Reddit reviews The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems

This is just a giant (one might even call it colossal) book of all the things that might make one love math.

Martin Gardner's The Colossal Book of Mathematics.

https://www.amazon.com/Colossal-Book-Mathematics-Paradoxes-Problems/dp/0393020231

Also look at the "frequently bought together" section on the Amazon listing. The Colossal Book of Short Puzzles and Problems is also a masterpiece. I hadn't seen My Best Mathematical and Logical Puzzles before, but now I'm getting it...

Professor Stewart's Cabinet of Mathematical Curiosities is also a lovely book of cool things in math.

https://www.amazon.com/Professor-Stewarts-Cabinet-Mathematical-Curiosities/dp/0465013023

In fact, I'd recommend all of Ian Stewart's books.

http://www.amazon.com/Colossal-Book-Mathematics-Paradoxes-Problems/dp/0393020231

Martin Gardner's Colossal Book of Mathematics. It has a lot of really cool recreational math that is accessible and engaging.

I recommend the following book for getting a good overview of modern mathematics: The Princeton Companion to Mathematics although it is a bit pricey (though less expensive than the average textbook). It is extremely well written, even if it doesn't necessarily hit all the details. It focuses more on an intuitive understanding of many modern mathematical concepts so that more formal and detailed treatments. The authors wrote the book to help math students get up to speed about various different fields of math as well as help working mathematicians better communicate across different disciplines.

Martin Gardeners books are good too. I specifically like The Colossal Book of Mathematics and The Colossal Book of Short Puzzles and Problems. His books tend to be very problem oriented rather than theory building, whereas the Princeton Companion is more expository. While Gardeners Colossal books are quite a bit shorter than the companion, I read them more slowly since I often stop to work on the problems he presents.

I think it helps to realize that there isn't any particular order to learning different kinds of math. High School and elementary schools set math up like there's a clear hierarchy to all the material, but that's not necessarily the case. For example, you don't need Calculus to do basic Graph Theory or elementary Set Theory.

There are lists of textbook recommendations on /r/math but these are the books I would recommend without knowing much about your current skills or interests.

Before you try to throw books at the problem, try to understand where your kids coming from. The public education system makes a huge effort to crush any enthusiasm a child may have for math; I know I didn't really like it when I was that old either. As a parent, you should read the essay A Mathematician's Lament, by Paul Lockhart. Math can be amazingly interesting and rewarding, but how would they know that? It is your job to show them, and this begins with you yourself becoming interested in and passionate about the subject.

Alright, now I'll start being helpful. Just promise me you'll read that essay.

Martin Gardner's books are kind of the classic books for getting kids into math. Check out the summaries and reviews of Aha! Gotcha, for example. You might also want to pick up The Colossal Book of Mathematics. Read it yourself and try to involve your kids in it as you do.

If they're more into hands-on stuff, check out How Round Is Your Circle?. It's all about building mathematical objects.

The Phantom Tollbooth is another great book, but not so mathematically oriented.

Basically, it's going to take a lot of work on your part, because you can't just hope they'll do it on their own. It's up to you to show them the wonder of mathematics.

Edit: I just realized they're not your kids, they're your niece and nephew. My mistake! Anyway, take from this what you will. Maybe you can convince the parents to get involved?

I will definitely be suggesting this book of Gardner's, thanks!