takes place from July 24 to August 11, 2000, at the University of Toronto's St.
George campus. It runs Monday through Friday, from 10:00 am to 3:00 pm. The
topic this year is NUMBER THEORY.
into Mathematical Sciences Summer Camp is an opportunity to explore a
challenging mathematical topic in a stimulating environment. Excellent high
school students, who can easily grasp new concepts, will soar into these
investigations of sophisticated university-level mathematics and be challenged
to think in different ways. SOAR 2000
will be a great way to see what life at the University of Toronto and
mathematical research are really like. You'll have the opportunity to explore
and use campus resources such as the mathematics library and some computer
facilities, as well as participate in recreational activities during the social
events. A typical week at SOAR 2000
will include lectures, tutorials, problem-solving sessions, and related games.
Since mathematics is best learned by doing, emphasis will be on solving numerous
problems related to number theory.
Number theory deals with the properties of the oldest mathematical objects studied by mankind: the natural numbers 1, 2, 3, etc. Despite the apparent simplicity of the objects of study and the ease with which questions about the natural numbers are posed, number theory contains some of the most complex and beautiful mathematics ever discovered. In the past, number theory has had very few practical applications, but it has recently evolved to play an important role in information transmission and retrieval, both in terms of reliability (error-correcting codes) and security (cryptography).
This introduction to number theory will cover topics such as the Euclidean algorithm, modular arithmetic (congruences), quadratic residues, factorization, the structure of codes, Egyptian fractions, and sums of squares. From this program you will gain a sound understanding of the foundations of number theory as well as exposure to several applications and areas of advanced research. Most of all, you will have the chance to immerse yourself in one of the most elegant areas of pure mathematics, one which has engaged scientists for over 4,000 years.
The program is
for students who are currently in grades 10 to OAC. Acceptance into SOAR will be
based on a competitive process which takes into consideration mathematical
aptitude, personal maturity, motivation, and the ability to work in a team.
Other desirable assets are experience with Mathematica (which will be used
during the program) and Maple, descriptive writing proficiency and artistic
ability. SOAR receives applications
from some of the best students in Ontario and elsewhere.
information is available for those who live beyond an easy commute. We
cannot take responsibility for the students outside program hours.
A fee of $300 per
student, payable to ‘University of Toronto’, is required for the three week
program and should accompany the application
form. Refunds (minus a $35 administration charge) will only be issued up to
June 30th. SOAR is a non-profit
program; the fee assists in covering the cost of lectures and computer time,
class notes, occasional lunches, daily snacks and other incidentals.
is financial assistance available on the basis of need. The Department of
Mathematics will support your request to reduce the cost of the camp jointly
with your school. If you feel that you would need such assistance, please
indicate this fact on your application.
Mail the application
form and the teacher
recommendation form, along with your registration fee and the
required supporting materials
(as listed on the application form), to the address below by Friday,
June 2, 2000. Late applications will be considered only if space is still
SOAR 2000 Mathematical Sciences Camp
Department of Mathematics
University of Toronto
100 St. George St, Room 4072
Toronto, ON M5S 3G3
Direct your inquiries to the
address above or:
Tel.: (416) 978-3472
Fax: (416) 978-4107
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This page was last updated: July 10, 2000