Here is the list of topics from my class from past years, which includes topics
students have already chosen for our class.
The term paper (due April 30)
You will need to both email a .pdf to me at sottile@tamu.edu,
and submit this to turnitin.com.
Here is the information for our class:
Math 629 History of Mathematics Class ID: 43151150 Class Enrollment Key: See Piazza.
This will be a fairly substantial paper.
It should include both non-trivial mathematics and non-trivial history.
I expect this to be well-researched with a number of sources, which should include some books
and/or journal articles, as well as easier to get (and less reliable) on-line sources.
This will be challenging, but using the TAMU library and its electronic resources, as well as libraries in your home town can be a help.
(I have often experienced the power of the TAMU library; For example, once I needed to research a topic for a book I was writing, and I was
able to get electronic versions of articles and one of the books I needed through TAMU libraries, which saved the day for me.)
Amazon is another quick source of books, and Dover is a source of often high quality books at very reasonable prices.
Here are two journals that have decent accessible articles, including some related to history:
The Mathematical Intelligencer (published by Springer) and the American Mathematical Monthly (published by the Mathematical
Association of America). I am an editor for the latter, and have read it off and on since I was given a subscription in High
school as a prize from a math contest.
A note about length: You will need space to develop your ideas.
I expect that it will be impossible to do this in a paper with fewer than 2000 words.
A note about formatting: Please use double (actually 1.5) spacing between the lines, so that I may scrawl my
comments in the more relevant place.
Also, please have a running head with your name on each page and page numbers, and a title.
While I expect that most of you will choose to write a paper, it is possible to fulfill this
without writing a paper; a comparable project in another medium of the same quality would be appropriate.
In one of Steve Fulling's classes, a student made a detailed time line for classroom use.
I can imagine, for example, a well-thought-out module about mathematics history relevant to a class you teach, say to
fill the weeks bizarrely inserted between the end-of-year standardized exams and the end of the school year.
(Everywhere else that has
such leaving exams does them after classes end, so as to not waste classroom time.)
To help move this along, there are several parts of this that I'd like to have done by certain dates:
| Milestone |
Delivery |
Due date |
| Topic; term paper proposal |
Piazza |
February 14 |
| Outline |
TBD |
February 28 |
| Draft |
email |
April 15 |
| Peer-review and feedback |
|
4/16 — 4/24 |
| Final Version |
email & turnitin |
April 30 |
Here are some additional sources of information.
These are included not to delineate what you will write about, but to stimulate your imagination and curiousity.
I prefer students to write papers on different topics, and will post topics on
the page as I hear from students.
- The list of topics from my class from past years
- Dr. Geller's list of example
term paper topics
I shall also steal these words of wisdom from her math 629 home page:
While a complete, in-depth analysis of the topic is not expected (that
would be a dissertation or book), a superficial discussion is not
sufficient. The term paper should be a thoughtful discussion of your
topic including the appropriate mathematics and history. I want to
know by reading the paper that you learned some things and thought
seriously about the topic.
- Here are some topics that spring to mind. I am free-associating, the lists of my predecessors may be a more sober place to begin.
- The four color theorem. This has an interesting story of its beginning (Francis Guthrie and Augustus De Morgan) through to the
controversy of its computer-assisted proof.
- Euler's formula, which began in his investigation of graphs, and in its modern form (the Euler characteristic) is a cornerstone of
topology and for surfaces is the same information as genus.
- Differential geometry. The story from Gauss, who created this subject while surveying the Kingdom of Hanover, to Einstein, who used
it as the basis for general relativity, and maybe even to Perleman's proof of Thurston's geometrization conjecture. (There is a lot here).
- While on this topic, the story of the Poincaré conjecture, from Poincaré to Smale to Freedman to Thurston to Perleman
is a possible story to learn about and discuss.
- The mathematical constant π is forever interesting. A topic that I like (I give talks on this) is why the four
measurements–circumference and area of a circle, and area and volume of a sphere–all involve the same constant π.
A priori each gives a different definition of a constant, and it is a great theorem of Archimedes that these are the same
number.
- There is a lot more on π. The article
I Prefer Pi: a Brief History and Anthology of Articles in the American Mathematical
Monthly by the late Jonathan Borwein and Scott Chapman is a great place to begin with π facts. They have a book, which
I think is available.
- More history of great Theorems: Attempts to prove Fermat's last Theorem led to many developments in Number Theory, and the
beginning and end of that makes a great story.
Last modified: Mon Mar 25 23:03:24 EDT 2024 by sottile