HONS390: Honors Seminar on "Mathematics in Fiction"

Introduction

Note that this class meets MWF 1:00-1:50 in room 200 of the building housing the Honors Program. This syllabus is available on the Web at http://math.cofc.edu/kasman/HONS390/default.html and may be updated from time to time throughout the semester.

Assigned Readings

• Uncle Petros and Goldbach's Conjecture by Apostolos Doxiades
• Proof by David Auburn
• and Arcadia by Tom Stoppard

We will read all of those together. In addition, the professor may provide the class with some of his own writings (which, in theory, should be published some time during this semester)! Realizing that he is not a particularly talented author, the professor promises not to force the class to read too many of these stories.

It is important to note that in addition to all of the common readings, each student will be expected to do some independent reading, which will be reported to the class in the form of papers and some oral presentations. In this way, the students will be able to read whatever sort of fiction they enjoy most (e.g. mysteries, science fiction, comedy, classical, etc.) The selection of individual readings is subject to approval by the professor. Refer to the Mathematical Fiction Homepage for assistance in selecting appropriate works of fiction. Although some students may wish to purchase materials for the individual readings, between my extensive "private library" of mathematical fiction, the College library and the Charleston County Public Library, I believe it should be possible for students to simply borrow the books they need.

Graded Assignments

• Reader's Diary: Each student is required to have a spiral bound, lined notebook which is designated as their Reader's Diary. For each of the reading assignments in the class, whether a common reading or an individual reading, the student should log the date and time that they are reading in the book and then record some of their most significant observations or thoughts related to the reading. In the case of common reading assignments, specific questions will be given in advance that the student should address in their diary, although other observations and realizations may be recorded as well. The professor will check these diaries occasionally and without much warning. They will be graded primarily for effort and not on the basis of quality as a way of ensuring that the student is actually doing the reading assignments.
• Class Participation: Each student is expected to contribute to the discussion in class. Although you are encouraged to speak up whenever you have something to say, a minimum of two contributions per week is expected. Those shy (or unprepared) students who do not have at least two things to say each week will find their class participation grade suffering as a consequence.
• Non-fictional Material Test: There will be a single test in the class (all multiple choice and/or matching) on the non-fictional material that we will learn as part of the class. In particular, you will be expected to identify some of the mathematicians and mathematical topics that we will encounter as part of our common readings in the class. The test will not involve any actual computation, but an understanding of some mathematical concepts learned in the class may be required to correctly answer some of the questions. The test will take up the entire class on April 18th.
• Short Paper: Each student will pick a novel to read (see "individual readings" in reading assignments above) and write a 3-5 page paper on the book. The report will be due on March 2, but one week prior to that date the student will be expected to make a very brief presentation in class describing the book they are reading and what they are going to say about it in the paper.

  Note that I will be looking for more than just a "book report" describing the work of fiction. A paper in which the grammar and writing are perfectly accurate which does no more than summarize the book will receive a grade of C+. To earn a B or an A will require an original contribution of thought, reasoned arguments, and appropriate evidence from non-fictional sources. That is, the student is expected to have something to say about the fiction and its connection to mathematics. Originality of thought and the effectiveness of argument will be factors in determining the grade.

  Hopefully, the student will get an idea of what sorts of questions might be considered beyond simply describing the work of fiction from observing our class discussions. Here are a few ideas one might use if Uncle Petros and Goldbach's Conjecture was to be the subject (which it can't be...):

  • Uncle Petros and Goldbach's Conjecture: Is there a connection between insanity and mathematics?
  • Uncle Petros and Goldbach's Conjecture: The real history of Hardy, Littlewood and Ramanujan and its role in the novel.
  • Uncle Petros and Goldbach's Conjecture: Why Gödel's Incompleteness Theorem is more important to the novel than the conjecture in the title.
  I've made a list of books that I think would be good choices for the report (both because they have enough to write about and because I know where you can get a copy). Click here to see the list.

• Term Paper: The most important assignment in the class will be the 7-10 page term paper in which you will discuss several works of mathematical fiction but focusing on some unifying theme or question. At least three novels or plays ought to be addressed (and let us state here that for the purpose of the term paper, two short stories are equivalent to one novel). At least one of the three novels should be one that was not previously used either for the short paper or as a common reading assignment. The paper itself will be due on April 27, however on two occasions prior to that date (two weeks before and one week before), the student will be expected to make a short oral presentation to the class describing the works they have selected and the ideas they hope to present in the paper.

  Again, as in the short paper, this paper is not expected to be a summary of the works of fiction. In fact, to be able to say anything meaningful in a seven page paper, there probably would not be much room to summarize at all. Instead, the student is expected to have an idea of something to say that is not merely a repetition of what appears in the stories and to support their idea using appropriate support from non-fictional sources.

  Here are a few examples, just to give you an idea of what I would be looking for. You may feel free to use one of these ideas, or simply to use them to come up with your own idea:

  • Isaac Newton in Mathematical Fiction: Long presented as a brilliant and flawless person, Sir Isaac Newton's more recent fictional representations are highly unflattering. Where does the truth lie and what brought about this change?
  • Mathematical Metaphors: It can be difficult for an author to describe mathematics, and the feelings that mathematicians have about the subject, to a general audience. What sorts of non-mathematical metaphors do they use for this purpose and how effective are they?
  • Geniuses, in fact and fiction: Often, the mathematical characters in works of fiction are described as being "geniuses". Conversely, geniuses in fiction are often presented as being mathematical. What is a "genius" and how do the real ones compare the the ones presented in mathematical fiction?
  • The Deification of Alan Turing: The real mathematician Alan Turing (or his proxy) appears in works of fiction surprisingly frequently. The area of computer science has certainly had a dramatic impact on society, and Turing played a fundamental role in its origins. How has this affected the way people write about him?
  • Women in Mathematical Fiction: It is undeniably true that women were excluded from mathematics at many times in history. What is it like for women in mathematics today? Is this accurately reflected in mathematical fiction? How can mathematical fiction actually influence the number of women going into mathematics?
  • Is Math Real? This is a deep philosophical question, and not one on which even mathematicians agree. When a mathematician makes a new definition or proves a theorem, are they creating something new that exists only in the human mind, or have they discovered something that already had a sort of independent existence? Real mathematical results that address this question, such as Gödel's Incompleteness Theorem, are popular subjects in fiction. Moreover, fantasy and science fiction can hypothesize situations that provide us with (sometimes surprising) answers to the question.
  • Communicating with Aliens: Mathematics often shows up in science fiction as a tool for communicating with extra-terrestrial aliens. Where did this idea originate? Are most of these science fiction stories drawing on a common source, or did the authors originate the idea separately? And, how realistic is the idea anyway? Do scientists who really look for alien life make use of these ideas?
  • The Stereotype of a Mathematician: In fiction, mathematicians are often smart but cold, brilliant but insane, or cowards who use numbers as a means to escape reality. Why do authors love using these stereotypes, and to what extent are they justified?

Calendar of Graded Assignments

Final Grade

Extra Credit

• Find works of mathematical fiction that I have not yet listed on my Website.
• Review works of mathematical fiction that I have not yet reviewed on my Website. (I have in mind a few that I was not able to read due to my limited abilities with foreign languages. Can you read French or Italian?)
• Write your own work of mathematical fiction!
• Get together a small group of actors from amongst the students in the class and perform some of the scenes from the plays we will read.

Internet Resources

To help eliminate this problem, I am providing you with a list of internet resources you can use in writing your papers. If you wish to make use of some other Webpage, please clear it with me first.

• Mathematical Fiction Homepage: Of course, you can and should make frequent use of my Website. It lists and reviews works of mathematical fiction.
• Mathematical Biographies: This Website contains concise and accurate biographies of many famous mathematicians.
• MathWorld: This online encyclopedia of mathematics is in some ways inferior to the print versions you can find in a good library, but it is reasonably accurate and you can't beat it for convenience.
• MathSciNet: This site (only available on campus because we have a subscription) provides reviews of articles and books on mathematics.
• The arXiv: This is a repository of mathematics research papers. You probably wouldn't be able to read and understand many of them, but it still might be a source of information since you can get an idea of what sort of research people are doing these days and how much of it there is. Note that these papers are not refereed, so there is no real check on the quality of the papers.
• Science Direct: This Website available from campus computers gives the user access to many refereed research papers in mathematics (as well as other fields).

• Mandelbrot Drawing Java Applet
• Leaf Drawing Applet #1
• Leaf Drawing Applet #2
• Logistic Map (chaotic population dynamics, or fun with a parabola)
• A simpler look at logistic map iteration (no parabola)

Professor's Contact Information