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A Primer of Analytic Number Theory: From Pythagoras to Riemann | 
 enlarge | Author: Jeffrey Stopple
Publisher: Cambridge University Press
Category: Book
List Price: $44.99
Buy New: $40.49
You Save: $4.50 (10%)
New (1) Used (9) from $30.82
Rating:  3 reviews
Sales Rank: 674536
Media: Paperback
Pages: 398
Number Of Items: 1
Shipping Weight (lbs): 1.2
Dimensions (in): 8.8 x 5.9 x 1
ISBN: 0521012538
Dewey Decimal Number: 512.7
EAN: 9780521012539
Publication Date: June 23, 2003
Availability: Usually ships in 1 to 3 weeks
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Product Description
This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. Jeffrey Stopple 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. The culmination 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.
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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| Customer Reviews:
A great bridge to analytic number theory July 19, 2005
D. Hinkel (Boise)
7 out of 8 found this review helpful
There seems to be a huge gap between the mathematical background required to understand a book on elementary number theory and that required to understand most books dealing with analytic number theory. This book assumes no familiarity with complex variables. The writing feels a bit like Silverman's "Friendly Introduction to Number Theory" and Derbyshire's "Prime Obsession." Stopple includes plenty of experiments for Mathematica and Maple. I think this could be a useful textbook for an undergraduate number theory course. The last few chapters include elliptic curves (mention is made of their L-functions and the Birch and Swinnerton-Dyer conjecture) and binary quadratic forms. I recommend this book to anyone who can read (and for those who can't, this book is good motivation to become literate).
One of my favorite math books June 23, 2007
D. Hollowood (Danville, CA United States)
3 out of 3 found this review helpful
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.
For the senior math undergraduate February 3, 2006
NumTheorWannaBe
5 out of 5 found this review helpful
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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