings in the plane will be given at the beginning of the talk.

**Title:** Visual Mathematics for the Visually Impaired: Reflections and Strategies

Author: Mandi Maxwell

Institution: Trinity Christian College

**Abstract:** Liberal Arts Math classes are exciting to teach because of their visual nature, but how do you instill this excitement in a student if s/he cannot see? In this presentation, I will reflect on strategies and techniques that I utilized in my Liberal Arts Math class to help a blind student “visualize” mathematics. I’ll discuss the challenge of balancing the needs of those who need to “see” in order to comprehend with the needs of students who cannot see. I’ll discuss specific strategies that we employed along with critiques of our successes and failures, as well as suggestions to help those who may face similar challenges.

**Title:** What Should a Geometry Course for Preservice Secondary Mathematics Teachers Look Like?

Author: Todd Oberg

Institution: Illinois College

**Abstract:** This session will continue a discussion started at the AMS/MAA Joint Meetings about designing and teaching a geometry course for preservice secondary mathematics teachers. Some of the questions to be contemplated by session participants are: How can undergraduate geometry courses prepare preservice teachers for the task of engaging their future students in comprehending how geometry provides a way to represent and understand the world. What geometric topics help our preservice teachers develop a deep understanding of the material in order to promote geometric learning in the classroom? What techniques used in undergraduate geometry courses will help students in their future teaching careers?

**Title:** The Keystone Method of Instruction in Basic Mathematics: Theory, Practice, Results, and Future

Author: M. Vali Siadat (speaker) with Euguenia Peterson, Cyrill Oseledets, Ming-Jer Wang

Institution: Richard J. Daley College

**Abstract:** The Keystone method is a synergistic system of assessing students’ learning and adjusting of teaching practices. It provides a medium for dialogue between the teacher and the students. This medium is represented by carefully designed quizzes which are frequent, cumulative, time restricted, and homework based. The quizzes are performance based and address students’ learning difficulties. They are followed by the teacher providing immediate and constructive feedback on all the problems. The difficult topics are re-taught until an appropriate level of mastery is attained. Statistical analysis of the quizzes, such as item analysis on each question, average time spent on each question, as well as the mean and standard deviation of the entire quiz, provide valuable information about the class performance. This in turn helps the teacher to plan the next lesson and construct the next quiz. The past results have shown dramatic improvements in student performance and retention in Keystone classes. A concomitant result has been improved concentration skills, and a better persistence of students in mathematics courses and at the college. We are now incorporating the Keystone methodology with state of the art computer technology to perform in-class computer quizzing and assessment, providing instant diagnostics and feed back to all students. Technological support will reduce the time spent on construction of quizzes and tests and will also provide assistance to students with their homework and other related assignments.

**Title:** GPS Tracking of a Roller Coaster

Author: Michael Sostarecz

Institution: Monmouth College

**Abstract:** In many calculus textbooks, a main example for motivating student interest in the relationship between position, velocity and acceleration is the roller coaster. Typically, these examples are a roller coaster only in the most idealized sense. In an attempt to obtain a more realistic point of view, students from Monmouth College acquired position data for the Six Flags St. Louis roller coaster “The Boss” using a Global Positioning System (GPS) device. This talk will discuss the ups and downs involved in the data collection and curve fitting from their roller coaster rides.

**Title: ***Multiple Representations on the TI-Nspire Graphing Calculator*

Author: Ron Thomas

Institution: Texas Instruments

**Abstract:** *With TI-Nspire, multiple representations of a problem can be dynamically linked. Changes to one representation are instantly reflected in the others. Participants in this session will see how this is done.*

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**Title:** Gift-wrapping a Polyhedron

Author: Cindy Traub

Institution: Southern Illinois University Edwardsville

**Abstract:** The process of cutting, folding, and taping flat paper around 3-dimensional objects is a standard exercise for gift-givers everywhere. If we restrict ourselves to wrappings that contain no overlapping gift paper, a wealth of interesting mathematical questions arise. In this talk, we consider closed polyhedral geodesics and their connections to the possible paths a ribbon might take around a polyhedral gift. We will also show tools developed with the dynamic geometry software Geogebra to visualize and explore polyhedral geodesics.

**Title:** Finitely Many Proofs of Inifinitely Many Primes

Author: Lena Folwaczny

Institution: University of Illinois - Chicago

**Abstract:** Several proofs of infinitely many primes using ideas from Number Theory, Analysis and Topology.

**Title:** Noncommutative Holomorphic Functions

Author: Andrew Greene

Institution: University of Iowa

**Abstract:** Holomorphic functional calculus is a method of evaluating holomorphic functions at an operator. For a fixed operator its spectrum provides a criterion for which functions are admissable. Commutative multivariable versions (evaluating multivariable functions at an *n*-tuple of mutually commuting operators) have also been carried out, but a noncommutative functional calculus has been rather unwieldy. In this talk we survey this problem and recent results.

**Title:** Evolutionary Predictive Modeling in Ecology

Author: Joshua Hallam

Institution: Illinois State University

**Abstract:** We implement genetic algorithm based predictive model building as an alternative to commonly used step-wise regression. Further more we also employed Information Complexity Measure (ICOMP) as a measure of model fitness instead of another commonly used measure of R-square.

**Title:** *Mary Had a Little Lamb*

Author: Katie Taylor

Institution: Illinois State University

**Abstract:** *Genetic algorithms emulate biological/evolutionary phenomena using mathematical equations and optimization. In this talk, I will use genetic algorithms to mate and mutate strands of code to reproduce music in successive generations. Mathematics, music, and computing is combined in this exploratory venture. *

**Title:** Survival Analysis-Censored and Truncated Data

Author: Debbie Witczak

Institution: Illinois State University

**Abstract:** We introduce the problem of analyzing time-to-event data, which is commonly faced by applied statisticians. We provide an overview of the common features of the data sets used, which include censored or truncated observations. The statistical techniques used in the analysis can be applied to many disciplines, but we concentrate on applying the techniques to biology and medicine.

**Title:** Creating Fractals of a Given Dimension

Author: Jackie Chalmers

Institution: Augustana College

**Abstract:** By exploring generalizations of the Sierpinski carpet, we will show how to construct a fractal of a given rational dimension between zero and two. We will also show computer generated examples of such fractals.

**Title:** *Computing the Arrow Polynomial*

Author: Kumud Bhandari

Institution: McKendree University

**Abstract:** *Determining if two knots are not equivalent in an efficient manner is important in the study of knots. The arrow polynomial, which is calculated from a virtual knot diagram and is invariant under the Reidemeister moves, can be used to determine if two knots are not equivalent and determine a lower bound on the virtual crossing number. In this paper, we present the necessary data structures and algorithms to represent a link diagram on a computer and calculate the arrow polynomial.*

**Title:** Eigenvalues of Trees

Author: Ming Wei Chang

Institution: Augustana College

**Abstract:** Trees are simple graphs without cycles. We'll define eigenvalues of graphs and compute them for some infinite families of trees.

**Title:** Chinese Remainder Theorem

Author: Isaak Daniels

Institution: Augustana College

**Abstract:** We will present the Chinese Remainder Theorem. We will do examples of varying difficulty illustrating its use.

**Title:** The Schwarzchild Solution of the Field Equation of General Relativity

Author: Tom Edwards

Institution: McKendree College

**Abstract: ***A discussion of the Schwarzchild Solution of the Field Equation of General Relativity*

**Title:** Golf Scheduling Problems

Author: Tyler Hyndman

Institution: Bradley University

**Abstract:** Consider a golf tournament in which twelve players split up into three groups of four to play five rounds. (Groups can be different in each round.) Is it possible for each player to play in a group with each other player at least once, but no more than twice? We explore this problem and generalizations, presenting mathematical results and computer algorithms.

**Title:** Orthogonal art galleries with holes

Author: YoungJu Jo (speaker) with Hemanshu Kaul

Institution: Illinois institute of technology

**Abstract:** *The original art gallery problem (V.Klee,1973) asked for the minimum number of guards sufficient to see every point of the interior of an n-vertex simple polygon.**Chvátal (1975) proved that guards are always sufficient. If all the edges of the* *given simple polygon are either horizontal or vertical, then such a polygon is called **an orthogonal gallery. Kahn, Klawe and Kleitman (1983) proved that guards* *are sufficient for such a n-vertex gallery. We are interested in orthogonal gallery **with holes, i.e, an orthogonal polygon enclosing some other orthogonal polygons called holes (interior of each hole is empty). In 1982, Shermer conjectured that any **orthogonal polygon with n vertices and h holes can be guarded by * *This conjecture remains open.The best known result shows that guards suffice (O'Rourke 1987). In* *this talk we will discuss the history of these problems and some of the proofs wewill outline our approach to proving that guards suffice for our orthogonal gallery with n vertices with h holes. This is joint work with Prof Hemanshu Kaul.*

**Title:** Binomial Asset Pricing Model

Author: David MacFadden

Institution: Augustana College

**Abstract:** The binomial asset pricing model is used to determine the fair price of an option. We'll provide definitions and some simple examples. We will also discuss volatility and how to calculate it. Using our model, we will compare our calculations to real world data.

**Title:** On Refinable Functions

Author: John Meuser

Institution: Illinois Wesleyan University

**Abstract:** A function is 2-refinable if it can be written as a linear combination of its two dilates and integer translates. We investigate interesting properties of refinable functions, and provide methods for extending compactly supported functions to refinable functions.

**Title:** Graph fall-coloring

Author: Christos Mitillos

Institution: Illinois Institute of Technology

**Abstract:** Christos Mitillos, Illinois Institute of Technology On Graph Fall-Coloring} Graph coloring deals with the partition of the vertices of a graph into sets, or color classes, of pairwise non-adjacent vertices. Graph domination studies sets of vertices which are within a distance of 1 from all vertices. Both concepts are often applied in real life scheduling and location problems on networks. We are interested in a common extensions of both these concepts. Fall coloring of graphs, introduced by Dunbar et al. (2000) asks for a partition of the vertices of a graph into color classes, each of which is also a dominating set. We study the question: When does a graph have a fall-coloring? Our results include characterization of fall-colorable threshold graphs and fall-colorable split graphs. We also study the fall-coloring of cartesian products of graphs and interval graphs. Finally, we construct a family of graphs which can be only fall-colored using predetermined, non-consecutive numbers of color classes. The results represent joint work with Professor Hemanshu Kaul of the Illinois Institute of Technology.

**Title:** Statistical Analysis of EVE Online

Author: Matthew Pruitt

Institution: Augustana College

**Abstract:** EVE Online is a massively multi-player online role playing game. Using game data on historical closing prices of key elements used as the building blocks of EVE alongside real world stock market data, I find significant correlations between the real world economy and the virtual economy.

**Title:** Measuring Sea Spray Over Wind Waves

Author: Cara Tacoma

Institution: Trinity Christian College

**Abstract:** Sea spray has long been considered important to small-scale ocean surface dynamics. One type of sea spray, spume drops, are torn from the crest of breaking waves. Although recent research shows that spume drops contribute to many fluxes at the marine boundary layer, few studies have been attempted to measure spume. In this study, we measured the sea spray generation function, focusing on spume drops, which are often neglected. The sea spray generation function is shown for three different wind speeds and compares favorably with previous theoretical models.