The spring 2013 meeting was held **April 6, 2013** at **Dickinson College**.

**Scott Chapman**(Sam Houston State University)*A Tale of Two Sequences: A Friendly Introduction to the Theory of Non-Unique Factorization in Integral Domains and Monoids*- The sequences 1, 5, 9, 13, 17, 21, ... and 4, 10, 16, 22, 28, ... both seem to be harmless arithmetic progressions of positive integers. By studying their multiplicative structures, we can show that the second sequence is much more complicated than the first. In doing so, we will introduce fundamental notions from the theory of non-unique factorizations in integral domains and monoids. This area has many different facets, some of which reach beyond basic algebra into combinatorics, finite abelain group theory, semigroups and even additive number theory. The talk will briefly review the history of this subject and give an overview of the direction of current research.
- Scott Chapman followed his undergraduate work at Wake Forest University with a master's degree in mathematics from the University of North Carolina at Chapel Hill and a Ph.D. in mathematics from the University of North Texas. As a professor at Trinity University in San Antonio from 1987 to 2008, he received three prestigious international fellowships from the Fulbright Commission (to Austria), the Consiglio Nazionale delle Richerche (the Italian National Science Foundation), and the Deutscher Akademischer Austausch Dienst (German Academic Exchange Service). In the spring of 2003, he was only the second recipient of Trinity University's faculty-wide award for Distinguished Scholarship or Research. He has authored or co-authored over 90 publications in refereed mathematical journals or refereed mathematical conference proceedings. These papers have been co-authored with over 60 different mathematicians from eight different countries. While at Trinity, he served for nine years as principal investigator and program director of the Trinity Mathematics Department's NSF funded Undergraduate Research Experiences in Mathematics Program (REU). Twenty-five of his joint publications have been written with 36 different undergraduate co-authors. Students he has directed in Trinity's REU have received or are currently pursuing graduate degrees at Harvard, Berkeley, UCLA, Rice, Chicago, Michigan, Rutgers, California Santa Barbara, Nebraska, and MIT. Three of his former research students have won NSF Graduate Fellowships. Five have attended the Tripos III Program at Cambridge. Another (Nathan Kaplan) was the 2008 winner of the AMS-MAA-SIAM Morgan Prize for outstanding undergraduate research in the United States. In August of 2008, Dr. Chapman accepted a position as full professor and Scholar in Residence at Sam Houston State University in Huntsville, Texas. After a national search in 2010, the Mathematical Association of America (MAA) selected Chapman to be the 30th editor of The American Mathematical Monthly, continuing the work of several noted mathematicians of the past 100 years. Today, the Monthly is the most widely read mathematics journal in the world (based on statistics involving downloads of articles managed by JSTOR and Ingenta). He and and his wife, Lenora, spend their spare time with their sons Jonathan (14) and Cameron (12).

**Klaus Volpert**(Villanova University)*On the Mathematics of Income Inequality*- The Gini-Index based on Lorenz Curves of income distributions has long been used to measure income inequality in societies. The single-valued index has the advantage of allowing comparisons among countries and within one country over time. However, being a summary measure, it does not distinguish between intersecting Lorenz curves, and may not detect certain societal and economic trends over time. We will discuss a two-parameter model for the Lorenz curves, which interpolates between self-similar behavior at the low and high ends of the income spectrum. This allows us to split in the Gini-index in two. We will present theoretical and empirical evidence for this model, discuss its mathematical properties, and its potential to discern hidden trends.
- Klaus Volpert is associate professor of mathematics at Villanova University. He won the University's Lindback Award for Excellence in Teaching in 2009 and the EPaDel's Crawford Award in 2011. Early studies in his native Germany and the 1989 PhD from the University of Oregon were in pure mathematics (algebraic topology), but he has more recently been interested in problems in applied mathematics, specifically at the intersection with finance and economics. Outside of mathematics, his greatest joy is making music with his family Heewon, Hannah, and Peter.

**Amy Shell-Gellasch**(Hood College)*Leveraging the Power of 2: An Exploration of How Different Cultures have used 2 to Facilitate Calculation*- Many young children will successively double or halve in order to calculate some simple arithmetic problems. And I also use doubling or halving to calculate or estimate items such as tax or tips. This approach is also found in the calculation schemes of many cultures throughout history, not just for simply arithmetical calculations, but for more complex problems as well. In this talk I will present the ways in which several cultures harness the power of 2 for calculation and briefly discuss why they work. I will also present ideas for using this in the classroom.
- Amy Shell-Gellasch is currently an assistant professor of mathematics at Hood College in Frederick, MD. After teaching with the non-profit organization Project SEED in the Detroit Public Schools, she went on to get her Master's degree from Oakland University and her Doctor of Arts from the University of Illinois at Chicago in 2000 in mathematics. While on a post-doctorate fellowship at the United States Military Academy at West Point, she met and married an officer. Now she has the enriching (though at times challenging) opportunities to live and teach in various parts of the county and the world. Dr. Shell-Gellasch's area of research is the history of mathematics and its uses in teaching. She has published numerous articles, edited volumes, and conducted workshops in these areas. Her doctorate thesis, In Service to Mathematics: The Life and Work of Mina Rees, was published in 2012.

Talk schedule (PDF)

Talk abstracts (PDF)

Student talk schedule (PDF)

Student talk abstracts (PDF)

The third-annual EpaDel Undergraduate Math Competition was a success. Ten teams of randomly-assigned students competed, with all teams getting at least two questions correct and two teams answering ten out of the twelve questions correct in the allotted 45 minutes. Ralph Beishline of Bloomsburg University took home the grand prize from the culminating head-to-head mental math competition.

This year's contest problems and solutions

**Overview: **Randomly assigned teams of three to four students
will work on a set of twelve competition-type problems for forty-five minutes.
The problems have answers that are easily verified, such as a single word or
number. Most problems do not require knowledge beyond freshman-level
coursework. Every time a team answers a problem correctly, each team member is
given a raffle ticket, which they can either place in the prize bucket or the
bonus-round bucket. Students will be allowed to resubmit answers if they are
incorrect on their first response. At the end of the forty-five minutes,
tickets will be drawn from the prize bucket to give away mathematically-themed
prizes and eight names will be drawn from the bonus-round bucket to compete in
the bonus-round tournament. The bonus-round will feature mental arithmetic
problems. The winner of the bonus-round tournament will win the grand prize.

- Students will be randomly assigned to teams as they enter the competition room. Any faculty member interested in assisting in monitoring the competition should come to the competition room or contact Molli Jones, mollijones77@yahoo.com.
- Students will be provided with the problem set, blank paper, and pencils. There are no calculators, cell phones, or other electronic devices allowed during the competition. Students will be given exactly forty-five minutes to work on the problems.
- If a team feels they have a correct answer, they will send one representative to a faculty monitor located at the front of the room. If the faculty monitor accepts the answer, each team member will be given one raffle ticket. If the faculty member does not accept the answer, the representative must consult with the team before submitting another response to the same problem. Teams may submit answers to more than one problem at a time.
- Students must write their names legibly on the raffle tickets
before placing them in the buckets located at the front of the room. Raffle
tickets may be placed in
__either the prize bucket or the bonus-round bucket__. - Once the forty-five minutes are complete and time is called, no new answers may be submitted. Any student already waiting to check answers with the faculty monitors will be checked, and all raffle tickets will be placed in the buckets.
- Six distinct names will be drawn from the prize bucket and prizes will be selected on a first-come, first-serve basis. The bonus-round buckets will be combined, and eight distinct names will be drawn. These eight students will compete in a bonus-round tournament. The winner of the bonus round will win the grand prize for the competition.

Section Governor, William Dunham, Muhlenberg College

January 2013

The MAA Board of Governors met on Tuesday, January 8, 2013, at the Joint Mathematics Meetings in San Diego. President Paul Zorn was in the chair.

The meeting began with Paul's remembrance of Doug Faires, a gifted teacher, successful textbook author, and devoted supporter of the MAA. Doug passed away last month. In 2011, he and wife Barbara (the MAA's secretary) were inducted into the Icosahedron Society, recognizing financial support of the highest order.

After this, our discussion moved to the 2013 budget. As MAA members know, finances have been a concern over recent years, as the organization has run deficits and drained away cash reserves. Our 2011 deficit was $109,000, and the deficit for 2012 came in around $240,000. At the previous Board Meeting, the governors voted for targeted "investments" in areas that would temporarily increase the deficit but that were meant to reap financial benefits in the not too distant future. See my report of August, 2012, for specifics.

Thus, for 2013, we considered a budget with a projected deficit of $627,000. This, needless to say, is an enormous amount of money, representing 7.6% of the overall $8.2 million annual budget. Prolonged discussion among the governors focused on whether the potential pay-off from the targeted investments was worth the risk of falling so far into debt. The MAA treasurer (Jim Daniel) and associate treasurer (Rick Cleary) addressed many questions on this proposal. They noted, for example, that next year's one-time expenditure of $200,000 -- necessary to change MAA customer service from an out-sourced to an in-house operation -- should quickly pay for itself. Indeed, Jim Daniel said he was optimistic that the MAA's budget, by 2015 at the latest, would be in the black, allowing the organization to rebuild its cash reserves.

When a vote was taken, the Board agreed to this 2013 budget.

Our other major topic was a new, streamlined dues structure for the MAA, to be implemented in 2014. Its key feature is a reduction of membership categories to just five (down from the current situation, where there are scores of different membership permutations). These new categories will be (1) Member, (2) Member Plus, (3) K-12 Teacher, (4) Student Member, and (5) Departmental Member. This should greatly simplify a chaotic situation.

Two striking features of this new dues structure are:

The basic individual MAA membership will

*decline*from the current $199 to $169! (That's an exclamation point, not a factorial.)Members will receive all four MAA journals -- the

*Monthly*,*Math Magazine*, the*CMJ*, and*Math Horizons*-- albeit in electronic form. Anyone wanting__paper__journals will have to pay an additional amount. For instance, a print version of the*Monthly*will cost an additional $57 per year.

It was noted that this sort of reform had been discussed for many years but had never before been brought to the Board. In a vote, the Governors approved the new fee system. Members should be alert to the transition in dues that will be forthcoming.

Beyond these changes, the Board discussed a few other matters. One was a proposed improvement for selling MAA books at Section Meetings. Of late, such sales have been complicated by tax concerns that have significantly reduced the ease of buying books in these venues. The new system should be in place for our spring meeting at Dickinson. Stay tuned.

As the meeting ended, the Board thanked Paul Zorn for his two years of service as MAA President and welcomed Bob Devaney of Boston University as Paul's successor.

Let me close with two final matters:

At the Prizes and Awards ceremony of the Joint Meetings, three EPaDel colleagues were recognized for their excellent work. One, Yuhou (Susan) Xia of Bryn Mawr College, was a runner-up for the 2013 Alice T. Schafer Prize for Excellence in Mathematics by an Undergraduate Woman. John Allen Paulos of Temple University received the Communications Award from the Joint Policy Board for Mathematics. And Robert Ghrist of the University of Pennsylvania won the MAA's Chauvenet Prize for his paper "Barcodes: The persistent topology of data" that appeared in the *Bulletin of the American Mathematical Society* in 2008. Congratulations on these fine honors.

Finally, with this meeting I completed my three-year term as EPaDel Governor. I have certainly enjoyed the opportunity to learn about the inner workings of the Mathematical Association of America and have appreciated the honor to serve in this capacity.

EPaDel members should be alert to the upcoming election to choose my successor. Please vote!