A Cascade of Numbers

This practical textbook introduces classical number theory using a variety of mathematical puzzles, problems and exercises, which lead the reader to rigorous proofs. Based on courses at both Exeter and Lancaster universities, the text adopts a lively, practical approach to the subject for students of number theory. The book is divided into 53 sections, arranged in three parts, each section consisting of two halves. The first half is raw material, encouraging student activity leading to pattern recognition and conjecture. In the second half, formal structures are identified and proofs are constructed, with comments and solutions. The aim is to provide an innovative approach to number theory which encourages a participatory style of learning, rather than a traditional system based on lectures. Students are encouraged to expand their understanding of the subject through active participation in solving the puzzles. No prior knowledge of the subject is required, but the contents of the book should be useful to student mathematicians, engineers and applied scientists.