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A Primer of Analytic Number Theory: From Pythagoras to Riemann 1st Edition

4.9 out of 5 stars 8 customer reviews
ISBN-13: 978-0521012539
ISBN-10: 0521012538
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Editorial Reviews

Review

"The book is interesting and, for a mathematics text, lively.... Stopple has done a particularly nice job with illustrations and tables that support the discussions in the chapters."
Chris Christensen, School Science and Mathematics

"... this is a well-written book at the level of senior undergraduates."
SIAM Review


"The book constitutes an excellent undergraduate introduction to classical analytical number theory. The author develops the subject from the very beginning in an extremely good and readable style. Although a wide variety of topics are presented in the book, the author has successfully placed a rich historical background to each of the discussed themes, which makes the text very lively ... the text contains a rich supplement of exercises, brief sketches of more advanced ideas and extensive graphical support. The book can be recommended as a very good first introductory reading for all those who are seriously interested in analytical number theory."
EMS Newsletter


"... a very readable account."
Mathematika


"The general style is user-friendly and interactive ... a well presented and stimulating informal introduction to a wide range of topics ..."
Proceedings of the Edinburgh Mathematical Society

Book Description

This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. The author pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs, as well as to the important open problems (some of which have million dollar prizes). The capstone of the book is a brief presentation of the Riemann zeta function, which determines the distribution of prime numbers, and of the significance of the Riemann Hypothesis.
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Product Details

  • Paperback: 400 pages
  • Publisher: Cambridge University Press; 1 edition (June 23, 2003)
  • Language: English
  • ISBN-10: 0521012538
  • ISBN-13: 978-0521012539
  • Product Dimensions: 6 x 0.9 x 9 inches
  • Shipping Weight: 1.5 pounds (View shipping rates and policies)
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #1,284,849 in Books (See Top 100 in Books)

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Top Customer Reviews

Format: Paperback
A great book for senior undergraduates in mathematics or anyone with some background in calculus and complex numbers. Proofs are at a level where a careful reading makes them clear, and the author tells the reader when he is not being rigorous. Historical background and logical development of topics makes this a good read too. Most surprising to me was how the author tied in topics from prior chapters into later chapters--he didn't just jump from one topic to the next willy-nilly, but made the book flow as a whole. Problems given to the reader were helpful though sometimes too hard for me, a math major.
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Format: Paperback
A little background on me. I have just finished my freshman year of high school, and this was my first book on number theory. However, I have read many other math texts. In the beginning of the book there are some new concepts introduced, but they are not too hard to understand. The middle is refreshing as it involves a lot of calculus, which the student is most likely familiar with. The latter part consists of a variety of new ideas, and the theorems can get quite lengthy. I do not fully understand all of them myself. The book is well written and also includes the history of many mathematical problems.
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Format: Paperback
There usually seems to be a pretty big gap between the background needed to understand books on elementary number theory and what's needed to understand most books on analytic number theory, and this book does a good job of making that gap seem smaller. The writing feels a bit like Silverman's "Friendly Introduction to Number Theory" and Derbyshire's "Prime Obsession." There are plenty of experiments for Mathematica and Maple. I could see this book being used in an undergraduate number theory class. It doesn't assume any familiarity with complex variables. If you can integrate and aren't too afraid of series or logarithms, this book should be no problem.

The book goes over multiplicative functions, Mobius inversion, the Prime Number Theorem, Bernoulli numbers, the Riemann zeta function (value at 2n, analytic continuation, functional equation, the Riemann Hypothesis), the Gamma function, Pell's equation, quadratic reciprocity, Dirichlet L-functions, elliptic curves (and EC L-functions and the BSD conjecture), binary quadratic forms, and an analytic class number formula for imaginary quadratic fields.

I recommend this book to anyone who can read. And for those who can't read, this book is good motivation to become literate.
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Format: Paperback Verified Purchase
This is a great book. It presents the material in a completely rigorous fashion, yet is always providing an intuitive description and a great deal of motivation. This is a real plus and a refreshing break from the usual theorem/proof litany of typical math books (of course there are some exceptions which are likewise outstanding). The pace of presentation is conducive to really absorbing the material, and all along the way, there are problems that clarify and enhance your grasp of what is presented. Generously, there are solutions in the back, so, if all else fails, you can resort to them and continue making progress.

EDIT: The more time I spend in this book, the more I like it. IT really is a gift in that it teaches you how to think in terms of analytic number theory. Too often texts are either too pithy or seem to think you are already familiar with the subject. Thus it is a rare find to have a text that is fully rigorous,but opens your eyes to what's really going on - so there is little tendency to miss subtle points or have aweak base of understanding.

Another feature of this book is that it is truly self-contained. There are sections devoted to background material (series, complex numbers, etc.) which are directly pertinent to the subsequent presentation. Even if you are familial with this material, the author has a knack for pointing out ways of looking at things that are quite relevant and that you might not have thought of.

Whether for a course or self-study, as a fellow member of a great math online website said: this book is a pleasure.

Regarding the KINDLE EDITION: as Bourbaki might say: WARNING - this book does not reproduce well.
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A Primer of Analytic Number Theory: From Pythagoras to Riemann
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