DS likes math-patterns (such as number-patterns/fractals)

[Osmosis Mom]

It is obvious there is a real interest there, but how to take him to the next level? He is a freshman, btw.

[In The Great White North]

Art of Problem Solving

http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=206

[Osmosis Mom]

Wow, nice book albeit very pricey. Ds would love this!

Thanks!

[Jane in NC]

Wow, nice book albeit very pricey. Ds would love this!

Thanks!

You also might want to look at some of the books in the online bookstore (https://www.maa.org/EBUSPPRO/) of the Mathematical Association of America. Their Anneli Lax series may have some appropriate titles.

Here is an idea: a good university library will have some of the MAA titles. Perhaps you can borrow a few? (Our nearest university only charges $15 per year for library privileges.)

[Osmosis Mom]

Hmm, it has never occurred to me (in all my years as a homeschooler) to get a university card. Guess I just assumed it would be off-limits. Perhaps I should take advantage of MIT being relatively nearby. Hmmm. Thanks, Jane!

[Kathy in Richmond]

Agreeing with the posters who recommended AoPS and MAA books!

A nice book to start with is

From Zero To Infinity (http://www.maa.org/reviews/ZerotoInfinity.html) by Constance Reid,

available in the MAA bookstore.

Has he read The Number Devil (http://www.amazon.com/Number-Devil-Mathematical-Adventure/dp/0805062998)? - easy reading, but full of big ideas.

How about The Joy of Mathematics (http://www.amazon.com/Joy-Mathematics-Discovering-All-Around/dp/0933174659)or other books by Theoni Pappas?

Someone gave me this little gem,

Fun with Mathematics (http://www.librarything.com/work/33349),

when I was in the fourth grade, and I never looked back...

hth,
~Kathy

[Janice H]

Good links and explorations here http://mathforum.org/workshops/usi/pascal/index.html

Lots of ways to use or relate mathematical situations to Pascal's triangle. See for example binomial theorem, probability, sequences, series, volume of a cube, options theory, and more. You could spend a long time just playing with the Pascal triangle pattern.

There's a lot more free stuff like this on the internet. Math geeks seem to be generous that way.

[Corraleno]

The Fractal Foundation website has all kinds of cool stuff, including a free download of the Xaos fractal-generating software:

http://fractalfoundation.org/

Jackie