189-346 / 377B: Number Theory
Professor: Henri Darmon
Classes: MWF 11:30-12:30, BH 1B23.
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.
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,
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
maturity and problem-solving skills.
Grading Scheme :
346: 40% Bi-weekly
40% final exam.
377: 20% Bi-weekly
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
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
in number theory are modest: a personal computer running a symbolic algebra
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
for more information).
L'université McGill attache une haute importance à l'honneteté
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