Northeastern Section of the MAA - 2001 Spring Meeting Contributed Papers

Session 1

3:00-3:15 p.m. Activity-Based Interdisciplinary Learning Of College Mathematics

Will Stout, Salve Regina University

The activity-based, guided-inquiry learning strategies can be an effective addition to the lecture approach in the college mathematics classroom. Students learn through their own experience at arriving at the "truth" about mathematics and its connection to other disciplines. We will share examples of learning activities that link mathematics with scientific and engineering concepts such as force, motion, electricity, excavation, and strength of materials.

3:20-3:35 p.m. Using Computers To Teach The Mathematics Of Investing

Andrew Perry, Springfield College

Many fundamental mathematical ideas are applied naturally in analyzing the stock market, and students readily appreciate the applicability of the math. In the Stock Market unit of my Business Math class, students select a portfolio of investments and follow its progress over the course of several weeks. The topics studied include percentage return on investment (including the effect of commissions), P/E ratio, dividends, stock splits, and computation of profits including use of the FIFO, LIFO and weighted average methods of valuation. The Internet is used as an investment-tracking tool and for company research, and a spreadsheet is used for computations and graphing.

3:40-3:55 p.m. Using Multivariate Calculus To Provide An Introduction To Filtering

Sarah L. Mabrouk, Framingham State University

Analysis of maxima and minima of functions of two or more variables is a standard topic in Multivariate Calculus. While students benefit from analysis of surfaces, they can also benefit from exploring problems that introduce them to techniques of mathematical modeling and lead to methods such as regression and/or introduce them to the tools of other disciplines, for example, the filters of Digital Signal Processing. In this paper, I will provide an introduction to filters and filtering and discuss how Multivariate Calculus can be used to enable students to derive filters in the time domain using a least squares analysis.

Session 2

3:00-3:15 p.m. Euler: Mathematician And Diligent Bureaucrat : The Great Balancing Act

John Glaus, Euler2007.com

Euler is the quintessential mathematician, but he also proved his worth to the Russian and Prussian imperial courts as an evenhanded, competent and tightfisted official. The intention of this paper is to show the human armor Euler developed to circumvent the complications caused by outrageous administrators and belligerent autocrats. The information contained in this talk has been taken from newly translated letters written from 1748-1763 to Kiril Razumovsky and Grigory Teplov while Euler was in Berlin. The introductions to Frederick II and de Maupertuis’ correspondence to Euler by Eduard Winter and Pierre Costabel, editors of the OO/SQA,Vol. VI are used as seminal references outlining Euler’s career in Berlin 1741-1765.

3:20-3:35 p.m. A Mathematics Teacher Reads The Headlines

Barry Schiller, Rhode Island College

In starting to clean out files to begin semi-retirement, I noted various newspaper and journal headlines and stories that I had clipped over the years with some expectation of their being useful in teaching some math class. So, perhaps appropriate for a lighter touch in a summer meeting, I will share some of these headlines and suggest how they might make some useful point in the classroom.

3:40-3:55 p.m. The New Kid On The Block

Tomas Kalmar, Goddard College

Tomás Kalmar will introduce himself by anecdotally comparing his experiences in mathematics education reform at Cal State University Monterey Bay with those at Goddard College, where he is now mathematician-in-residence. Plenty of time for questions and dialogue.

Session 3

3:00-3:15 p.m. Fibonacci Groups

Vince Ferlini, Keene State College

The recursive property idea of Fibonacci numbers can be adapted to define a collection of cyclically presented groups called Fibonacci groups. The first question considered is whether the groups are of finite or infinite order. We then look at the abelianization (the inclusion of the commutative property) of these groups and draw a connection between them and the Lucas numbers.

3:20-3:35 p.m. Periodicity And Boundedness Nature Of Positive Solutions

Of A Max-Type Difference Equation

Michael Radin, Mercey College

x[n+1] = max { A[n] / x[n], 1 / x[n-1] } , n = 0,1,2,......

where A[n] is a finite periodic sequence of positive real numbers and the initial conditions x[-1], x[0] are positive real numbers.

3:40-3:55 p.m. Some Examples Of Nontrivial Homotopy Groups Of Modules

C. Joanna Su, Providence College

In 1955, Professor Peter Hilton discovered and did the first work on the analogies between the usual homotopy theory of topological spaces with base points and the homotopy theory of modules over unitary rings. Unlike homotopy theory in topology, there are two homotopy theories of modules, the injective theory, and its dual, the projective theory. In this talk, we introduce the first nontrivial examples of absolute homotopy groups of modules.

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