"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
Firstly, I would like to thank the pioneers in that course: Samuel Chong, Nikhil Garg, Matthew Harris, Ryan Hoegg, Masha
Sapper, Andrew Trister, Nathaniel Wise and Andrew Wong. I would also like to thank the victims of the summer 1994: Karen
Acquista, Howard Bernstein, Geoffrey Cook, Hobart Lee, Nathan Lutchansky, David Ripley, Eduardo Rozo, and Victor Yang.
I would like to thank Eric Friedman for helping me with the typing, and Carlos Murillo for proofreading the notes.
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.
A note on the topic selection. I tried to cover most Number Theory that is useful in contests. I also wrote notes (which I
have not transcribed) dealing with primitive roots, quadratic reciprocity, diophantine equations, and the geometry of numbers.
I shall finish writing them when laziness leaves my weary soul.
I would be very glad to hear any comments, and please forward me any corrections or remarks on the material herein.
David A. SANTOS
dsantos@ccp.edu"
indirmek için tıklayınız.
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
Firstly, I would like to thank the pioneers in that course: Samuel Chong, Nikhil Garg, Matthew Harris, Ryan Hoegg, Masha
Sapper, Andrew Trister, Nathaniel Wise and Andrew Wong. I would also like to thank the victims of the summer 1994: Karen
Acquista, Howard Bernstein, Geoffrey Cook, Hobart Lee, Nathan Lutchansky, David Ripley, Eduardo Rozo, and Victor Yang.
I would like to thank Eric Friedman for helping me with the typing, and Carlos Murillo for proofreading the notes.
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.
A note on the topic selection. I tried to cover most Number Theory that is useful in contests. I also wrote notes (which I
have not transcribed) dealing with primitive roots, quadratic reciprocity, diophantine equations, and the geometry of numbers.
I shall finish writing them when laziness leaves my weary soul.
I would be very glad to hear any comments, and please forward me any corrections or remarks on the material herein.
David A. SANTOS
dsantos@ccp.edu"
indirmek için tıklayınız.
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