Book Description
This book thoroughly examines the distribution of prime numbers in arithmetic progressions. It covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetical progressions, the theorem of Siegel, and functional equations of the L-functions and their consequences for the distribution of prime numbers. In addition, a simplified, improved version of the large sieve method is presented. The 3rd edition includes a large number of revisions and corrections as well as a new section with references to more recent work in the field. ... Read more

Customer Reviews (2)

An extraordinary Book
Ever since I first read about the prime number theorem, I have been roaming the mathetmatical landscape, looking for the best proof of this result. I believe this book has it. It's not the simplest or the shortest proof, but it gives the deepest understanding of why the prime numbers behve like they do. In addition to this, it shows you the historical perspective in these proofs. All too often today math books give one short and slick proofs that leave you wondering how on earth they came up with it. In this book, however, one can almost feel the thoughts going through Riemann and Dirichlet's heads as they came up with the theorems. This book also has the proof of Dirichlet's theorem and Vinogradov's partial proof of the ternary goldbach conjecture. The vinogradov and following sections are considerably harder, partly because they were not written by Davenport himself. Anyway, if you're serious about Analytic number theory and how mathematicians think, this books needs to be on your bookshelf.

A good historical approach to Analytic Number Theory
I like this book because it gives you a good understanding of where the difficulties in the subject are. It takes a historical approach, following more or less the same steps that the original discoverers of these results took. Today we have very slick proofs for many of these results, and it is sometimes hard to understand why it took so long to discover them in the first place, but this book will give you this understanding; Dirichlet in particular practically had to invent Analytic Number Theory to prove his theorem on primes in an arithmetic progression.

The book works up gradually to each result, for example proving Dirichlet's theorem first for a prime modulus (as Dirichlet did himself), then the general modulus. In most cases it proves first the result for all primes (zeta function) and then the generalization for primes in an arithmetic progression (L function), pointing out which parts generalize easily and which cause special difficulties.

Some of the more advanced results covered are exponential sums, Vinogradov's theorem that every large odd number is the sum of three primes, and Bombieri's theorem about the average distribution of primes in arithmetic progressions.

I haven't seen the previous (1980) edition; this new edition seems to be lightly revised from the previous one. The last chapter is up-to-date and gives a brief survey of new results and of new books on the subject. ... Read more

Book Description
Updated in a seventh edition, The Higher Arithmetic introduces concepts and theorems in a way that does not require the reader to have an in-depth knowledge of the theory of numbers, and also touches on matters of deep mathematical significance. This new edition includes state of the art material on the use of computers in number theory, as well as taking full account of the proving of Fermat's last theorem. ... Read more

Customer Reviews (2)

Good book, but if you have the money, there are better
Well, this is definitely a very good introduction to number theory.The author provides clear, readable proofs of all the most basic theorems on topics such as congruences, sums of squares, etc.He explains things quite well.However, despite costing almost 2.5 times as much, I would recommend Hardy and Wright's book An Introduction to the Theory of Numbers more highly than Davenport's book.Seriously, although it may seem good that Davenport doesn't require a knowledge of calculus as a prerequisite for his book (which Hardy DOES require), one probably shouldn't learn number theory until one has a good backrground on topics ranging from improper integrals to infinite series.Because Davenport does not require calculus as a prerequisite, he neglects HUGE aspects of what could actually be considered BASIC number theory: namely, the basic analytic aspects (such as Tchebycheff's results on the Prime Number Theorem) and the additive theory (i.e. partitions and such, as well as the basics of the generalized theory surrounding Waring's problem for high powers of integers).So, my recommendation is, wait until you know integral calculus and the theory of infinite series BEFORE buying a book on number theory, and then buy Hardy and Wright's book rather than this one.

This is a MUST BUY if you want to learn Number Theory!
This book is an AMAZING introduction to the Theory of Numbers. It assumes no previous exposure to the subject, or any technical mathematical knowledge for that matter. Its prose is lucid and the style appealing.Davenport chose NOT to write a lemma-theorem-proof kind of book, and theresult is a marvelous, eminently readable introduction to the subject. Itswonderful to read a book where good prose is used to appropiatelysubstitute a massive collection of uninviting symbols. I've also beenreading other books on Number Theory, such as Hardy & Wright, but noneare as clear as this one.

I found the chapter on quadratic residues(which includes the reciprocity law) to be especially well written. Thesection on computers and number theory is excelent as well. A concise andcoherent discussion of crytography and the RSA system is included here.The organization of the book's chapters is fantastic. Each chapter buildsup on results proven in the previous ones, showing well the connectionsbetween the different aspects of Number Theory. The exercises of the bookrange from simple to challenging, but are all accesible to someone willingto put effort into them.

This would be an excelent source for learningnumber theory for mathematical competition purposes, such as the ASHME,AIME, USAMO, and even for the International Mathematical Olympiad. The bookcontains much more than what is needed for these competitions, but theolympiad/contest reader will benefit greatly from a study of Davenport'swork.

The book can certainly be used for an undergraduate course inNumber Theory, though it might need supplementary materials, to cover asemester's worth of work. I know the book has been used in the past inprevious editions as the main text for Math 124: Number Theory at HarvardUniversity.

I would also recommend this book to anyone interested inacquanting themselves with Number Theory.

Awesome!There is simply noother word that describes The Higher Arithmetic. ... Read more

Book Description
Day surgery is a major innovation in the delivery of medical care to a growing number of patients. It presents many new and unique challenges for nurses. Principles of Day Surgery Nursing provides comprehensive coverage of all aspects of day surgery with which nurses and their support staff will need to be familiar. ... Read more

Book Description
This is the sixth in a series of conference proceedings of international conferences on computer algebra held in Europe. All the preceding ones have also been published as Lecture Notes in Computer Science. They contain original research material not published elsewhere, and a few invited lectures summarising the state of the art. Computer algebra is the science of using computers to do algebraic calculations, rather than the purely arithmetic calculations which we all know computers can do. These calculations may be polynomial-like calculations - one thread of the conference was devoted to polynomial algorithms - or may relate to other areas of mathematics such as integration, the solution of differential equations, or geometry - a second thread was devoted to those topics. The calculations can be applied in a wide range of scientific and engineering subjects, and in branches of mathematics. Physics has benefitted especially from these calculations, and the proceedings contain many papers on this, and also papers on applications in computer aided design and robotics, to name but a few other applications. The third thread of the proceedings was devoted to these applications and to the computer algebra systems which perform these calculations. ... Read more

Book Description

This book constitutes the refereed proceedings of the Second International Conference on Mathematical Knowledge Management, MKM 2003, held in Betinoro, Italy, in February 2003.