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

Beginner Books?

  1. Dec 29, 2004 #1
    Hi, I'm a high school senior in my first semester of Calculus, so my math is pretty limited at the moment. I was wondering if you guys could recommend any introductory number theory books that you think are about at my level. Any suggestions would be really appreciated. Also, sorry if I should've posted this in the book review sections. Thanks for your time.
  2. jcsd
  3. Dec 29, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I like Burton's Introductory Number Theory, but I think you'd do better reading the relevant chapters from a more general text like Hall & Knight's Higher Algebra.
  4. Dec 30, 2004 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    leveque fundamentals of number theory
  5. Dec 30, 2004 #4
    Wow thanks Matt :) Just called the bookstore and they have a copy. woohoo!

    They should reprint more math texts with recycled paper, or the governemnt should provide a subsidy or something.
  6. Jan 3, 2005 #5


    User Avatar
    Science Advisor
    Homework Helper

    the great andre weil wrote a book called "number theory for beginners" but it seems hard to locate a copy. i also recommend the disquisitiones of gauss.
  7. Jan 13, 2005 #6


    User Avatar

    Stopple's "A Primer of Analytic Number Theory" is a good introduction to analytic number theory for those without complex analysis. However, it would probably help to have a good background in elementary number theory before starting it.
  8. Jan 14, 2005 #7
    Here is a text, originally written in 1940 by Courant, "What is Mathematics?" I thought this was a truly great work that is definitively aimed at the beginner. I does not go through the usual song and dance in terms of pedantic definitions and exercises, but rather is intended to give the serious, inquiring student a chance to really think about the subject.

    It does get into quadratic residues and other number theory subjects. It has been a very popular work and you get it online, even a used copy. SO CHECK IT OUT!
  9. Jan 16, 2005 #8


    User Avatar
    Science Advisor
    Homework Helper

    courant and robbins is truly a great book, and at the price you cannot afford to be without one. check this out:

    Courant, Richard; Robbins, Herbert
    What Is Mathematics
    Cary, North Carolina, U.S.A.: Oxford Univ Press, 1978*Soft Cover. Very Good-/No Jacket. 8vo - over 7¾" - 9¾" tall. Moderate shelf wear to the outer extremities, w/ bumping to t/b spine, and tips. Modest rubbing/soiling to f/b. Tips have a slight curl to them. Heavy rubbing to the joints, and creasing to the spine. ISBN sticker on back wrap. Page black has a light wave to it. Hinge faintly tender, but binding is tight. Interior appears clean, and unmarked. Great copy!
    Bookseller Inventory #008799

    Price:*US$*8.98 (Convert Currency) Shipping:*Rates & Speed

    Bookseller:*TRMCOLLECTIBLES, PO Box 99960, Lakewood, WA, U.S.A., 98499

    compared to this, no textbook today is worth its price.
  10. Jan 21, 2005 #9
    You could try Pickover's Chaos in Wonderland, Mazes for the Mind, or especailly Keys to Infinity. Because you said introductary. See, those books do contain number theory, among other intresting and fun topics, without going too deep. If you are looking for some more hard-line number threory, try something else.
  11. Jan 22, 2005 #10
    I used Joseph H. Silverman's A Friendly Introduction to Number Theory, ISBN 0130309540, and liked it very much. The author makes it clear in the beginning that the book is written so as to be understandable to non-math majors, and he means it. As a non-math major, I appreciated this. If you look at the reviews on amazon, you'll see not everyone does. At any rate, I thought the material that he chose to include was presented very well, with a good balance of practical motivation and rigor. Only complaint: at 84 clams, it is a bit spendy. Check if they have it at the library.
  12. Jan 29, 2005 #11
    Studying Number Theory directly might not a good idea -- because some of the results can be easily derived from "Group Theory". You probably can try the book

    "Topics in Algebra" - I. N. Herstein

    And only read the first two chapters and apply the result
    on Number Theory.

    If you still can not make decision about what book to study,
    you might just browse


    to get some "feeling"...
  13. Jan 29, 2005 #12


    User Avatar
    Science Advisor
    Homework Helper

    on the other hand, it seems clear from reading gauss, that his results in number theory preceded and gave rise to the basic concepts of group theory. so number theory is in that sense a good place to begin to study groups.

    it is usually better pedagogically to study the earlier form of an idea than the later more general one.
  14. Jan 30, 2005 #13
    But mathwonk, I have a distinct memory of you saying that you were taught the analytical definition of the trigonometric functions (i.e as the solutions of certain differential equations, or perhaps e^(ix) := cos(x) + isin(x)), rather than the "older" definition that most people encounter first (i.e "sin(x) is the ratio of the opposite side and the hypotenuse of a right triangle"). You also said that you were better off for this.

    Doesn't that contradict what you just said?

    (Of course, it might not have been you that said this. If this is so, just ignore this post).
    Last edited: Jan 30, 2005
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook