Topics in the Theory of Numbers

by Erdos, Paul; Suranyi, Janos; Guiduli, Barry

• ISBN13: 9780387953205
• ISBN10: 0387953205
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Springer Verlag

Summary

This rather unique book is a guided tour through number theory. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent discoveries, interesting method, and unsolved problems. In particular, we read about combinatorial problems in number theory, a branch of mathematics co-founded and popularized by Paul Erdös. Janos Suranyi's vast teaching experience successfully complements Paul Erdös' ability to initiate new directions of research by suggesting new problems and approaches. This book will surely arouse the interest of the student and the teacher alike.Until his death in 1996, Professor Paul Erdös was one of the most prolific mathematicians ever, publishing close to 1,500 papers. While his papers contributed to almost every area of mathematics, his main research interest was in the area of combinatorics, graph theory, and number theory. He is most famous for proposing problems to the mathematical community which were exquisitely simple to understand yet difficult to solve. He was awarded numerous prestigious prizes including the Frank Nelson Cole prize of the AMS.Professor Janos Suranyi is a leading personality in Hungary, not just within the mathematical community, but also in the planning and conducting of different educational projects whiich have led to a new secondary school curriculum. His activity has been recognized by, amongst others, the Middle Cross of the Hungarian Decoration and the Erdös Award of the World Federation of National Mathematical Competitions.rian Decoration and the Erdös Award of the World Federation of National Mathematical Competitions.

Table of Contents

Preface

Facts Used Without Proof in the Book

Divisibility, the Fundamental Theorem of Number Theory

Congruences

Rational and irrational numbers

Approximation of numbers by rational numbers. (Diophantine approximation.)

Geometric methods in number theory

Properties of prime numbers

Sequences of integers

Diophantine Problems

Arithmetic Functions

Hints to the more difficult exercises

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.