20050417, 23:02  #1 
May 2003
2×131 Posts 
Number Theory Textbook
I was wanting to learn more about prime numbers, particularly the Riemann hypothesis, and it has become apparent to me that my background in math is not enough at the moment. I was wondering if anyone could recommend a good number theory textbook and possibly other texts so I can expand my knowledge of math. I have taken a calculus course, but that was a while back.

20050417, 23:32  #2 
May 2004
2^{4}·5 Posts 
The link between prime numbers and the Riemann hypothesis lies in analytic number theory  indeed the Prime Number Theorem was first proved using complex analysis.
The only book I've read on this is T. Apostol, "Introduction to Analytic Number Theory" which contains the standard dose of elementary number theory, proves the PNT and discusses the Riemann Hypothesis (but not in a great deal of depth). The calculus course will help, some prior knowledge of complex analysis is helpful too. The book is very readable, insofar as such books ever are. Dave 
20050421, 04:17  #3  
Bronze Medalist
Jan 2004
Mumbai,India
2052_{10} Posts 
Number Theory Textbook
Quote:
It’s a long uphill climb from the theory of numbers to culmination with the Riemann hypothesis. If it will be any help to you I present a list of books in my collection which I can personally vouch for, although you have mentioned only one book. None of them requires a previous knowledge of number theory or the calculus except the last mentioned which requires some background of advanced calculus. This also deals with the Riemann Hypothesis and the zeta function. I have put my list in order of difficulty starting with the elementary first. 1)’Invitation to Number Theory’ by Oystein Ore. 2)’An adventurers guide to Number Theory’ by Richard Friedberg 3)’Number Theory and its History’ by Oystein Ore [good for self study] 4)’An introduction to the Theory of Numbers’ by Ivan Niven and Herbert S. Zuckerman (text book type with many problems) If you can get this far consider that you have reached a good level. 5) ‘Introduction to Analytic Number Theory’ By Tom M. Apostol ( knowledge of Calculus required) One must remember that Number Theory is one of the most difficult branches of Mathematics and even Gauss the founder of modern number theory called it the ‘Queen of maths’ and the ‘Higher Arithmetic’.And Euclid said 'There is no royal road to mathematics' If you want to cut down the ground work and go straight on to RH then a suitable introduction to primes and the RH is a book for the layman ‘The Music of the Primes – Searching to solve the Greatest Mystery in Mathematics’ by Marcus du Sautoy. This book is a must for any mathematician worth his salt. Mally 

20050519, 20:21  #4  
"Jason Goatcher"
Mar 2005
3×7×167 Posts 
Quote:
Everything but the "calculus" book, unless it's cheap. 

20050828, 12:42  #5  
Nov 2004
India
5 Posts 
you can look.....
Quote:
WHAT IS MATHEMATICS By: Curant And Robins I forgot the name of the publisher but the name of the book and authers are nice i hope you may reinforce your mathematical Ideas. it is little bit philosophical THANKING YOU ASIF AHMAD 

20050828, 16:04  #6  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
Number Theory Textbook
Quote:
The publishers are Oxford Univ. Press. ISBN 0195025172 pbk Its an excellent book and Im surprised how I didnt recommend it earlier on. Mally 

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