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Edward B. Burger

Exploring the Number Jungle: A Journey into Diophantine Analysis (Student Mathematical Library, V. 8) Paperback – July 25, 2000

by Edward B. Burger (Author)

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Welcome to diophantine analysis--an area of number theory in which we attempt to discover hidden treasures and truths within the jungle of numbers by exploring rational numbers. Diophantine analysis comprises two different but interconnected domains--diophantine approximation and diophantine equations. This highly readable book brings to life the fundamental ideas and theorems from diophantine approximation, geometry of numbers, diophantine geometry and $p$-adic analysis. Through an engaging style, readers participate in a journey through these areas of number theory. Each mathematical theme is presented in a self-contained manner and is motivated by very basic notions. The reader becomes an active participant in the explorations, as each module includes a sequence of numbered questions to be answered and statements to be verified. Many hints and remarks are provided to be freely used and enjoyed. Each module then closes with a Big Picture Question that invites the reader to step back from all the technical details and take a panoramic view of how the ideas at hand fit into the larger mathematical landscape. This book enlists the reader to build intuition, develop ideas and prove results in a very user-friendly and enjoyable environment.

Print length

151 pages
Language:

English
Publisher

American Mathematical Society
Publication date

July 25, 2000
Dimensions

5.75 x 0.25 x 8.75 inches
ISBN-10

0821826409
ISBN-13

978-0821826409
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Editorial Reviews

Review

"A wealth of information ... designed as a textbook at the undergraduate level, with lots of exercises. The choice of material is very nice: Diophantine approximation is the unifying theme, but the tour has side trips to elliptic curves, Riemann surfaces, and $p$-adic analysis. The writing style is relaxed and pleasant ... For this trip, the guide has chosen an ascent to an accessible summit, but with the emphasis always on teaching and motivating important techniques so that the beginner can advance to a higher level." ---- MAA Monthly

"The author invites the reader right from the beginning, through his engaging and motivating style, to develop ideas actively and to find proofs for himself ... Remarks at the end of each of the 20 short sections, into which this readily readable introduction to diophantine analysis is divided, extend the material and stimulate the reader to deeper study and involvement with it." ---- Zentralblatt MATH

"This short book presents a nice enjoyable introduction to Diophantine analysis, which invites the motivated reader to rediscover by himself or herself many of the fundamental results of the subject, with hints given in an appendix for the more difficult results." ---- Mathematical Reviews

From the Inside Flap

Here ... is something truly different ... number theory is such a large subject, and so much of it is initially accessible without too many prerequisites, that one would expect to see a different take on the subject every once in a while. And that, happily, is what we have here both, in content and in style of presentation ... For professors with the requisite background, this may be just the right book to use in an upper-level undergraduate seminar. Students working through this book will learn some nice material and will probably also emerge from the course with a much greater confidence in their ability to do mathematics.

--MAA Online

Product details

Publisher : American Mathematical Society; First Edition (July 25, 2000)
Language: : English
Paperback : 151 pages
ISBN-10 : 0821826409
ISBN-13 : 978-0821826409
Item Weight : 7.2 ounces
Dimensions : 5.75 x 0.25 x 8.75 inches

Best Sellers Rank: #662,337 in Books (See Top 100 in Books)
- #87 in Algebraic Geometry (Books)
- #206 in Number Theory (Books)

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2 ratings

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anthony fratis

Five Stars

Reviewed in the United States on May 19, 2015

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edward b burger is good

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reader

godawful

Reviewed in the United States on April 20, 2013

this is - and I don't say this lightly - one of the
worst math(?) books ever written ---
like junk food very little effort went into
its preparation and it will make you sick to
digest it ---
just as we suffer from a dearth of food inspectors,
we also seem to be without the services of competent book
editors who refuse to suffer fools gladly or in any other
mood --
this tripe is no more than a thin outline
of standard material (just bald statements - sans proofs)
far inferior to the material online (free!) --
shame on the publisher for accepting this blight -- certainly
the lamest entry -- in its stml series
it has been famously observed that today's banquet is
tomorrow's sewage -- well, in this case, we don't need
to wait for tomorrow

2 people found this helpful