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Number Theory Is Introduction to Theory of Numbers by Hardy good ?

  1. Sep 26, 2016 #1
    I am currently an undergraduate students at university and i am keen on learning some mathematics that is not taught in school and i have chosen number theory as my main topic . Recently I have picked number theory by Hardy but I found it is quite hard to understand sometimes as I have quite a lot of symbols and notation that I don't understand like (big O , little o , f=O(phi) means that mod(f) < A(phi) ) . Should I continue on learning this book or any other book recommendations which is more suitable for undergraduates with light knowledge on calculus and algebra?
  2. jcsd
  3. Sep 26, 2016 #2


    Staff: Mentor

    Here's some discussion on it:


    and they recommend:

    https://www.amazon.com/Classical-In...&qid=1474946672&sr=8-1&keywords=ireland+rosen by Ireland and Rosen

    although this is a graduate level text.

    Another one I found was this one by Prof of Mathematics William Stein of the Univ of Washington:


    while I can't vouch for these references personally the Stein book is freely downloadable and could get you started on your topic.

    @micromass, @Mark44 or @Krylov may have better references for undergrads.
    Last edited by a moderator: May 8, 2017
  4. Sep 27, 2016 #3


    Staff: Mentor

    The only book I have on number theory is one I got for a class in 1976, "Elements of Number Theory," by Anthony Petto frezzo and Donald Byrkit. That's the only number theory book I have. Amazon shows a 2nd edition of this book, and the one review it got was 5 stars.
  5. Sep 27, 2016 #4
    If you do not have strong background in calculus, then Hardy/Wright is definitely not a suitable book for you; in order to read it, you need to have a strong grasp of the advanced calculus and some knowledge from complex analysis. If you would like gentler books, then I have some suggestions:

    Elementary Number Theory by D. Burton
    Elementary Number Theory with Applications by T. Koshy
    Elementary Methods in Number Theory by M. Nathanson
    Introduction to Analytic Number Theory by T. Apostol

    If you did not yet mastered basic proof techniques, you can actually learn them with Burton and Koshy. They are very gentle books that will also teach and sharpen your proof skills.

    Nathanson is not quite gentle as it assumes you have elementary knowledge in the advanced calculus, but you can learn the necessary concepts as you read (he also teaches you some basics like Fourier analysis). He covers basics of elementary number theory, followed by good overview of the analytic number theory (mostly multiplicative). After reading his book, you can actually jump to his two-volume set in the additive number theory, which covers Goldbach Conjecture and Waring Theorem.

    Apostol is not quite gentle either but you could learn first few chapters well.
  6. Sep 27, 2016 #5
    No wonder I found it hard for me to read the Hardys book even just for the first few pages .I think I will give D .Burton a try , thanks anyway !
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