FYS 105A (Spring 2004): Fermat, Uncle Petros and Pi
Instructor: Manil Suri
(The above is a poster used to advertise the main project of the class.)
- Manil Suri,
Math/Psych 419, (410) 455-2311, firstname.lastname@example.org,
office hours: MW 4-5. Also by appointment.
- Lectures: MW 5:30-6:45, ITE 237
- Primary Texts: "Fermat's Enigma" by Simon Singh
"A Beautiful Mind" by Sylvia Nassar
- Additional readings to be selected from the following: "Uncle Petros and Goldbach's Conjecture" by Apostolos K. Doxiadis, "The Universal Computer: The Road from Leibniz to Turing" by Martin Davis, "The Curious Incident of the Dog in the Night Time" by Mark Haddon, and other books.
The cult film Pi and the Oscar-winner A Beautiful Mind are two recent examples of popular works revolving around mathematicians. Other examples include the Pulitzer-winning Broadway play Proof, the international bestseller Fermat's Enigma and the acclaimed novel Uncle Petros and Goldbach's Conjecture. In all of these works, some mathematical idea has been used as a starting point to create an absorbing story that has captured the public's imagination. In this course we will examine the above interaction: how technical ideas can be combined with narrative techniques to create works of broad appeal. Can mathematics be packaged in story form to be made accessible to non-technical audiences? What cultural role does does mathematics play in our society? We will first gain a perspective on contemporary mathematics by examining the actual mathematics behind the above works. We will study the extent to which this body of knowledge has been communicated (e.g. by comparing the film and book versions of a Beautiful Mind). Next, we will find original ways to use this knowledge - in writing assigments and other creative endeavors that students might propose. We will try our hand at mathematical fiction and exposition, always keeping in mind that we are speaking to a non-mathematical audience. Field trips (such as to appropriate films, readings and perhaps a mathematical conference) will be included. Students interested in writing as well as those interested in mathematics will find this class appealing. The goal will be to broaden horizons through mutual interaction.
Nuts and Bolts
We will start by going through "Fermat's Enigma", followed by "A Beautiful Mind." We will discuss a chapter per class. In order for this to be successful, you would have to read the material beforehand, keeping in mind some specific issues that are raised in the text- see example at end of syllabus. There will be both writing and mathematical-type homework assignments, as well as a project. The grade will be based on these - there will not be any tests or exams. The actual emphasis of the assignments (as well as the course in general) will be adapted to suit student interests. The first field trip will be to see the play "Proof" in Baltimore, in February.
Computers and MATLAB
You should have a computer account (see the UMBC webpage for starting up). It may be useful to have some elementary knowledge of Matlab, a program that can perform various mathematical calculations. (An introduction will be given in class.) Matlab is available on UMBC computers, and also can be purchased in student versions. (We will be only using fairly elementary commands.)
STEM Tie-inA recent NSF grant by Professor John Lee of UMBC provides for funds for STEM faculty (Science, Technology, Engineering and Mathematics) to be funded for first-year seminars that involve K-12 pedagogical components. This seminar falls within the targeted category.
The goal of this seminar is for students to learn how to take a technical topic in mathematics and make it accessible to a lay audience, or one that is not at the level where such a topic would ordinarily be introduced. Through such exercises, students in the seminar will gain experience in techniques of conveying the ideas behind technical (and often difficult) ideas in non-technical, more accessible forms.
The central project is an hour long powerpoint presentation that explains the concept of "cardinality'' of a set, and in particular, the difference between countable and uncountable infinity. This material is generally introduced to university math majors in their junior year, under a course such as "Introduction to Mathematical Analysis.'' However, it only requires knowledge of numbers such as integers, fractions and irrational quantities like pi (which cannot be written as a fraction). The presentation (which uses several graphical and pictorial devices) goes through this introductory material on numbers, introduces the concept of counting, then goes on to discuss the different types of infinity. Although the ideas are deep, they are presented in a way that is accessible, in particular, to students from grades 8 and up.
After initial tests on non-math/science audiences at UMBC, the presentation will be given to 8th graders at Meade Middle School in Anne Arundel County, MD (contact teacher: Angela Sasse). Then it will be given (on 21 May) to sophmores and juniors at Benjamin Banneker High School, in Washington, DC (contact teacher: John Mahoney). The latter is a public magnet school with 98% minority enrollment.
Ways will also be explored to make the presentation available in the future to school teachers who might be interested in using this material for their classes. The material is not covered in schools, but should be interesting (and useful) especially to those who might want to pursue a career with a math/science type background.
Please note the standard policy statement that follows.
By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, or the UMBC Policies section of the UMBC Directory.
Reading Chapter 1 of "Fermat's Enigma"
We will discuss this on February 4, so you should read it before coming to class. Please think of the following questions while reading it.
- What is the difference between Science and Pseudo Science? (see handout from "Philosophy of Science" by Samir Okasha) Would you label Astrology a science? What about Mathematics?
- This chapter could have been written in a much more dry fashion, as if it were a textbook chapter. Instead, it seems to read more like a story. What techniques does the author use to propel the narrative forward and keep you reading? Are there some technical points that are explained particularly well or particularly poorly?
- Any ideas on how one could prove that there are an infinity of Pythagorean triples?
- Suppose you had to pick a very dramatic part of the first chapter and write a one-scene play based on it. What would you pick and how would you dramatize it?