The Art of Problem Solving books have caused me immeasurable misery. I tried Introduction to Counting and Probability and gave up after ten chapters. I tried Introduction to Geometry and gave up after eight chapters.
After the geometry fiasco, I decided to finally let go of AOPS. I just couldn’t learn from their books. Or so I thought.
This past year I decided to give them one more try. This time I picked up Introduction to Number Theory, and I can finally say that I completed an AOPS book.
When I did Counting and Probability and Geometry, there were two major problems I encountered. The first was that, like a super smart college professor, the book would begin to assume that the student already has some base knowledge. Granted in the middle of the book, the student should have some knowledge. But occasionally a really hard problem comes up and if it every facet of the problem was explained in the solution, instead of assuming that the student must already know, it would be possible to fix my mistake and move on. Unfortunately, that’s not how AOPS works.
The second major problem is that I constantly felt like the book was showing me tricks to solve the problem quicker without explaining the math behind the problem in the first place. This was infuriating. Like I threw the book across the room infuriating. When I tried to solve the problem logically, I would get it wrong and the solution would just say, “Oh, look here no need for math because there’s a shortcut. Of course, you can only understand this shortcut if you know the math necessary to solving this problem, but we’re not going to tell you what that is.”
Just, UGH!!! Why?
Thankfully though, Number Theory did not espouse these problems. I finished the whole book in one semester and enjoyed it immensely.
I think it was really important to learn the “counting” taught in this book because it strengthened my basic math, which makes it easier to approach complex problems. Also it presented numbers in a way that I might not have thought of before.
I think this book would’ve been even more beneficial if I had done it before algebra 1. I would definitely do it again. Introducttion to Number Theory is the one AOPS book I can wholeheartedly reccommend.