Essay & Presentation Guidelines

Applied Math 206
Fall 2016


The purpose of these essays is for you to study some topic beyond the syllabus in depth, and understand it well enough to be able to explain it in your own words. The essay should contain a significant amount of prose, which explains the motivation for the material, highlights the main ideas, and gives intuition for the mathematics. Of course, this prose should be supporting a mathematical development, with precise definitions and statements of results. You need not include proofs of all lemmas and theorems; selectively decide which to include or sketch according to how informative and important they are. Further originality beyond the exposition is of course welcome too. This may come in the form of examples, new proofs of some lemmas, or even some small new results. Be sure to clearly identify anything that is new! In order to ensure that you present things in your own words (and really understand the material), I recommend that you study the source material carefully, but then try to write your essay without looking at the source material (only consulting it when you get stuck).


Each AM206 student will give a 20 min presentation on one of her/his essay topics on Monday, December 5 (during reading period). This is a chance for you to share something interesting you have learned with the rest of the class. Since the presentations are relatively short, you need to be even more selective about what to include; avoid the temptation to squeeze in too much material. If the audience leaves with one memorable idea or concept and an interest to learn more about the subject, you will have succeeded. Again due to the short time, you are encouraged to use slides/powerpoint (but again avoid the temptation to fill them with too much math). You may choose either your first or second essay topic for the presentation. The exact length and scheduling of the presentations will be done closer to the end of term.

Other Guidelines


Below is a list of suggested topics with some suggested references, which will be updated periodically. You should feel free to suggest your own topic, e.g. one that relates to your own interests or research. If you do, you must discuss the topic and the references you plan to use with Madhu for approval no later than 1 week before the essay is due.

Essay Topics on Groups

Essay Topics that involve Rings & Fields