Projects

The writing assignment for the second half of the course is a paper, written in LaTeX, that has been revised twice, on a topic closely related to the material in 18.100. For example, one could start with one or more exercises in Rudin related to a common topic (e.g., Baire's theorem, the Cantor set, Cauchy sequences, conditionally convergent series, the Riemann zeta function etc.). Then, the subject can be developed by consulting some other reference (e.g., a short note or article in the American Mathematical Monthly, or a section in some other book). The final paper should be approximately 5 pages long. The writing should be aimed at a typical MIT math major.

Some suggested topics can be found here. (PDF)

Deadlines

The table below indicates the due date of each project phase.

The following are examples of student papers. All papers are courtesy of the students named and used with permission.

"A Formal Treatment of Deterministic Fractals" by Justin Curry (PDF)

"The Gamma Function" by Thu Ngoc Doung (PDF)

"Fourier Series and Their Applications" by Rui Niu (PDF)

"Fulfillment" by Annie Raymond (PDF)

"Convergence of Fourier Series and Fejer's Theorem" by Lee Ricketson (PDF)

"Bernoulli Numbers and their Applications" by James B. Silva (PDF)