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189-346 / 377B: Number Theory

Professor: Henri Darmon
Classes: MWF 11:30-12:30, BH 1B23.

Office hours:
Henri Darmon: MW 1:30-2:30 in room 1111

You may also avail yourself of the services of the Math Help Desk, which is open Monday-Friday from 12:00 to 5:00 PM, in BH 911.

Recommended Texts:

Winfried Scharlau and Hans Opolka, From Fermat to Minkowski: Lectures on the Theory of Numbers and its historical development.

William J. LeVeque, Fundamentals of Number Theory, Dover Books.

Syllabus: This course will cover the standard syllabus for an introductory undergraduate course in number theory. The content and pace will be challenging: emphasis will be placed on rigorous proofs, and on developping mathematical maturity and problem-solving skills.

Grading Scheme :

346: 40% Bi-weekly assignments , 20% midterm, 40% final exam.

377: 20% Bi-weekly assignments , 20% term project, 20% midterm, 40% final exam.

Alternate schemes: If you do better on the final than on the midterm, the final will count for 60% of the final grade and the midterm will be discarded. The component of the grade based on assignments and term project can not be made up for by a strong performance in the final exam.

Extra office hours:
Friday April 13, 10-2.
Monday, April 16, 10-3.
Tuesday Aril 17, 10-12.

Final Exam date: Tuesday, April 17.

Project due date: Monday, April 23.


Computation and experimentation are an important facet of Number Theory, a tradition that does back at least to Gauss who was a prodigious calculator. Because of this, Number Theory is the branch of pure mathematics that is perhaps the closest to physics. (This may seem surprising in light of Number Theory's reputation as the purest part of pure mathematics, well removed from the "real world".)

Unlike physics where experiments often rely on costly apparatus that can only be carried out in well-endowed laboratories, the requirements for experimentation in number theory are modest: a personal computer running a symbolic algebra package is all that you will need. A number of questions in the assignments will rely on calculations on such a symbolic algebra system. Pari/GP, which is freely available on the web, is the system I recommend. (But you are free to use an equivalent system, like Maple, Mathematica or Magma if you prefer.)

Before writing Assignment 1, you should download Pari onto your computer. You might want to seek help from a classmate if you have trouble in doing this.

The usual disclaimer:

McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see Academic Integrity for more information).

L'université McGill attache une haute importance à l'honneteté académique. Il incombe par conséquent à tous les étudiants de comprendre ce que l'on entend par tricherie, plagiat et autres infractions académiques, ainsi que les conséquences que peuvent avoir de telles actions, selon le Code de conduite de l'étudiant et des procédures disciplinaires (pour de plus amples renseignements, veuillez consulter le site Academic Integrity.)