Vilenkin Combinatorial Mathematics torrent

Combinatorial Mathematics by N. Vilenkin.

In the present book, the aim has been to set forth a variety of
combinatorial problems in popular form and understandable language.
At the same time, an attempt is made to present some rather involved
combinatorial problems and to give the reader an idea of the methods
of recurrence relations and generating functions. The first chapter
is devoted to the general rules of combinatorics, the rules of sum and
product. In the second chapter we investigate permutations and
combinations. This traditionally grade-school material is accompanied
by an analysis of some amusing examples. In the third chapter, a study
is made of combinatorial problems in which certain restrictions are
imposed on the combinations. Chapter IV considers problems involving
partitions of numbers into integers and- contains a description of
certain geometrical methods in combinatorics. Chapter V is devoted to
random-walk problems and to a variety of modifica tions of the
arithmetic triangle. Chapter VI takes up recurrence relations, and
Chapter VII discusses generating functions and, in particular, the
binomial formula.

The last section of the book is devoted to combinatorial problems of
which there are over 400. This material has been taken from a variety
of sources, including Whitworth's Choice and Chance (London, 1901),
John Riordan's An Introduction to Combinatorial Analysis (New York,
1958), an interesting book by A. M. Yaglom and I. M. Yaglom entitled
Nonelementary Problems in an Elementary Exposition (Moscow, 1954), and
various collections of problems given at mathematical olympiads in
the USSR.

This book was translated from the Russian by George Yankovsky. The
book was published by first Mir Publishers in 1972.

All credits to the original uploader.

DJVU | 3.8 MB | Pages: 205 | OCR

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Table of Contents

Preface

CHAPTER I. THE GENERAL RULES OF COMBINATORICS

CHAPTER II. PERMUTATIONS AND COMBINATIONS

CHAPTER III. COMBINATORIAL PROBLEMS WITH RESTRICTIONS

CHAPTER IV. THE COMBINATORICS OF PARTITIONS

CHAPTER V. COMBINATORICS AND CHESS

CHAPTER VI. RECURRENCE RELATIONS

CHAPTER VII. COMBINATORICS AND SERIES

Solutions and Answers 152

Index 205