18.104 | Fall 2006 | Undergraduate

Seminar in Analysis: Applications to Number Theory


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


The prerequisite for this class is Analysis I (18.100A, 18.100B, or 18.100C). We will emphasize those topics which use methods taught in a typical first semester course in Analysis.


Young, Robert M. Excursions In Calculus: An Interplay of The Continuous and The Discrete. Washington, DC: Mathematical Association of America, 1992. ISBN: 0883853175.

There is also a recently published (2006) book, which I find very suitable for a topics course like ours:

Miller, Steven J., and Ramin Takloo-Bighash. An Invitation to Modern Number Theory. Princeton, NJ: Princeton University Press, March 6, 2006. ISBN-10: 0691120609, ISBN-13: 9780691120607.

The following books may be useful for reference:

Davenport, Harold. The Higher Arithmetic: An Introduction to The Theory of Numbers. 7th ed. Cambridge, UK: Cambridge University Press, 1999. ISBN: 0521632692, 0521634466. (pbk)

Niven, Ivan, Herbert S. Zuckerman, and Hugh L. Montgomery. An Introduction to The Theory of Numbers. 5th ed. New York, NY: Wiley, c1991. ISBN: 0471625469.

Format and Expectations

The two main components of this seminar course are:


The students will take turn in giving presentations. One such presentation (in the second part of the semester) will use slides (computer or overhead projector). The recitations will be interactive, therefore attendance is required. The students are allowed two unexcused absences during the semester.


One paper on a topic related to the course of approximately ten pages will be required. It must be written in Latex. See some instructions and helpful information about writing mathematics and using Latex in the related resources section.

The writing should be aimed at a typical MIT math major, and it should reflect your own understanding of the subject. Please also review the MIT published handbook on academic integrity and avoiding plagiarism, and the guide on general scientific writing (both found in the related resources section).

Assignments and Exams

In addition, there will be 3 homework assignments to complement the lectures. There are no exams.


Homework 20%
Class Work 40%
Paper 40%

Course Info

As Taught In
Fall 2006
Learning Resource Types
Problem Sets
Presentation Assignments with Examples