Product Description

The theory of numbers is generally considered to be the ‘purest’ branch of pure mathematics and demands exactness of thought and exposition from its devotees. It is also one of the most highly active and engaging areas of mathematics. Now into its eighth edition The Higher Arithmetic introduces the concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical significance. Since earlier editions, additional material written by J. H. Davenport has been added, on topics such as Wiles’ proof of Fermat’s Last Theorem, computers and number theory, and primality testing. Written to be accessible to the general reader, with only high school mathematics as prerequisite, this classic book is also ideal for undergraduate courses on number theory, and covers all the necessary material clearly and succinctly.

Product Details

• Amazon Sales Rank: #338982 in Books
• Published on: 2008-10-23
• Original language: English
• Number of items: 1
• Binding: Paperback
• 248 pages

Review
‘Although this book is not written as a textbook but rather as a work for the general reader, it could certainly be used as a textbook for an undergraduate course in number theory and, in the reviewer’s opinion, is far superior for this purpose to any other book in English.’ From a review of the first edition in Bulletin of the American Mathematical Society

‘… the well-known and charming introduction to number theory … can be recommended both for independent study and as a reference text for a general mathematical audience.’ European Maths Society Journal

About the Author
Harold Davenport F.R.S. was the late Rouse Ball Professor of Mathematics at the University of Cambridge and Fellow of Trinity College.

Customer Reviews

Awesome book
This was the first book I read on the theory of numbers. It is a fascinating subject, and this book is the perfect introduction. It is written by Harold Davenport, a famous number theorist of the 20th century. It gives an introduction to several areas of the subject (primitive roots and quadratic residues, sums of squares, continued fractions, quadratic forms, Diophantine equations) which are accessible without much prior mathematical knowledge, and sticks to elementary methods whilst providing hints and pointers to the use of analytic methods (Dirichlet's theorem on primes in arithmetic progressions, Diophantine Approximation) and elliptic curves in the subject.

Also from quite an early point in the book (the first chapter) the author mentions various unsolved problems, some of which are more famous (Goldbach's conjecture) than others (Erdos' covering problem). The reader might get the impression that it is easy to come up with propositions which one can neither readily prove nor dispose of, and this is true on a global and historic scale.

The book is not written in a lemma-theorem-proof style at all. Of course for a more advanced book, the more structured approach is useful. But for a book of this kind, the more continuous approach works brilliantly.

Gentle book on number theory topics
Introduction

Several years ago, a tutor showed me her copy of this book and highly recommended it as a primer for this topic. I have compared the contents list (seventh edition, 1999) of mine, against this new copy contents list and both are pretty close to each other. Although this edition will be much updated.


Why is this book worth recommending?

This book encourages the reader to return to its pages again-and-again. This book i.m.h.o has a high level of initial readability, rather than featuring many equations, to create a level of understanding that is rewarding. For example, the initial topics gently explain about 'primes'. Then book clarifies this by branching into topics such as 'Congruences' and 'Quadratic residues' in a way that an author of a few complex analysis books would be proud.

Conclusion

This is a book thats not your final destination in mathematics, but a book to help you reach it.