Number Theory for Mathematical Contests
These notes started in the summer of 1993 when I was teaching Number Theory at the Center for Talented Youth Summer Program at the Johns Hopkins University. The pupils were between 13 and 16 years of age.
The purpose of the course was to familiarise the pupils with contest-type problem solving. Thus the majority of the problems
are taken from well-known competitions:
AHSME American High School Mathematics Examination
AIME American Invitational Mathematics Examination
USAMO United States Mathematical Olympiad
IMO International Mathematical Olympiad
ITT International Tournament of Towns
MMPC Michigan Mathematics Prize Competition
(UM)2 University of Michigan Mathematics Competition
STANFORD Stanford Mathematics Competition
MANDELBROT Mandelbrot Competition.
Due to time constraints, these notes are rather sketchy. Most of the motivation was done in the classroom, in the notes I presented a rather terse account of the solutions. I hope some day to be able to give more coherence to these notes. No theme requires the knowledge of Calculus here, but some of the solutions given use it here and there. The reader not knowing Calculus can skip these problems. Since the material is geared to High School students (talented ones, though) I assume very little mathematical knowledge beyond Algebra and Trigonometry. Here and there some of the problems might use certain properties of the complex numbers.
http://ifile.it/m9lpnar/e6bd5cf6d01.pdf
