A Pathway Into Number Theory

This book leads readers from simple number work to the point where they can prove the classical results of elementary number theory for themselves.

R. P. Burn (Author)

9780521575409, Cambridge University Press

Paperback, published 28 November 1996

280 pages
22.9 x 15.2 x 1.5 cm, 0.4 kg

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

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.

Preface to the second edition
Introduction
1. The fundamental theorem of arithmetic
2. Modular addition and Euler's Phi function
3. Modular multiplication
4. Quadratic residues
5. The equation xn+yn=zn, for n=2, 3, 4
6. Sums of squares
7. Partitions
8. Quadratic forms
9. Geometry of numbers
10. Continued fractions
11. Approximation of irrationals by rationals
bibliography
Index.

Subject Areas: Number theory [PBH]