Which Introductory Number Theory Book for High School?

[Kevin Licer]

Hello, I'm looking for an introductory number theory book for high school. Any recommendations are welcome. Thanks.

 

[David Lewis]

Dr. Keith Devlin at Stanford offers a free online course: https://www.coursera.org/course/maththink
After you sign up, it takes you to his video series. Click on Lecture 9A (Introduction to Number Theory).
The accompanying textbook is available on Amazon for about $10.

 

[Kevin Licer]

Thanks! I'll look into it, but I'd prefer studying from a book written in a somewhat self-study fashion. I'm not so big on watching videos.

 

[micromass]

What math do you know? What number theory do you want this to cover?

 

[Kevin Licer]

Well, I have an understanding of basic high school algebra and geometry, some rudimentary linear algebra (2x2, 3x3 and their properties, and solving system linear equations), basic trigonometry (we are going to start learning about the graph of trig functions soon) and etc. Well I want it to contain things like congruences, primes, multiplicative function, divisibility, euler's function and theorem and so on.

 

[micromass]

Would you be alright with learning some basic abstract algebra or discrete math?

 

[Kevin Licer]

Well, I suppose since I do want to learn the subject without any gaps, I mean if it is more beneficial, then why not?

 

[micromass]

The book by Pinter "A book on abstract algebra" can be found for very cheap, and it contains all the topics you listed. On the downside, you need to complete quite some bit of the book to reach those topics. But Pinter is really well-written and elementary (which can not be said from similar books on the same topic), and the topics found in Pinter are very useful if you want to go on in number theory.

If you want some help with self-studying Pinter, feel free to PM me!

 

[Kevin Licer]

I saw the book on amazon (the second version) and it does seem to take time to get to number theory. I would like to self-study it, but I don't know if I'm going to have that much time for it because the reason I'm looking for a book on number theory is that our school books are terrible and incomprehensible and we're studying the subject matter right at the moment. So that's why I wanted to self-study the material, to actually understand some of it. Even though the book definitely looks like a must have.

 

[mathwonk]

Here are a few free pages online that look accessible right away:

https://www.math.brown.edu/~jhs/frintch1ch6.pdfHere is another little book my son used successfully as a youngster. I don't know if it is as well written as pinter, but does get right to the number theory.

https://www.amazon.com/dp/048646931X/?tag=pfamazon01-20

 

[Kevin Licer]

Looks like I'm going to get the book by Dudley. Thanks to everyone for the suggestions, it was really helpful.