Product Description

This book gives an undergraduate-level introduction to Number Theory, with the emphasis on fully explained proofs and examples; exercises (with solutions) are integrated into the text. The first few chapters, covering divisibility, prime numbers and modular arithmetic, assume only basic school algebra, and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics. Elementary ideas about groups and rings (summarised in an appendix) are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares; in particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

Product Details

• Amazon Sales Rank: #45213 in Books
• Published on: 1998-07-31
• Original language: English
• Number of items: 1
• Binding: Paperback
• 200 pages

Customer Reviews

A smooth introduction to number theory
This is a nice little book (290 pages), which can be used as course litterature for an introductory course in number theory or a by-side reading for somebody taking a first course. It's exposition is so pedagogical and clear that I could study the book from the beginning to the end on my own without help. This is pretty rare for a mathematical book. It covers not only the basic subjects likes divisibility, primes and congruences but more advanced subjects like Euler's functions, quadratic residues, Riemann zeta function as well. there is even a final chapter on Fermat's Last Theorem, which is quite accessible. I would not hesitate to recommend this book to anybody starting to study number theory. Finally it contains complete solutions to all exercises.

An excellent introduction to number theory
This is an excellent textbook. It is very clear and self-contained, making it possible to work through it without the need to refer elsewhere. I found that it was pitched at just the right level, challenging but not overwhelming, and a good mix of exercises, all with full solutions. The structure is very well thought out, so that it is always clear where arguments are heading. Probably the best maths textbook I've ever read; other authors please take note!

Superb introduction to number theory
This book is one I would have liked to have read when I was an undergraduate. It is quite the best mix of 'old style' and 'new style' number theory that I have ever seen in a book. Compared to, say, Hardy and Wright's classic book it is much more accessible, and uses terminology and techniques that are now commonplace to modern (under)graduate readers to both simplify and demystify the subject. Then again, it covers less ground than H. and W., but as a starting point it succeeds admirably.

I came to this book just as I was myself trying to gather together everything I knew (or could redisover) about the Phi groups (the groups of units of the rings Z_n); this book did it all for me; and mostly in a way that delighted the mind. I was reluctant to read it (I prefer to try myself before 'cheating') but when I did I found all that I needed there: and authors sympathetic to my own viewpoint. What a delightful feeling of coming home.