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The Prime Number Theorem (London Mathematical Society Student Texts) Paperback – April 21, 2003

3 customer reviews
ISBN-13: 978-0521891103 ISBN-10: 0521891108 Edition: 1st

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Editorial Reviews

Review

"...strongly recommended to those wishing to teach some analytic number theory at the undergraduate level." Mathematical Reviews

Book Description

The prime numbers appear to be distributed in a very irregular way amongst the integers, but the prime number theorem provides a simple formula that tells us (in an approximate but well-defined sense) how many primes we can expect to find that are less than any integer we might choose. This is indisputably one of the the great classical theorems of mathematics. Suitable for advanced undergraduates and beginning graduates, this textbook demonstrates how the tools of analysis can be used in number theory to attack a famous problem.
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Product Details

  • Series: London Mathematical Society Student Texts (Book 53)
  • Paperback: 264 pages
  • Publisher: Cambridge University Press; 1 edition (April 21, 2003)
  • Language: English
  • ISBN-10: 0521891108
  • ISBN-13: 978-0521891103
  • Product Dimensions: 6 x 0.6 x 9 inches
  • Shipping Weight: 15.5 ounces (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #2,126,646 in Books (See Top 100 in Books)

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28 of 30 people found the following review helpful By Paul Filipski on December 2, 2004
Format: Paperback
As an armchair mathematician, I can't remember how many times I'd read books that said things like "The prime number theorem, the proof of which is beyond the scope of this book, shows that the average number of primes less than any integer, n, is approximately n / log n." What a remarkable, intriguing statement! I was thrilled, therefore, to finally come across Professor Jameson's book, which is a proof of this theorem - no more, no less. Well, slightly more: he includes some interesting applications of the theorem, too.

The book is extremely well organized. It presents all necessary background material for the proof, and it does so in a refreshingly lucid manner. Topics are all well-motivated, and Jameson moves smoothly between them. He provides enough expository comments to guide the reader through the proof, but at heart this is a book of mathematics. I appreciated its utterly thorough proofs of all its statements, but those put off by equations will not enjoy this book.

Personally, the going got a little tough towards the culmination of the proof, around the midpoint of chapter 3. Those with a stronger background in analysis will doubtless find these sections easier to absorb.

Overall, this is a beautiful book. It clearly presents the theorem and the deep, subtle links between number theory and analysis. I highly recommend it.
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5 of 5 people found the following review helpful By William S Rea on October 22, 2011
Format: Paperback Verified Purchase
This book is volume 53 of the London Mathematical Society Student Texts.
Both its inclusion in this series and its structure marks it as a textbook.
However, it subject matter is not what one would normally expect to find
as the sole subject matter of a textbook so I will break this review into
two parts. First, I will address what sort of textbook this is and where
it would sit in the University mathematics curriculum. Secondly, I will
review the contents of the book itself.

The author, G.J.O. Jameson was a mathematician at the University
of Lancaster in the UK. Thus it is natural to assume that he had the
British, rather than American, University system in mind when he wrote it.
The New Zealand University is based on the British system so I will outline
where it would find its place here.

The way the degree structure works is that all students
complete a three year undergraduate degree. The good students then
have a chance to enter the ``honours'' programme. By good we require
students to have completed 50 percent more courses than the minimum required for
the ordinary B.Sc. degree and to have obtained a minimum of a B+ average
in those courses. The B.Sc. Honours degree is a one
year post-graduate degree consisting of a number of courses and
a small research project. The emphasis changes between the undergraduate
and honours degrees. In the undergraduate degree each course aims to
provide the student with a broad level of appreciation, knowledge,
skill and understanding in the topic studied. At the honours
level the courses are focused on a narrow topic and are intended to
cover that topic in some depth.
Read more ›
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0 of 1 people found the following review helpful By Indikos on August 16, 2012
Format: Hardcover Verified Purchase
The Prime Number Theorem is one of the truly great theorems of mathematics,
first broached by Gauss and Legendre. I have always to wished to understand
the theorem and ancillary material better, particularly the proof.
With this book my desire has been satisfied. The book is well organized,
the development rigorous, the proofs understandable.
The material is well-motivated and the historical asides greatly enhance the text.
The book is suited for self study; the material is covered at the beginning
graduate/senior undergraduate level.
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