Book Description
Using a background of analysis and algebra, the reader is led to the fundamental theorems of number theory; the uniqueness of prime number factorization and the reciprocity law of quadratic residues. Cyclotomy is treated in some detail because of its own significance and as a framework for the elegant theorems on Gaussian sums. Asymptotic laws are discussed as a foretaste of analytic number theory; also, Dirichlet's theorem about primes in an arithmetic progression and V. Brun's theorem on twin primes. ... Read more

Customer Reviews (1)

A gem of a number theory book
This is my favorite of all time number theory books. It does a lot of pretty high-powered number theory starting with things that a well-prepared and committed math undergrad should know: strong algebra and decent background in real analysis: no previous number theory required.

Prof. Rademacher starts naively with Farey fractions (fractions with bounded denominator arranged by size). He then proceeds in a highly readable way to do the basics: prime factorization, the GCD and its properties, congruences, and rational approximations. The proofs are elementary and very well presented.

He then moves on to some more exciting material: primitive roots and a beautiful exposition of the contruction of the 17-sided polygon. Gauss' insights are displayed clearly, and explanations and motivation are supplied everywhere. Rademacher is not afraid to display computations at length, but these are organized in such a way as to make the general principles crystal clear. This section of the book ends with a nice proof of Quadratic Reciprocity, using "finite Fourier series".

This is followed by a pleasant diversion on lattice points, mobius inversion, and a nice application of the zeta function as a measure of the density of lattice points with relatively prime coordinates.

Now come the real treats.

First, there is a totally self-containedtreatment of Dirichlet's theorem on primes in arithmetic progressions, including a quick intro to group characters and L-series. This is a great introduction to the methods of analytic number theory.

Finally, the book concludes with a hard-to-find-elsewhere account of V. Brun's theorem on prime pairs: the sum, of the reciprocals of primes that differ by 2, converges. This is one of the hardest chapters in the book, but the result and the insight gained in proving it is well worth the effort. ... Read more

Book Description

Customer Reviews (2)

The Real Beauty and Exhiliration of Math
This is a superb book, and the best way to first sample the delights of math for its own sake. Don't let the subtitle "Selections from Mathematics for the Amateur" turn you off. True, the math involved is elementary, not going beyond high school algebra and geometry. But the material won't be found in most textbooks, having been chosen with elegance and beauty, rather than utility, in mind (which isn't to say that it doesn't have its important uses). Even the professional mathematician who has already seen most of the contents will profit from studying the book's exemplary treatment of its topics. The authors are some of the best math expositors who have ever lived. Each idea in the book is developed admirably, and strikes the perfect balance between conciseness and lucidity. You probably can't do better in choosing an introduction to prime and perfect numbers, the four-color problem, regular polyhedra, Pythagorean triples, pedal triangles, periodic decimal fractions, Waring's problem, the number 30 (sic!), and many other fascinating intellectual tibdits.

At Dover's low price, this book is a great buy. Get it! If you have more mathematical knowledge, then I also recommend "Proofs from the Book" by Aigner, et al., which is written for mathematicians in a similar style.

An excellent collection of problems at the elementary level
Written by two top-notch mathematicians, requiring the mathematics that a high school student can do, this book takes you on a journey that is easy to follow and yet shows the power of mathematics. It is an excellent bookfor high school enrichement or early undergraduates.

Even if you are amathematician you will be suprized at many of the results and enjoy tryingto solve some of the problems. Many of the problems are quite hard. Eventhough some of the problems are the standard ones, many are off the beatentrack. No matter what your level of expertise, I am sure you will enjoythis book. ... Read more

Book Description
This book contains papers presented at the Hans RademacherCentenary Conference, held at Pennsylvania State University inJuly 1992. The astonishing breadth of Rademacher's mathematicalinterests is well represented in this volume. The paperscollected here range over such topics as modular forms,partitions and $q$-series, Dedekind sums, and Ramanujan typeidentities. Rounding out the volume is the opening paper, whichpresents a biography of Rademacher. This volume is a fittingtribute to a remarkable mathematician whose work continues toinfluence mathematics today. ... Read more

Book Description
Den beiden Autoren ist es auf hervorragende Weise gelungen, das Ziel ihres Buches zu verwirklichen und dem interessierten Nichtmathematiker einen tiefen Einblick in das Wesen der Mathematik, ihre Schönheit und Tiefe zu ermöglichen. So werden in 26 in sich abgeschlossenen Kapiteln ausgewählte Themen der klassischen Mathematik - unter anderem Probleme der Zahlentheorie, der analytischen Geometrie und der Topologie - in fesselnder Form vorgetragen. Der Schwerpunkt liegt dabei aber nicht auf der mathematisch-stofflichen Tatsache, sondern auf dem Ablauf des Geschehens, auf der Methode der Fragestellung und auf der Methode, gestellte Fragen zu lösen. Dieses Buch für Liebhaber der Mathematik hat seit seinem Erscheinen im Jahre 1930 nichts von seiner Frische und Faszination verloren. ... Read more

Product Description
THIS IS A TRANSLATION FROM VON ZAHLEN UND FIGUREN:PROBEN MATHEMATISCHEN DENKENS FUR LIEBHABER DER MATHEMATIK, BY HANS RADEMACHER AND OTTO TOEPLITZ, SECOND EDITION ECT. ... Read more

Book Description
Kein anderer naturwissenschaftlicher Forschungszweig ist so vielgestaltig wie die Geowissenschaften. Forscher zahlreicher Fachrichtungen - Geologen, Mineralogen, Physiker, Chemiker - arbeiten intensiv zusammen, um die Geheimnisse des Planeten Erde zu erkunden. Herausgegeben von der Senatskommission für Geowissenschaftliche Gemeinschaftsforschung und geschrieben vom Wissenschaftsjournalisten Horst Rademacher (F.A.Z.) wird in diesem reich illustrierten Buch nicht nur der Stand vieler geowissenschaftlicher Forschungsdisziplinen in Deutschland dargestellt. Es bringt dem Leser auch auf allgemeinverständliche Art die Bezüge zwischen den Wissenschaften von der Erde, der Gesellschaft und der Politik nahe. ... Read more