Short Course and Minicourses

Short Course

• Financial Mathematics

  Steven Shreve, Carnegie Mellon University

  Over the past 20 years, mathematical methods have permeated the finance and insurance industries. Universities have responded by offering undergraduate courses or degree programs in mathematics related to finance. This short course is based on the core of such a program at Carnegie Mellon. The purpose of this short course is to acquaint potential undergraduate instructors of financial mathematics with the main financial concepts and mathematical methodology that one can include in an undergraduate curriculum on this subject.

  The first part, Introduction to Mathematical Finance, requires only that students are familiar with differential calculus. It presents calculations related to loans, annuities and bonds, no-arbitrage pricing of derivative securities, and mean-variance analysis. Part two, Discrete-Time Finance, requires students to understand probability on finite event spaces. It covers dynamic models for financial markets within that context and a derivation of the Nobel-Prize-winning Black-Scholes formula as a limit of a discrete model.

  The third part, Continuous-Time Finance, expects students to know calculus-based probability and have the facility to handle analysis arguments at an undergraduate level. It introduces Brownian motion and stochastic calculus, and then derives the Black-Scholes formula within this context. We conclude with an introduction to problems in optimal consumption and investment, which provide opportunities for student projects in financial mathematics.

  A more complete description and schedule can be found in PDF format.

Minicourses

• #1 — A Beginner's Guide to the Scholarship of Teaching and Learning in Mathematics

  Jackie Dewar, Loyola Marymount University

  Part 1: Thursday, August 6, 1:00 – 3:00 pm

  Part 2: Friday, August 7, 1:00 – 3:00 pm

  This course will introduce participants to the scholarship of teaching and learning in mathematics. We will present a framework that illustrates the similarities between disciplinary research and SoTL work, offer examples of SoTL projects in mathematics at varying stages of development, discuss methods for investigation, and help participants begin projects of their own. Participants will be guided in transforming a teaching problem of their own into a problem for scholarly investigation. Suggestions for how to make this work public will also be given.

• #2 — Effective Placement Testing for Introductory College Mathematics Courses

  Raymond Cannon, Baylor University

  Marilyn Carlson, Arizona State University

  Wade Ellis, West Valley College

  Bernard L. Madison, University of Arkansas

  Gordon Woodward, University of Nebraska

  Part 1: Thursday, August 6, 1:00 – 3:00 pm

  Part 2: Friday, August 7, 1:00 – 3:00 pm

  This minicourse will describe and analyze ways to develop or modify placement testing programs so that they are more effective in placing students into challenging introductory courses where they can succeed. The topics will include innovations in item types and cognitive design, the increasingly complex transition testing landscape, structuring a placement program, and available testing resources. Both participants who are just beginning placement testing work and those with considerable experience are welcome.

• #3 — Preparing Students to Communicate Mathematics

  Lew Ludwig, Denison University

  Michael Orrison, Harvey Mudd College

  Part 1: Thursday, August 6, 3:30 – 5:30 pm

  Part 2: Saturday, August 8, 1:00 – 3:00 pm

  The number of oral presentations by undergraduate mathematicians at local, regional, and national meetings continues to increase. Moreover, effective oral communication is a skill highly sought by employers. In this course, participants will learn how to instruct students in effective oral communication skills and how to evaluate their outcomes. By the end of the minicourse, participants will have developed a working model of a course with an oral communication component that they can incorporate at their institution. In addition, each person will receive a copy of an instructional DVD on effective oral communication, developed under an NSF grant, and training on how to best use these materials in their curriculum.

• #4 — Combinatorially Thinking

  Arthur T. Benjamin, Harvey Mudd College

  Jennifer J. Quinn, University of Washington, Tacoma

  Part 1, Thursday, August 6, 3:30 – 5:30 pm

  Part 2, Saturday, August 8, 1:00 – 3:00 pm

  Faced with an identity, how do you create a combinatorial proof? This hands-on minicourse will provide you with some useful combinatorial interpretations, well-selected examples, and the challenge of finding your own combinatorial proofs. Along with numbers that are defined through counting (binomial coefficients, Stirling numbers, Catalan numbers), you will acquire a combinatorial appreciation for quantities like harmonic numbers, continued fractions, determinants, Fibonacci numbers, and the golden ratio. An extensive list of identities – some with known interpretations and others without – will serve as the basis for your exploration. Of course, you are welcome to bring along your personal favorites to add to the excitement.

• #5 — A Game Theory Path to Quantitative Literacy

  David Housman, Goshen College

  Rick Gillman, Valparaiso University

  Part 1: Friday, August 7, 3:30 – 5:30 pm

  Part 2: Saturday, August 8, 3:30 – 5:30 pm

  Game Theory, defined in the broadest sense, can be used to model many real world scenarios of decision making in situations involving conflict and cooperation. Further, mastering the basic concepts and tools of game theory require only an understanding of basic algebra, probability, and formal reasoning. These two features of Game Theory make it an ideal path to developing habits of quantitative literacy among our students. This audience participation mini-course develops some of the material used by the presenters in their general education courses on Game Theory and encourages participants to develop their own, similar, courses.

• #6 — Creating Demonstrations and Guided Explorations for Multivariable Calculus using CalcPlot3D

  Paul Seeburger, Monroe Community College

  Part 1, Friday, August 7, 3:30 – 5:30 pm

  Part 2, Saturday, August 8, 3:30 – 5:30 pm

  It is often difficult for students to develop an accurate and intuitive understanding of the geometric relationships of calculus from static diagrams alone. This course will explore a collection of freely available Java applets designed to help students make these connections. Our primary focus will be on visualizing multivariable calculus using CalcPlot3D, a versatile new applet developed by the presenter through NSF-DUE-0736968. Participants will learn how to customize this applet to create demonstrations and guided exploration activities for student use. Images created in this applet can also be pasted into participant's documents. See http://web.monroecc.edu/calcNSF/. Some basic HTML experience is helpful.