Introductory Number Theory Books for High School Seniors

[Malex]

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.

 

[Gokul43201]

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.

 

[matt grime]

leveque fundamentals of number theory

 

[gazzo]

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.

 

[mathwonk]

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.

 

[CTS]

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.

 

[robert Ihnot]

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!

 

[mathwonk]

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.

 

[The Divine Zephyr]

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 interesting and fun topics, without going too deep. If you are looking for some more hard-line number threory, try something else.

 

[PBRMEASAP]

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.

 

[oookhc]

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

http://www.ScienceOxygen.com/math.html
http://planetMath.org/

to get some "feeling"...

 

[mathwonk]

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.

 

[Muzza]

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).