Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Looking for a good number theory book(

  1. Aug 20, 2011 #1
    Here is my situation,

    In short I want a number theory book that doesn't assume knowledge of previous number theory but assumes all knowledge of mathematics. I have been knowing multivariable calculus since about 4 years(learned it from Thomas 4th edition(this book was not like the later watered down editions of his book)). From various books I picked up from my grandfather(quantum chemist working on ligand field theory) I learned differential equations well(Ordinary, Partial, Nonlinear especially from strogatz)

    WARNING: WHAT FOLLOWS IS LONG. IF YOU DON'T WANT TO READ THE REST YOU CAN SKIP IT.(though if you are feeling helpful or heroic you can read on

    I am going into 11th grade. I know my mathematics very well. I recently finished strogatz nonlinear dynamics, landau and liftgarbagez mechanics, landau and liftgarbagez quantum mechanics. So I basically know all my mathematics necessary for an applied sense. But i have always wanted to know number theory well. The problem is that most number theory books I know assume that you don't know calculus and therefore most books complicate simple results that can be easily proved from a sound knowledge of mathematics.

    I don't really want hardy's book on number theory because it is not quite systematic(almost as a bunch of snatches of number theory put together).

    I have considerable mathematical maturity. Please take this into account while helping me choose a suitable book.
  2. jcsd
  3. Aug 20, 2011 #2


    User Avatar
    Gold Member

    Apostol - Introduction To Analytic Number Theory is well organized and oriented as the title suggests towards the analytic side of number theory which might suit your interests and background. OTOH Ireland and Rosen - A Classical Introduction to Modern Number Theory is more on the algebraic side. I fondly recall reading the precursor to Ireland and Rosen shortly after it was published one stormy weekend on Martha's Vineyard. And Niven and Zuckerman - An introduction to the theory of numbers, 5ed attempts a middle of the road treatment at the upper undergraduate level.
    Last edited: Aug 20, 2011
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook