The spring 2016 meeting was held April 2, 2016 at Muhlenberg College.
- Robert Buchanan (Millersville University)
The Black-Sholes Option Pricing Formula
- Options are financial contracts used as a form of insurance against untoward future movements in prices. Options have been used for more than 2000 years, but a formula for a fair and rational price for options was only developed in 1973. This formula developed as the solution to a partial differential equation that can be thought of as a fundamental mathematical model of option prices. The prices for the myriad of different option types are obtained through the application of different boundary and payoff conditions. The development of the mathematical model for option prices will be traced, the solution will be outlined using only undergraduate-level mathematics, properties of option prices will be explored, and example uses of options for risk reduction will be described.
- Greg Coxson (United States Naval Academy)
Radar-Worthy Complementary Code Sets (Through Mathematics)
- From the early days of radar, pulse compression has been used to solve an apparent trade-off between long range and the ability to resolve closely spaced targets. This technique relies on finding binary and polyphase codes with certain autocorrelation properties, but the search for good codes tends to be a computational exercise whose cost grows exponentially with code length. Furthermore, there is a fundamental performance limit when using single codes to encode radar pulses. Luckily, there exist sets of codes for which this limit can be ignored; these are the so-called complementary code sets. Even better, these sets are easier to find than their apparently performance-limited single colleagues. For example, there exist simple construction methods for building larger CCMs from smaller ones. The weaknesses of these code sets become apparent when these sets are taken from the computer lab and used to encode real radar or communication systems; in particular, complementarity falls apart when handling targets with unknown, or even imprecisely known, range rate. Hence, complementary codes have seen very little application in radar, despite having been discovered over 50 years ago. This is not the end of the story, however -- Mathematics is coming to the rescue, again, in an interesting way.
- Suzanne Weekes (Worcester Polytechnic Institute)
Reaching Outside of the Ivory Tower
- Mathematics and statistics problems abound in business, industry, and government, and mathematics students and faculty can make real contributions and can help to answer interesting and challenging questions. In order to enhance the educational and research experiences for students and faculty ,the Center for Industrial Mathematics and Statistics (CIMS) was established at Worcester Polytechnic Institute in 1997. Faculty and students work with business, industry, and government partners on real-life problems that are of both industrial and mathematical significance. CIMS academia-industry activities have included research projects for mathematical sciences students during the regular academic year, a summer REU program, workshops for secondary school teachers, and running industry-academia study groups. In this talk, we will give more details on our experience working with over 75 companies in CIMS. Prof. Weekes will also talk about “PIC Math” which is an NSF-funded MAA and SIAM with the overarching goal of working and supporting mathematical sciences faculty across the U. S. to better prepare their students for careers in industry.
Faculty Contributed Paper Session
Faculty talk schedule (PDF)
Faculty talk abstracts (PDF)
Student Contributed Paper Session
Student talk schedule (PDF)
Student talk abstracts (PDF)
Section Governor, Annalisa Crannell, Franklin & Marshall College
This—my very last Governor's report—has two parts:
- One easy way for you to make a big difference in the life of someone you admire,
- Updates on departmental memberships, social media, and MAA governance.
(Exciting stuff—woo-hoo for Governance!)
- You and a person you admire:
You can make a difference. There are several MAA prizes and awards for which, not only do we welcome nominations, but even more, selections committees are not allowed to consider people for these awards unless those people have been nominated.
Last year, there were no nominations for the Solow Author's Award, and so no authors won the prize, even though we all know there are many transformative books that have influenced undergraduates in mathematics.
So think about mathematicians you know who are praise-worthy (and possibly prize-worthy, too).
Updates on big MAA ventures.
- Did you have a favorite math professor when you were in college? George Berzsenyi won the Gung and Hu Distinguished Service Award because of his incredible mentorship of many people, and also based on the beautiful and moving letters written by his former students.
- Do you have a young colleague who you think is a rising superstar? You could add sparkle and luster to that person's career by submitting a nomination for the Alder Award.
- Is there a mathematician whose teaching has been an inspiration to you and others around you? The committee that selects the EPaDel Crawford Award for Distinguished Teaching is always looking for good nominations.
- For a complete list of MAA Awards, look at http://www.maa.org/programs/maa-awards
Departmental memberships seem to be a success! From the MAA membership department: “Althoug we have 70% of the number of departmental members we had last year, we have 4.7 times as many Student Members.” Signing up students seems to be quick, easy, and a great way to enhance students' extra-curricular mathematical experience.
President Francis Su is pushing hard on effective use of social media (so much better than antisocial media)! Su is assembling a Social Media Task Force whose goal is to bring forth a report with recommendations by March. Ideas are welcome!
The new governance structure (replacing a large, unwieldy Board of Governors with a lithe and agile Board of Directors) is moving forward with a new outline. Your next Governor will get to see a proposal with the details of this outline, and within that person's three-year term of service, you'll get to vote on By-Laws that will transition the MAA into a new organizational structure.
Finally, there's good behind-the-scenes work happening at MAA headquarters. Currently MAA has 14 federal grants (total budget $12 million) and four privately funded programs (annual budget of $475,000). As a “for-example”, one of these grants funded the Common Vision report, a joint work with many other societies on issues and approaches to teaching collegiate mathematics. You can read an on-line version http://www.maa.org/sites/default/files/pdf/common-vision/common_vision_final.pdf. The MAA will be mailing copies out to all mathematics and statistics departments in the country early this year.