The 2013 Annual Meeting

of the Illinois Section

of the Mathematical Association of America

The 2013 Annual Meeting of the Illinois Section of the MAA will be held April 5 and 6, 2013, at the Chicago Campus of Roosevelt University in Chicago, Illinois.

Meeting Links

Purchasing MAA Books at a Discount

Registration Information - Registration will be located in the Congress Lounge

Lodging, Transportation and Parking

Campus Map -Map of Auditorium Building

Four plenary speakers each giving an hour talk. At present, this year's plenary speakers are: Fusun Akman, Illinois State University; Brian Hopkins, Saint Peters University; **Terrell** **Hodge**, Western Michigan University (also will be doing the workshop); **Chawne Kimber**, Lafeyette College.

Here is information regarding the plenary talks and the speakers:

**Title**: Towards a New and Improved Theory of Partitions

**Speaker**: Fusun Akman, Illinois State University

(Joint work with Papa Sissokho)

**Time**: Saturday 8:30 - 9:30 AM

**Location**: Congress Lounge

Abstract: An integer partition of n is a sequence of positive integers (parts) a1 · · · as
with sum n. The number of partitions of n is the partition function p(n), an
important quantity in combinatorics. A set partition of the set n = {1, . . . , n} is
a collection of disjoint nonempty subsets of n whose union is n. The number Bn
of set partitions of n is called the nth Bell number. Thus, an integer partition of n is also a multiset that counts the number of elements in each part of a set partition of n; we say that an integer partition is the type of a set partition. For example, both set partitions {1, 2, 3}, {4, 5}, {6, 7} and {5, 6, 7}, {3, 4}, {1, 2}

of 7 are of type (3, 2, 2) (an integer partition of 7).

Our ongoing work is an attempt to construct q-analogues of the concepts of set
and integer partitions. In general, q is recognized as a “deformation” parameter
inserted in defining equations such that one recovers the original structure as

q ! 1. We have found that the natural q-analogue of p(n) comes from counting
a genuine combinatorial object and not just from insertion of some q’s. Let
V = V (n, q) be an n-dimensional vector space over the field with q elements.
A subspace partition of V is a collection of nonzero subspaces of V with zero
intersections that cover V . The set of all subspace partitions of V is a lattice,
similar to the lattice of all set partitions of n, under “refinement” partial ordering. Most importantly, the number of subspace partitions of V , denoted by
B(q)
n , is congruent to Bn modulo q−1 for all n and all q. How about the number

of types of subspace partitions versus p(n)? Tune in for many other interesting
discoveries, and clues as to why this is the best q-analogue.

**Title**:
Hypergraphs, Path Algebras, and Evolution of Metabolic Pathways

**Speaker**: Terrell Hodge, Western Michigan University

**Time**: Friday 12:50 - 2:00 PM

**Location**: Congress Lounge

Abstract:
Mathematically, networks of metabolic pathways can represented as hypergraphs, and aspects of their evolution inferred from the phylogeny of genomes of related organisms, such as by a Bayesian approach (Mithani et. al.). In this talk, we discuss a linked algebraic framework employing a representation-theoretic approach that generalizes path algebras for directed graphs (quivers).

**Title**: The Symmetric Group and Fair Division: Does Knowledge Matter?

**Speaker**: Brian Hopkins, Saint Peters University

**Time**: Friday 7:30 - 8:30 PM

**Location**: Banquet (Congress Lounge)

Abstract: Sports drafts and divorce settlements are examples of situations where players take turns selecting indivisible goods. Like other topics in fair division, the situation is made more interesting because people may value the goods in different ways. In this talk, we focus on the case of two players, where the machinery of permutations is surprisingly applicable. How many possible outcomes are there? In what circumstances do both players get their best possible outcomes? How can one best take advantage of knowing the other's preferences? What happens when a player's motivation switches from greed to spite, the common good, or selfless altruism? In this colorful talk, we'll sample some applied algebraic combinatorics and address these issues along with the provocative question of the title.

**Title:** When and How Order Matters
When and How Order Matters

**Speaker**: **Chawne Kimber**, Lafayette College

**Time**: Saturday 12:10 - 1:10 PM

**Location**: Congress Lounge

**Abstract**: We will gently survey the main contributions of the study of compatibly-ordered algebraic structures (with particular concentration on commutative rings) highlighting the major current open questions and the benefits and pitfalls of our approaches to solving them. Although the objects of interest are algebraic, we will use categorical, topological and analytic tools along the way.

Conference Workshop: Integrating Applications of Modern Discrete Mathematics to Molecular and Systems Biology into Mathematics Curricula

Speaker: Terrell Hodge, Western Michigan University

**Time**: 8:45 - 11:45 AM

**Location**: WB 1016 (WB = Wabash Building)

Abstract: It is now widely accepted that a main push in biology during the coming decades will be toward an increasingly quantitative understanding of biological functions, and that the new generation of biologists will routinely use mathematical models and computational approaches to frame hypotheses, design experiments, and analyze results. This in turn drives the need for educational change at the interface of mathematics and biology. So far, however, the numerous responses to calls for change at the undergraduate level have been biased toward calculus-related curricular additions that illustrate how to model the evolution of biological systems through space-continuous dynamical systems described by difference and differential equations.

Since calculus and basic statistics comprise the traditional nexus of biology and mathematics majors’ curricula, these curricular changes represent a fundamental step forward. Nonetheless, calculus-based methods constitute only one end of the rich variety of mathematical approaches used in biology. Alternative methods, including elementary discrete mathematics, graph theory, linear algebra, Boolean networks, abstract algebra, and polynomial algebra have been applied to successfully create models of genetic and signal transduction networks, DNA sequence evolution, RNA and protein folding, phylogenetic trees, and many others. We refer to this selection of (non-calculus based) methods as *modern discrete mathematical methods. *Particularly notable in this group is the field of *algebraic geometry* . Further combining algebraic geometry and other methods from modern discrete mathematics with concepts from probability and statistics is the province of *algebraic statistics.*

Aspects of modern discrete mathematics and algebraic statistics have had a significant impact in molecular biology, and can provide accessible windows for students in biology and mathematics to learn about mathematical framing and modeling even without extensive exposure to calculus-based mathematics. Exposing undergraduate students to elements from modern discrete mathematics and algebraic statistics is critically important for adequately equipping them to meet the challenges posed by new-generation questions in molecular and systems biology, along with other fields. In this workshop, we will survey several "points of entry", drawn from an NSF CCLI (now TUES) curriculum development project whose products ("modules") have been turned into a new book, *Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models*, edited by PIs Robeva at Sweet Briar College (SBC) and Hodge. Following the survey, we will take a hands-on approach to working with a selection of the modules (chapters) in more depth. Though these materials take a major step to providing access to undergraduates (and others) to this area, research on TUES programs’ success and on implementing change in STEM education more generally suggests that the availability of resources alone is not sufficient for initiating and sustaining curricular revisions and is only a first step in best-practices paradigms toward institutionalizing change. Thus, we hope to engender a discussion of potential strategies for testing and implementing the material from our CCLI and TUES modules in a wide range of non-calculus based classes and for sustaining and institutionalizing these changes.

**Purchasing MAA Books at a Discount**

Illinois Section members may purchase books through the MAA website at a 35% discount using coupon code ILLISPR3 from March 31, 2013 through April 13, 2013.

If you use this code, the section will get credit for the books purchased.

Student Pizza Party: Open to all undergraduate student participants.

Friday, April 5, 6:15 PM, Location: Wabash 1016.

You have a deck of 10 cards and on each card there is a single digit between 0 and 9, inclusive. The digit on the top card equals the number of cards which have a zero on them, and so forth until the digit on the last card is the number of cards with a nine on them. What are the digits, in order from top to bottom, on the cards?

Is this the sort of problem that intrigues you? Then you should consider competing in our Thirteenth Annual Student Mathematics Contest which will be held on the afternoon of Friday April 5, 2013 at 4:45 - 6:00 PM in Wabash 1015 during the Annual Meeting of the Illinois Section of the MAA at Roosevelt University in Chicago, Illinois. The Contest is likely to have a minimum of four problems for the teams to consider. A team from a particular college is to consist of up to 3 undergraduate students. A college or university may enter more than one team. Team members may work together in solving the problems and will submit one team solution for each. Electronic computational devices (and slide rules and log tables and abacii) are not allowed. Competitors will have their conference registration fee waived.

Teams need not register until the day of the Contest. The participating teams will receive the results of the contest as soon as they become available. The Contest results will also be posted on the ISMAA website.

**OUTSTANDING UNDERGRADUATE RESEARCH (OUR) AWARDS**

The Illinois Section of the Mathematical Association of America invites submissions for the 2013 Outstanding Undergraduate Research (OUR) Awards. Up to three awards will be given for papers authored and presented by undergraduate students at the upcoming ISMAA meeting. Working in collaboration with a faculty advisor, undergraduate students who wish to apply for the OUR Awards should submit the following materials electronically (either as a PDF or MS Word document):

1. a brief, one-page cover letter stating the nature of the project and identifying the researchers involved;

2. a complete, original research paper;

3. a letter of support from the faculty advisor which also describes the student’s contribution to the work.

Submissions may be emailed to Tony Bedenikovic, Awards Committte Chair, at abedenik@bradley.edu. Please include "OUR Awards" in the subject heading.

Papers need not have been submitted for publication in a professional journal at the time of consideration, but must be complete manuscripts, even if only a subset of the research will be presented at the meeting.

Applicants should make arrangements (see the ISMAA home page) to give a talk in the student session of the upcoming ISMAA meeting. Applicants will be evaluated both for quality of research and for quality of presentation. Monetary gifts accompany these awards. The deadline for OUR Awards submissions is **March 22, 2013**.

Questions? Email abedenik@bradley.edu.

Project NExT (New Experiences in Teaching) is a professional development program of the MAA, with major funding provided by the Exxon Education Foundation, and additional funding from several other sources. This program is designed to support new college faculty in their teaching, scholarly, and professional activities and to help these new faculty members to get involved in the mathematical community beyond their own institutions. The success of Project NExT on the national level has prompted a number of MAA sections to organize their own local versions of this program.

The Sixteenth Annual ISMAA Project NExT Program will be held in conjunction with the ISMAA annual meeting at Roosevelt University in Chicago, Illinois, April 5-6, 2013. Up to nine 2013 ISMAA Project NExT Fellows will be selected. Anyone within their first four years of teaching mathematics (after finishing a master's or doctoral degree) at any two or four-year college or university in Illinois is eligible, as well as any graduate students at universities in Illinois who are completing their PhD this year and have a position in Illinois for the 2013-2014 academic year. 2013 ISMAA Project NExT Fellows' meeting registration, pre-conference workshop registration, opening banquet fees, and Friday and Saturday lunches at the annual meeting will be paid for by the ISMAA Project NExT for the 2013 and 2014 ISMAA Annual Meetings.

The 2013 Program will begin on the morning of Friday, April 5, 2013, with the pre-conference workshop. The workshop is followed by an opening lunch during which new ISMAA NExT fellows will have an opportunity to get to know one another as well as other sectional Fellows and national NExT Fellows. The ISMAA Project NExT program will conclude on the afternoon of Saturday, April 6, 2013, following the closing address of the ISMAA meeting. Over lunch, the group will discuss issues pertinent to young faculty, centering on the theme, “What I wish I’d known starting my first job.” At this time, we will also match new ISMAA NExT Fellows with a Mentor. It is expected that each Mentor-Fellow pair will continue to communicate about professional development issues throughout the following academic year.

Application materials for 2013 ISMAA Project NExT Fellows can be accessed via the links below. For further information, please contact the Director for the ISMAA Project NExT Program:

2013 ISMAA Project NExT Application (MS Word)

2013 ISMAA Project NExT Application (pdf)

Cindy Traub

Department of Mathematics and Statistics, Southern Illinois University Edwardsville

Edwardsville, IL 62026-1653

Phone: 618-650-2356

email: cytraub@siue.edu

The registration deadline for the 2013 ISMAA Project NExT Fellows is February 28, 2013.

Important: Section members will be asked to vote on an important motion from the IMACC (Illinois Mathematics Association of Community Colleges). For more information click here.

Travel funds are available to support student attendance at the ISMAA meeting. Up to $50 per student is available for Illinois institutions to use in support of student travel, with a max of $250 per institution. Limited funds are available.

We ask that institutions which already provide full support not request these funds. Travel funds are not available to the hosting institution or to institutions within 30 miles of the meeting site. Travel awards are available for all students (secondary, undergraduate, or graduate); however, preference will be given to students presenting at the meeting.

The travel form is available as a Word document or as a PDF document. Please send completed forms electronically to Pat Kiihne (pkiihne@mail.ic.edu) by March 27, 2013.

For additional information on participating in the program or to suggest a speaker please contact the program committee or:

Tim Comar

Department of Mathematics

Benedictine University

5700 College Road

Lisle, Illinois 60453-0900

(630) 829-6555

tcomar@ben.edu

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