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Rating: 
Summary: A beautiful guide to the Prime Number Theorem
Review: 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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