In the **independent research and paper writing** (Summer Session 1, 2023) class, each student will select an advanced topic to learn about in depth. Before the beginning of the class, each student will meet with the instructor to decide on a topic, which might be an important theorem, or a significant area of mathematics. Students will then begin by learning about the topic by reading books and papers on it, with the help of the instructor and teaching assistants. For a while, this can be done in groups of students working on related topics, and topics will be assigned so that no student will have to work on a project completely unrelated to the others.

Students’ main output from this class will be a detailed expository paper explaining the topic studied. This will be more in-depth than the papers that students typically write in the advanced classes; it will be around 20 pages long. Students will also give presentations to the class on their topics in the final week. There will be several sessions by the instructor on mathematical writing, using LaTeX, BibTeX, Overleaf, and Beamer proficiently, presentation style, and so on. There will also be a range of talks by mathematicians introducing exciting areas of mathematics.

This class is inspired by and modeled after the University of Chicago REU, which has been a very successful program for many years. Many students in our other advanced classes have read papers written for this REU and have found them among the most helpful papers for learning new areas of mathematics. Students in this class are expected to write papers that are similarly helpful to the Euler Circle community and perhaps the wider mathematical community.

This class will run for 5 weeks, from June 12 through July 14, meeting Mondays, Tuesdays, Thursdays, and Fridays from 5:00–7:00 PM Pacific time. There may be additional optional (but strongly encouraged) sessions at other times. Students will be expected to do a considerable amount of work outside of class; this is expected to be the students’ primary activity for the duration of the class. The class will primarily be held on Zoom, but we may schedule optional extra in-person sessions for local students if there is sufficient interest.

Applications for this class are due April 9. Click here to apply!

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