Each week there will be two lectures, one on wednesdays and another on
thursdays, times to be announced below. The material covered in the
lectures will be identical, the students can attend the lecture that
is more convenient. Each lectures will be followed by a short discussion/
problem solving session.

Topic: Number Theory, including
division, prime numbers, factorization, greatest common divisor and
Euclid's algorithm, congruences and modular arithmetic,
Fermat's little theorem, Chinese remainder theorem, Euler function,
other topics as time permits.

Time (for all lectures in February):
Wednesdays, 16:45-18:15, McGill, Burnside Hall, Room 1B23.
After 18:00: Burnside Hall, Room 1214
Thursdays, 18:00-19:30, McGill, Burnside Hall, Room 1205.

The material covered in the lectures on february 4,5 can be found in
Chapter 1 of W.W.L. Chen's lecture notes.

The lectures on February 11, 12 will continue the material in
Chapter 1 in Chen's notes, and possibly start covering the material
in
Chapter 3 of W.W.L. Chen's lecture notes.

The lectures on February 18, 19 will cover selected topics on
arithmetic functions and possibly quadratic reciprocity (if time permits).
That material is covered in
Chapter 2 and
Chapter 4 of W.W.L. Chen's lecture notes.

THERE WILL BE NO LECTURES ON FEBRUARY 25, 26 (this is
a reading week period at McGill). The lectures will resume in March.

Problem Set 1 for number theory:
ps and
pdf. It is, of course, optional.

Wednesday, April 1: Prof. A. Shnirelman (Concordia),
16:45-18:15, McGill, Burnside Hall,
Room 1B23. After 18:00: Burnside Hall, Room 1214

Thursday, April 2: Prof. A. Shnirelman 18:00-19:30, McGill,
Burnside Hall, Room 1205.

Lectures on April 8, 9: Topic: Graph Theory. Lecture notes:
pdf and
ps.

Wednesday, April 8: Prof. D. Jakobson (McGill),
16:45-18:15, McGill, Burnside Hall,
Room 1B23. After 18:00: Burnside Hall, Room 1214

Thursday, April 9: Prof. D. Jakobson 18:00-19:30, McGill,
Burnside Hall, Room 1205.

Lectures on April 15, 16: Topic: Uncountable sets and games Summary: How many whole numbers are there? The answer is
clearly infinity. How
many numbers are there between zero and one? The answer is again
infinity, but surprisingly, it is a "larger" infinity than the first
one. In this talk, I will explain what it means for one infinite
quantity to be larger than another. I will also explain why there are
"more" numbers between zero and one than there are whole numbers, with
the help of a simple two-player game. References:
A paper by M. Baker titled "Uncountable sets and an infinite
real number game,"
arXiv:math/0606253v1; and
Cantor's diagonalization argument

Wednesday, April 15: Prof. L. Addario-Berry (U. de Montreal),
17:00-18:30, McGill, Burnside Hall, Room 1B23

Thursday, April 16: Prof. L. Addario-Berry 18:00-19:30, McGill,
Burnside Hall, Room 1205.

Lectures on April 22, 23: Topic: Introduction to Combinatorics
Lecture notes:
A. de Mier

Wednesday, April 22: M. Radziwill,
17:00-18:30, McGill, Burnside Hall, Room 1B23

Thursday, April 23: M. Radziwill,
18:00-19:30, McGill, Burnside Hall, Room 1205.

Lectures on April 29, 30: Topic: Introduction to Combinatorics
Lecture notes:
A. de Mier

Wednesday, April 29: G. Gauthier,
17:00-18:30, McGill, Burnside Hall, Room 1B23

Thursday, April 30: G. Gauthier,
18:00-19:30, McGill, Burnside Hall, Room 1205.

The lectures will stop after that and will resume in September 2009.

Directions

Directions to Burnside Hall, 805 Sherbrooke Street West:
google map link; and a campus map
link. It is
a tall building on your right as you enter the campus at the
intersection of Sherbrooke and McGill College avenues.
Here is a photo.

The room 1B23 is in the basement (reached by elevator or stairs), close
to a food kiosk.

The room 1205 is on the 12th floor (take an elevator), across from
elevator doors.

Language: In the beginning, most of the lectures will
probably be in English, but we hope to have several French lectures
and to keep the discussion bilingual.

Assignments: We plan to assign a few easy problems,
and one or two more difficult problems after each lecture. Solutions to
difficult problems will be corrected, and the
person with the best solutions will get a prize at the end of the
course, details to be announced.

Contact:

Dmitry Jakobson
Office: McGill University, Burnsude Hall (805 Sherbrooke Street West),
Room 1212
Tel: 398-3828
E-mail: jakobson@math.mcgill.ca
Web Page:
www.math.mcgill.ca/jakobson

Possible Topics:

Introduction to number theory, combinatorics, graph theory,
topology and geometry, fractals, recreational mathematics (including
Rubik's cube), complex numbers, differential equations,
probability and statistics, groups and symmetries, functions and set theory

Other lecturers to be announced. We expect several students
and professors from McGill and other Montreal universities to give
lectures and to lead discussions.

Web Links

We shall be typesetting our own lecture notes for the course in the
near future. Meanwhile, the following lecture notes (selected chapters!)
can serve as references for the upcoming lectures on different subjects: