senior seminar: Preparation for life after college, The

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Dec 2001 by Hathawayl, Dale K, Atkinson, David

ABSTRACT: This article describes a one semester hour mathematics senior seminar course at Olivet Nazarene University. The course has four main requirements: a resume packet, a short article presentation, a poster, and a project presentation. We describe how these four assignments fit together to provide a development of the mathematical maturity of our students. Additionally we discuss the strengths and weaknesses of the course.

KEYWORDS: Seminar, resume, poster, projects, assessment, oral preentation.

INTRODUCTION

At Olivet Nazarene University a senior seminar course is required of all mathematics and mathematics education majors. This course was created 8 years ago to provide a way to expose our senior students to mathematics beyond what fits into our course structure. It has also proven to be helpful as an assessment tool. Strengths and weaknesses of our program have been identified in the senior seminar.

Our school is a liberal arts school in the Midwest. Typically 4-8 mathematics majors graduate each year with approximately half of these being mathematics education majors who plan to teach at the secondary school level. Our senior seminar course is a I semester hour course that meets one hour each Wednesday afternoon of each fall semester. It is team taught by two professors each year, both of whom receive load credit, in a rotation with each professor in the department taking a turn at the course. Students are required to take the course the fall semester of their senior year. While most of our mathematics education majors student teach in the spring, occasionally one will use four and a half years to finish and will student teach in the following fall. For these students, they take the seminar in the fall of the previous year.

COURSE CONTENT

The course generally contains two parts. The first 10-12 weeks consist of talks given mainly by the professors of the course, while the last 3-4 weeks are student presentations. The faculty talks vary from year to year and depend on the interests of the faculty, though an attempt is made to present talks on a variety of interests. Listed below are the talks given in the Fall of 2000.

1. CMJ Problem #478 [51- This problem, generalized in the seminar, deals with integer solutions, in arithmetic progression, of a cubic polynomial. Its solution involves Pell's equation, encountered in number theory. Exposure to the problem sections of mathematics journals is part of what we want to accomplish in this course.

2. Ractals and Chaos - We feel this is a topic that our students should be exposed to, but it does not fit elsewhere in our curriculum.

3. Probability of x successes in time t- This is just an interesting probability problem dealing with the Poisson distribution. It gives an application of the Maclaurin series for ex and also involves a function of 2 variables, one discrete and one continuous.

4. Derangements - Another interesting probability problem that provides an additional application of the Maclaurin series for em.

5. Image Compression - This talk is based on an elementary wavelet scheme from [7).

6. Pascal's Hexagon - This talk is based on a generalization of Pascal's triangle found in [6].

7. Dandelin Sphere proof of conics - A unified treatment of conics not often seen 111. This is very useful for Secondary Education majors.

8. Birthday problem variations

(a) Including February 29 - An unpublished paper showing the exact calculation of birthday probabilities if February 29 is not ignored.

(b) Each person chooses k distinct dates - This variation is based on the article [101.

(c) Match with one among the first k - This variation is based on the article [9].

(d) Birthday lies - An unpublished article on what happens to birthday probabilities if some of the students are less than truthful about their birthday in an effort to avoid a match.

9. ACCA talk (outside speaker) Statistics - Each fall the seminar class is taken to the fall ACCA (Associated Colleges of the Chicago Area) mathematics talk. This gives them exposure to an outside speaker. The topics vary from year to year and this past fall the speaker presented two talks on statistics.

Since a major component of the course is for students to choose a topic of interest to them and present it to the class we try to provide a breadth of topics. We do this to show them how to present a topic in a single class period and to provide them with a variety of ideas. Their topics may be extensions of classroom work, going beyond what was covered in the class, solving a problem posed in a journal, or investigations of topics of interest that they may not have seen before.

On the other hand we recognize the importance of not just a breadth of coverage, but also some depth. The birthday problem provides a more in-depth investigation that all our students can follow no matter what their course work to this point. (The students may or may not have had a calculus based statistics course before they take the seminar, but they will have had basic probability and combinatorics.) Four variations are presented to the birthday problem to demonstrate how to dig into a problem and generate solutions to new questions.