Solving Math Challenges with Art of Problem Solving

[Opus_723]

I'm tutoring some high school kids right now, but I don't actually own any high-school level math books. We've just been working out of the books they use at school. But I'm getting very irritated with their books. One kid has this geometry book that makes me want to pull my hair out. It's trying so hard to be informal that the kids aren't even aware of what the subject of the chapter is. So I'd like to purchase some books on my own. They'd be a good investment for my tutoring, and ideally I'd like something that could challenge good students. Heck, if I could learn something from it, even better.

I was looking at the Art of Problem Solving series, which is apparently intended for competition level math, but they have a full curriculum, so I figured it would have the basics as well as challenging problems. Has anyone else heard of this series? Any good? If not, what should I look at instead?

 

[Bipolarity]

The AoPS series is mostly geared towards children who aim to compete at the Olympiad level (AMC,AIME,USAMO,IMO). It covers many theorems which ordinary curricula do not cover, which can make everything more time consuming. For instance, Ptolemy's theorem was not taught in my geometry class, but it is present in one of the AoPS books. So use it at your own discretion.

BiP

 

[genericusrnme]

I think you'd be better of just writing your own textbook to use yourself, that's what I did the last time I did any tutoring.

 

[mathwonk]

AoPS is a good geometry book. Euclid is even better.

 

[pascal12]

As Bipolarity stated, these books are meant for Olympiad level and would not be suitable for tutoring according to a high school curriculum, as they only cover the basics briefly and would likely frustrate you even more. I believe they has some excerpts on their website if you would like to look.
If your purpose was to challenge yourself or good students (at the level that would not need tutoring anyway), then they are definitely a good read. I used these books myself in high school for preparing for these competitions, and even after finishing calculus, going through these books were still challenging. So they are definitely not for a typical high school student.

 

[Opus_723]

Good to know. I was hoping they'd cover all the basics and then have some extra material and challenging problems for those that want it. But if they're mostly geared toward advanced students, I suppose they won't do my kids a lot of good.

 

[chiro]

There are specific examples that relate to high-school level math in George Polya's "How to Solve It", which although is an old book, has some relevant information regarding how even problems at a high school level can be analyzed and solved systematically (a form of heuristics).

I don't know about buying this book, but if you can pick it up from a library somewhere and take a read of it (even if you can't borrow, you should be able to at least get if off the shelf), then you can decide whether it has anything of value or not for yourself.

 

[Infinitum]

Polya's book is one of my favorites, but its totally based on 'how' to approach various problems, and not learning much content in the subject itself(like theorems etc). You can take a sneak peak into the contents and some more over here,

https://www.amazon.com/dp/069111966X/?tag=pfamazon01-20