The fall 2012 meeting was held October 27, 2012 at Millersville University.
- Bonnie Gold (Monmouth University)
What is the Philosophy of Mathematics and What Should It Be?
- Traditionally, the philosophy of mathematics considered questions such as “Are mathematical truths infallible?” and “Why is mathematics useful in the world?” However, starting in the mid-nineteenth century, almost all work in the philosophy of mathematics focused on the foundations of mathematics. It wasn’t until the middle of the last century that attention returned to these traditional questions. Since then, however, the focus of philosophers has been somewhat different from that of mathematicians who consider philosophical questions involving mathematics. In my talk, I will discuss some of this history, and then look at what both mathematicians and philosophers have been discussing in recent years.
- Jennifer Quinn (University of Washington, Tacoma)
Mathematics to DIE for: The Battle between Counting and Matching
- Positive sums count. Alternating sums match. So which is "easier" to consider mathematically? From the analysis of infinite series, we know that if a positive sum converges, then its alternating sum must also converge but the converse is not true. From linear algebra, we know that the permanent of an n × n matrix is usually hard to calculate, whereas its alternating sum, the determinant, can be computed efficiently and it has many nice theoretical properties. This talk is one part performance art and three parts combinatorics. The audience will judge a combinatorial competition between the competing techniques. Be prepared to explore a variety of positive and alternating sums involving binomial coefficients, Fibonacci numbers, and other beautiful combinatorial quantities. How are the terms in each sum concretely interpreted? What is being counted? What is being matched? Do alternating sums always give simpler results? You decide.
- James Sandefur (Georgetown University)
Why Do Students Have Problems Constructing Proofs?
- For over 10 years, the speaker has been videotaping his students trying to construct proofs of mathematical statements. In this audience‐participation talk, we will watch and discuss edited versions of several of these videos. In particular, we will reflect on why we think the students are having difficulties and what we can do to help them.
- Dr. James Sandefur received his Ph.D. in Mathematics from Tulane University and is currently a Professor in the Department of Mathematics and Statistics at Georgetown University. He received the Dean's Award for Excellence in Teaching, 2006, and the MAA Polya Award for Expository Writing, 2006. His interests are in mathematics education at secondary and college levels, differential equations, and discrete dynamical systems. He has written nearly 40 mathematics papers and is the author of the texts "Discrete Dynamical Systems: Theory and Applications", "Discrete Dynamical Modeling", and "Elementary Mathematical Modeling: A Dynamic Approach". He was the Principal Investigator on three different NSF grants, a Teacher Enhancement Institute, a Teacher Leadership Grant, and the Curriculum Development Grant, Hands-on Activities for Algebra , to develop hands-on models for developmental college math courses. He is a writer for the NCTM's Standards 2000. Dr. Sandefur was a program officer at NSF in the Instructional Materials Development Program. He has been a Visiting Professor at the Cornell University Center for Applied Mathematics, the University of Iowa, and the Freudenthal Institute at the University of Utrecht.
- James Sellers (Penn State University)
On Euler's Theorem Relating Odd‐Part and Distinct‐Part Partitions
- In the mid‐18th century, Leonhard Euler single‐handedly began the serious study of integer partitions and made fundamental contributions to the area for the next few decades. In particular, he proved a remarkable result which says that the number of partitions of the integer n into distinct parts equals the number of partitions of n into odd parts. My goal in this talk is to discuss Euler's impressive work on partitions, including snapshots of historical (original) publications of Euler, and then to describe numerous 20th and 21st century results which spring from Euler's original result. The talk will be self‐contained and geared for both students and faculty alike. It promises to be an entertaining and enjoyable talk.
Student Contributed Paper Session
Student talk abstracts (PDF)
Student Game Session
The Game of Set: Counting Problems and Underlying Geometry
Liz McMahon and Gary Gordon, Lafayette College
This session is designed for those of you out there who enjoy playing games. The session will start with a quick introduction to the game of Set, and then we will let you dive in and play. We will provide some interesting questions to start you thinking about the underlying mathematics of the game. After you have had time to play, Liz McMahon and Gary Gordon will give a short talk on the questions that have been circulated during the session. To add to the excitement, every time someone wins a game of Set, they will receive a raffle ticket. At the end of the session, names will be drawn, and copies of the game will be given to the raffle winners!
Section Chair's Message
Section Chair, Kevin Hartshorn, Moravian College
It looks like we have another terrific slate of activities for our Spring 2012 meeting at Shippensburg University. Not only do we have a terrific slate of speakers, our lunch table topics, and our undergraduate math competition, we also will be joined by the Pennsylvania State System of Higher Education in Mathematics (PASHEMA). There should be plenty of activities for everyone. Be sure to see the schedule on the EPaDel page for a full list of activities.
I would like to encourage you to think about some of our ongoing activities. First, you should encourage your undergraduates to come to the meeting. They can share their research through the Undergraduate Student Session, attend the opening talk in the morning by Francis Su (Harvey Mudd),and participate in the second annual undergraduate mathematics competition.
For the second year in a row, we have having a New Colleagues Session. This is a chance for recently hired colleagues to become acquainted with the section and share their work with us.
Dan Kalman will be our final speaker at the meeting. In addition, PASHEMA is hosting a dinner and math talk with Dan Kalman Friday evening before the conference. If you are interested, you are more than welcome to join the discuss and reception that follows. You can decide whether to attend when you register for the conference.
We are happy to have Jon Meier, our 2010 Crawford teaching award winner, giving a talk just after lunch. At the business meeting to follow, we will be announcing our 2012 Crawford teaching award winner.
Finally, when you register, don't forget to take a look at the lunch table topics for discussion. These are not formal discussions. Rather, they are a chance to meet with your colleagues and peers to discuss a topic that is of particular interest to you.
EPaDel has been a tremendous source of collaboration and camaraderie because of the effort put in by faculty members across the section. Here are just a few ways that you can contribute:
- Sign up for or make use of our section speaker list.
- Encourage your students to participate in the Student Paper Competition. Papers need to be submitted by June 15.
- If you will be hiring new faculty members this year, or if you have visiting or pre-tenure members in your department, encourage them to participate in our "New Colleagues" session. This will be held every spring, and is a great way to get new faculty members involved in the section.
- Mark your calendars for the fall meeting at Millersville University on October 27, 2012.
Section Governor, William Dunham, Muhlenberg College
The MAA Board of Governors convened on Wednesday, August 1, 2012, at MathFest in Madison, Wisconsin. President Paul Zorn was in the chair.
The primary topic of business – as it has been at all recent meetings of the Board – was MAA finances. Let me give some background:
Our organization has an annual operating budget of about $8 million. In 2010, we ran a deficit of $145,000. In response, the MAA leadership did some belt-tightening, with the result that our 2011 deficit fell to $109,000. Although still troubling, the figure indicated a downward trend, and there was talk of a balanced budget for 2012.
Instead, our deficit for the current year is likely hit a quarter of a million dollars. This is a most unwelcome reversal. In response, Executive Director Michael Pearson and others in the MAA leadership recommended not that we retrench but that we “invest” in ventures that promise to increase revenue down the road. Among the areas for targeted investment that Michael presented to the Board were:
- Publications. The MAA continues to push its textbook line (EPaDEL members take note) as a source of high quality and relatively low cost books for our students as well as a source of revenue for the organization. On another front, it was suggested that we hire a full-time acquisition editor for new books, a position that has been unfilled since the retirement of the legendary Don Albers. The hope is that this will increase the quantity and quality of books and thus the income from their sales, especially if we can publish works that sell beyond the MAA membership. But, of course, a full-time acquisitions editor will cost money.
- American Mathematics Competitions. This is a high school mathematics test that is put out by the MAA and is presently taken by about 375,000 students per year. The hope is that, with increased effort, we can attract more schools and students to participate in this program. By the way, the MAA is looking for colleges/universities to host these contests; if your institution might be interested, information can be found at http://amc.maa.org/.
- Membership. Over recent years, the MAA has seen a decline in membership to around 20,000. An increase in this number would help our bottom line. Our young colleagues, particularly, should be encouraged to join, and there was discussion of outreach to international members and to secondary mathematics teachers (see http://www.maa.org/membership/secondary_teacher.html).
- New Website. A significant amount of money is being spent to improve the MAA website. The new site should be much easier to use and should provide additional features like members’ electronic access to all MAA journals and a better procedure for purchasing books on-line.
- Development. In the year 2015, the MAA will turn one hundred years old (mark your calendars!). It thus seems like a propitious time for a fund-raising campaign. Such a venture – the “Second Century Campaign” – is in the works. This will necessitate an increase in development staffing.
Each proposal here requires an investment whose short-term cost will, one hopes, be offset by long-term revenue. The Board of Governors discussed these at length, with attention paid to the dangers of spending more in difficult times. In the end, the Board passed a motion of general support for “… significant investments intended to substantially improve financial performance.” Of course, the Board must approve specific budgetary proposals prior to implementation.
Two other topics of note came before us at the meeting. The first involved the policy of double blind (a.k.a. “double masked”) review for all MAA print journals. Last January a motion was proposed jointly by the Council on the Profession, the Council on Prizes and Awards, and the Joint Committee on Women to adopt such a policy. However, a subsequent investigation revealed that many members of journal editorial boards opposed double-masked review. After vigorous debate, the Board approved the double-masked refereeing policy, with the proviso that editors retain broad latitude for exceptions to the policy and that current editors are not required to adopt the policy during their terms.
The Board of Governors also passed an anti-bias policy. All MAA members, and particularly those on nomination, award, and program committees, are urged to review the statement at http://sections.maa.org/avoiding_bias.pdf.
Let me close with a few matters that should be of special interest to EPaDEL members. David Richeson of Dickinson College has been named the new editor of Math Horizons. Kay Somers of Moravian was elected chair of the MAA’s Council on Programs and Students. And Michael Posner of Villanova received one of the Alder Awards for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member. In addition, my previous report failed to mention the 2012 Chauvenet Prize that went to Dennis DeTurck, Herman Gluck, Daniel Pomerleano, and David Shea Vick of Penn for their joint paper “The Four Vertex Theorem and its Converse” (see http://www.ams.org/notices/200702/fea-gluck.pdf). Congratulations to all of these EPaDEL honorees.