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Spring 2011 meeting of the Indiana Section of the Mathematical Association of America

Friday-Saturday, April 8-9, 2011

Indiana Wesleyan University

 

Preliminary Program: with times, rooms, and titles of talks: PDF (last update Wednesday, April 6)

Preliminary list of talk abstracts: PDF

    All events except the ICMC will be held in the Barnes Student Center (CSC) 

   


Tickets for Friday Dinner and Saturday Lunch will be sold during early registration. NOW CLOSED

Friday Dinner Buffet Menu: Teriyaki Chicken Breast, Baked Cheese Manicotti (vegetarian), Wild Rice Blend, Fresh Vegetable Medley, Green Beans Almandine, and Chocolate Cream Pie.

Saturday Lunch in IWU Dining Commons.

 

Call for Papers NOW CLOSED.
Web-based registration (via EventBrite.com) NOW CLOSED.

2011 ICMC pre-registration NOW closed.


Invited Talks

Gerard Venema, Calvin College

Dimension Theory for Undergraduates

In this talk I will explore the concept of dimension and how our intuitive understanding of dimension relates to various rigorous mathematical definitions.  Undergraduates encounter a definition of dimension in a course on linear algebra and sometimes also in third term calculus.  It is natural to assume that those definitions will generalize in a straightforward way.  But the discovery in the early twentieth century of some surprising examples showed that dimension is more elusive than that and forced a reexamination of the whole concept of dimension.  Several competing definitions of dimension emerged from that process.  Those definitions do not all give the same answer when applied to a subset of Euclidean space and do not even necessarily yield integers as answers.  We will review the definitions from an elementary point of view and look at lots of examples.  Among the examples studied will be numerous "fractals," which are spaces whose dimension has different values depending on which definition of dimension is being used.



Fractals and Wild Cantor Sets


Subsets of Euclidean space often have extremely complicated local structure, but many of their geometric properties can still be approximated by sets, called Cantor sets, that appear to have very little substance.  In this talk I will review the definition of a Cantor set and then I will illustrate some of the surprising ways in which Cantor sets can capture the geometry of a variety of spaces. 

Antoine's necklace is a classic example of a Cantor set in Euclidean 3-space.  It is "wild" in the sense that it cannot be "tamed."  (Definitions to be supplied.)  I will explain why the Hausdorff dimension of an Antoine's necklace Cantor set must always be at least 1 and I will explain how to construct an Antoine's necklace of Hausdorff dimension s for every s in the range 1 <= s <= 3.  This is a special case of a much more general theorem that relates Hausdorff dimension to embedding dimension and implies that every wild Cantor set is a fractal.

 


Jeffrey Watt, IUPUI

The Central Indiana STEM Talent Expansion Program:
Making the Transition from High School to College Successful and Increasing the Number of STEM Graduates 4 Years Later

It is imperative, for continued intellectual leadership and economic prosperity as a nation, that educators make efforts to increase the quantity, quality, and diversity of STEM graduates as one of our highest national priorities.  Jeff Watt will discuss the motivation, development, and current results of a National Science Foundation grant that focuses on increasing the quantity, quality, and diversity of STEM graduates in the Central Indiana region by implementing retention strategies in the STEM education pipeline.  This program takes a coordinated and systemic approach to increasing undergraduate success in STEM at all levels, from pre-college, to the important first year experience, to the sophomore year and onto graduation, through leadership and career development.


Student Workshop

Lesley Wiglesworth of Centre College

Graph Theory is one of the newest branches of mathematics and is extremely accessible to undergraduate students. It has numerous applications. Facebook, the world wide web, and a city map can all be represented as graphs. In this workshop, we will investigate several applications of graph theory, focusing primarily on planar graphs. Using paper, M&Ms, and icing, hands‑on activities will guide our investigation into some of the most famous mathematical theorems in this branch of mathematics.

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