MATHEMATICAL EXCURSIONS
Introductory lectures in Mathematics aimed at CEGEP students This web page:
http://www.math.mcgill.ca/jakobson/mathexcursions.html
FALL 2009
First Lecture:
Time: Tuesday, October 20, 18:00-19:30, Burnside Hall, Room 1205
Lecturers: D. Jakobson
Topic: orientable and non-orientable surfaces.
The material covered during the lectures is similar to the
material in the course lecture notes by T. Voronov,
chapter 4.
Second Lecture:
Time: Tuesday, October 27, 18:00-19:30, Burnside Hall, Room 1205
Lecturers: D. Jakobson
Topic: orientable and non-orientable surfaces, continued.
The material covered during the lectures is similar to the
material in the course lecture notes by T. Voronov,
chapter 5.
Third Lecture:
Time: Tuesday, November 3, 18:00-19:30, Burnside Hall, Room 1205
Lecturer: N. Dimitrov
Topic: orientable and non-orientable surfaces, continued.
In lecture 2 we discussed fundamental
groups and covering spaces in dimension 2. This will be continued in
lecture 3, with discussion of surfaces of higher genus, Euler formula
for orientable surfaces, and chromatic number of graphs on surfaces of
genus g.
Fourth Lecture:
Time: Tuesday, November 10, 18:00-19:30, Burnside Hall, Room 1205
Lecturer: N. Dimitrov
Topic: orientable and non-orientable surfaces, continued.
N. Dimitrov will continue the discussion of orientable and
non-orientable surfaces, including graph coloring, 4-color theorem and
its analogs on surfaces of higher genus.
A Wikipedia
article about the four color theorem.
Fifth Lecture:
Time: Tuesday, November 17, 18:00-19:30, Burnside Hall, Room 1205
Lecturer: N. Dimitrov
Topic: orientable and non-orientable surfaces, conclusion.
N. Dimitrov will conclude this semester's discussion of orientable and
non-orientable surfaces.
Sixth Lecture:
Time: Tuesday, November 24, 18:00-19:30, Burnside Hall, Room 1205
Lecturer: N. Dimitrov
Topic: to be announced.
Seventh Lecture:
The seventh lecture is CANCELLED.
There will be no more lectures in December. We shall resume briefly
for 1 or 2 lectures by Professor Shnirelman in january 2010, time to
be announced on this web page. After that, the lectures will not continue.
WINTER 2009
Poster: in English and
in French
Lectures:
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.
Lecture during the first week:
Wednesday, January 28, 16:30-18:00. McGill, Burnside Hall, Room 1B23.
Lectures in February:
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): 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.
Problem Set 2 for number theory:
ps and
pdf .
Problem Set 3 for number theory:
ps and
pdf .
Lectures on March 4,5: Topic: Recreational Mathematics: Rubik's cube.
Wednesday, March 4: G. Gauthier, 16:45-18:15, McGill, Burnside Hall,
Room 1B23. After 18:00: Burnside Hall, Room 1214
Thursday, March 5: Philippe Carphin, 18:00-19:30, McGill,
Burnside Hall, Room 1205.
Lectures on March 11,12 and March 18,19: Topic: Complex Numbers.
Complex Variables Website by J. Mathews
Wednesday, March 11: G. Gauthier, 16:45-18:15, McGill, Burnside Hall,
Room 1B23. After 18:00: Burnside Hall, Room 1214 Wednesday, March 18: G. Gauthier, 16:45-18:15, McGill, Burnside Hall,
Room 1B23. After 18:00: Burnside Hall, Room 1214
Lectures on March 25, 26: Topic: Escher's paintings.
Preview.
The talk is based on the following article:
English version ; and
French
version .
Wednesday, March 25: P. Carphin, 16:45-18:15, McGill, Burnside Hall,
Room 1B23. After 18:00: Burnside Hall, Room 1214
Thursday, March 26: P. Carphin, 18:00-19:30, McGill,
Burnside Hall, Room 1205.
Lectures on April 1, 2: Topic: Even and odd numbers in
Pascal's triangle.
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
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
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.
Mathematical translation links: a short
page
about French math vocabulary, mathematical translation pages,
English to French, and
French to English.
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
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
Lecturers:
Wednesdays: Gabriel Gauthier,
gabriel.gauthier@gmail.com
Thursdays: Maksym Radziwill
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
Number Theory:
W.W.L. Chen and
N. Diamantis
Graph Theory:
J.A. Bondy and U.S.R. Murty
Combinatorics:
W. Trotter and
A. de Mier
Topology:
T. Voronov (especially lectures 4 and 5, B. Purvis)
Other links to be added shortly
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