Product Description

Number theory is concerned with the properties of the natural numbers: 1, 2, 3 … During the seventeenth and eighteenth centuries, number theory became established through the work of Fermat, Euler and Gauss. With the hand calculators and computers of today the results of extensive numerical work are instantly available and the road leading to their discoveries may be traversed with comparative care. Now in its second edition, this book consists of a sequence of exercises that will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A modern secondary school course in mathematics is sufficient background for the whole book which is designed to be used as an undergraduate course in number theory to be pursued by independent study without supporting lectures.

Product Details

• Amazon Sales Rank: #430491 in Books
• Published on: 1996-11-28
• Original language: English
• Number of items: 1
• Binding: Paperback
• 280 pages

Review
‘I’m pleased to report there is a new edition of R. Burn’s A Pathway into Number Theory, a book that takes readers quickly and painlessly from simple facts about whole numbers to the wonders of the quadratic forms, Pell’s equation and Minkowski’s theorem.’ Ian Stewart, New Scientist

‘… admirably suitable for those meeting number theory for the first time and for unsupported individual study.’ Nick Lord, The Mathematical Gazette

Customer Reviews

This book completely fulfills the promise of its title.
Written in a very unusual style, this book provides an excellent introduction to number theory. Unlike a normal textbook, there are no expositions or formal proofs. Instead, each chapter consists of a sequence of questions and problems, building one on top of another, which lead the reader step by step to discover key results in number theory, from the infinitude of primes to quadratic reciprocity. There is an emphasis on numerical examples to establish motivation and background at the beginning of each chapter.

A knowledge of complex numbers and 2x2 matrices is assumed. Topics covered include sums of squares, partitions, quadratic forms and continued fractions. Each chapter includes a summary of main results, a brief historical note, and hints or answers to all questions.

As the author promises in the Introduction, if you work through this book step by step you will have completed an undergraduate course in number theory. Alternatively, working through selecetd topics will help you to understand more formal number theory texts.