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Old 2005-04-21, 04:17   #3
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Jan 2004

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Thumbs up Number Theory Textbook

Originally Posted by ThomRuley
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.

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.
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