Term paper, topic proposal
Term paper, topic proposal
In this assignment you will choose a topic and one or more sources for your term paper.
As a reminder, from the syllabus, this paper is:
a term paper (6–15 pages) about a topic of the student’s choice within real analysis.
Assignment
In this assignment please look at some books and papers (recommended sources are listed in the course syllabus) in order to identify a topic for your term paper. You will write 0.5-2 pages to describe the main topic of your term paper, and address at least some of the following questions:
- What will your paper be about?
- Why is it an interesting topic? Why are you interested in it? (How will you make it interesting for the reader?)
- What will be the “main takeaway” or main point of your paper? What parts and technical details will you skip over, to get to the main point?
- What one or more high-quality sources will you use for your paper?
Formatting
- Please write your responses in a PDF file created using LaTeX.
- Upload the PDF to BlackBoard and/or GradeScope (TBA)
Topics
The chosen topic must be at a similar level to the course and related to real analysis. Topics that are directly related to course material are preferred, but not required.
You may not write a paper about your own research unless you discuss it with me first.
You are invited to freely select a topic of your own choice. Choose something you are interested in, something that excites you! If you don’t know where to start, some suggestions include:
- choose an inequality (Cauchy-Schwarz, arithmetic-geometric mean, etc.) and write about applications/corollaries of it;
- the Basel problem;
- the Gamma function;
- the Cantor set and the Cantor function;
- nowhere differentiable functions and other “paradoxes”;
- Stirling’s approximation for central binomial coefficients and factorials;
- summability methods such as Abel summation;
- space-filling curves.
- Some “challenging” exercises from Lebl’s textbook might also be good starting points for term paper topics.
- Also, many excellent articles are available from the MAA Writing Awards web page, https://www.maa.org/programs-and-communities/member-communities/maa-awards/writing-awards. Some of them are about analysis.
Sources
Recommended sources include the American Mathematical Monthly, College Mathematics Journal, Mathematics Magazine, Math Horizons, Involve: a journal of mathematics, and What’s Happening in the Mathematical Sciences; as well as textbook sections not covered in class. Allowed sources are restricted to ones listed in MathSciNet (https://mathscinet.ams.org).
Advice
No matter what topic you choose, you will have to explore sources to find ones that are right for you, and find ways to “make the topic your own”—learn from multiple sources, but then explain the topic in your own words.
Importantly, you will have to choose a narrow slice of your topic to focus on. Don’t try to tell the whole story of a major subject; choose one or two interesting examples and theorems. To write about an interesting but difficult theorem, skip over part of the proof, or focus on a simpler special case (e.g., give the proof only for 1 or 2 variables, only for continuous functions, etc.), or just roughly sketch the proof but instead give a detailed workthrough of an example. Find the right balance where you can tell a story that’s still interesting, but simple enough for beginning students to understand, within a 6-15 page scope.
You don’t have to work that all out right now, but keep it in mind. So don’t pick something easy but boring (“the commutative rule for addition”) and don’t pick something too big (“introduction to operator analysis”).