1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Number Theory Undergraduate Number Theory Book Recommendations

  1. Jun 23, 2017 #1
    Hi , everyone! This is my first post/thread/anything on this forum so first I apologise if I slip up or make any mistakes. Anyway, my question is about recommendations for textbooks for Undergraduate Number Theory. So far, I have studied Calculus 1-3 (including things like line integrals, Stoke's Theorem, divergence theorem, etc.) abstract algebra (undergraduate abstract algebra Serge Lang), some analysis and linear algebra. I have not really done much number theory before but know a few of the more obvious results (things like Chinese Remainder Theorem). I am actually planning to self-teach myself Number Theory so I am looking for a book ideally that has plenty of examples and exercises to cement my knowledge. So, do any of you have any recommendations or advice?

    Thank you

    (Also do you think given what I know so far I am prepared to tackle Number Theory?)
  2. jcsd
  3. Jun 23, 2017 #2
    Kenneth H. Rosen's Elementary Number Theory is a decent low level survey and introduction. It's nothing special, but it's serviceable, and the 5th edition and before are cheap used.
  4. Jun 25, 2017 #3
    Anyone else? (Thank you The Bill for the one above - how advanced would you say it is and would you say it is advanced enough for undergraduate level?)
  5. Jun 25, 2017 #4
    Rosen's book is aimed at undergraduate math students. At the university I went to, a class based on it would probably be mostly attended by second through fourth year students as an in-major elective. It has minimal prerequisites. If you're studying university level maths at all, you're ready for it.
  6. Jun 25, 2017 #5

    Wrichik Basu

    User Avatar
    Gold Member

    Problem Solving Strategies by Arthur Engel, Springer Publication.

    The book doesn't have much of theory but some of world's unsolved sums. :oldeek::oldsurprised:
  7. Jun 26, 2017 #6
    Since you have studied abstract algebra from Serge Lang. You may be able to forget about Rosen, and try a more challenging book. Maybe give Apostols number theory book a go.

    You can always supplement it with Rosen if it is too hard.
  8. Jun 28, 2017 #7
    @MidgetDwarf Thank you very much for your response and from what I have read the Apostles book is rated very highly. I do notice however that it is only analytic number theory. I was hoping for a number theory book that was both algebraic and analytic. Do you think I should buy a number theory book with both algebraic and analytic in one, or two separate books one for analytic number theory (e.g. the Apostols) and algebraic number theory (e.g. Lang)?
  9. Jun 28, 2017 #8


    User Avatar
    Science Advisor
    Homework Helper

    for starters i would suggest one more elementary than either algebraic or analytic number theory, say Elementary Number theory by Vanden Eynden. the point is that this book has few prerequisites.

    Algebraic number theory, say by Neukirch, tends to assume you know already Galois theory for example. and analytic number theory assumes complex analysis. So I think you seem ready for the more elementary approach. And I recommend it.

    after glancing at the book by apostol. it also seems excellent. i have found his writing vastly superior to that of Lang in general, i.e. more precise, correct, and understandable, although occasionanlly Lang is inspiring and useful. but apostol always considers the needs of his student audience and works hard to eliminate errors. Lang is brilliant but often seems just to wing it.

    a quick look at langs book reveals a high level of sophisticated algebraic prerequisites, such as local rings and dedekind domains, making it probably suitable for a second year graduate course.
    Last edited: Jun 29, 2017
  10. Jul 1, 2017 #9
    For algebraic number theory, I'd recommend James Milne's notes on the subject, available freely online. You can find them by googling.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted