Analytic Combinatorics - Philippe Flajolet & Robert Sedgewick

"Analytic combinatorics aims to enable precise quantitative predictions of the properties
of large combinatorial structures. The theory has emerged over recent decades
as essential both for the analysis of algorithms and for the study of scientific models
in many disciplines, including probability theory, statistical physics, computational
biology and information theory. With a careful combination of symbolic enumeration
methods and complex analysis, drawing heavily on generating functions, results
of sweeping generality emerge that can be applied in particular to fundamental structures
such as permutations, sequences, strings, walks, paths, trees, graphs and maps.
This account is the definitive treatment of the topic. In order to make it selfcontained,
the authors give full coverage of the underlying mathematics and give a
thorough treatment of both classical and modern applications of the theory. The text is
complemented with exercises, examples, appendices and notes throughout the book to
aid understanding. The book can be used as a reference for researchers, as a textbook
for an advanced undergraduate or a graduate course on the subject, or for self-study.
PHILIPPE FLAJOLET is Research Director of the Algorithms Project at INRIA Rocquencourt.
ROBERT SEDGEWICK isWilliamO. Baker Professor of Computer Science at Princeton
University."

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David A. Santos - 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
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"

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All-Soviet Union math competition

"This file contains the problems, suggested for solving on the Russian national mathematical competitions
(final part).
I've posted this stuff in a number of articles in rec.puzzles. But I have got many requests for the missing
parts. So I have decided to put this material here, having provided it with the answers on the common
questions.
==================collected articles start======================
I'm going to send some problems from the book Vasil'ev N.B, Egorov A.A. "The problems of the All-
Soviet–Union mathematical competitions",–Moscow.:Nauka. 1988 ISBN 5–02–013730–8. (in Russian).
Those problems were submitted for the solving on the competition between the pupils of 8, 9, or 10 forms
for 4 hours. So they do not contain something of the advanced topics, –– all of them can be solved by a
schoolboy. They can not go out of the common school plan bounds.
Most of the problems are original and the book contains all the necessary references. I am not going to
translate all the book, so I shall not send the solutions. Please, accept those messages as they are, to say
more exactly – as I can. I have to do my job, and this is hobby only, but nevertheless, that should be
enjoyable to solve those problems.
"Nobody can embrace the unembraceable."
Kozma Prutkov.
(beginning of the XIX c.)
May be those postings are just a harassment, but I hope, that most of You will not only enjoy the problems
solving, but will be able to use them in Your work with the students.
"Zeal overcomes everything."
"Sometimes zeal overcomes even the common sense."
Kozma Prutkov.
There are some wonderful books in Russian, that have not been translated into English yet, for example,
"Problems of the Moscow mathematical competitions",–compiled by G.A.Galperin, A.K.Tolpygo.,–
Moscow, Prosveshchenie, 1986.
A.A.Leman "Collection of Moscow mathematical competitions problems", –Moscow, Prosveshchenie,
1965."


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