Okay, I am considering signing up DS for one of the math courses via AOPS. It will probably be Counting & Probability due to the timing - he needs math curriculum for the last quarter of school this year. However, he may balk at the instructional time as it takes an hour and a half one day a week, during his usual free time. DS may be more amenable to just indepenedently studying the book along with practicing problems on Alcumus, particularly if I can confirm that his once a week math instructor will provide any needed instructions. If this doesn't meet with the school's approval, I can easily provide the instruction myself but in smaller chunks (certainly not 90 minutes at a time once a week).

Anyhow, there I was at the AOPS website to order the books. Then I decided I wanted both the Counting & Probability set and the Number Theory Set so DS will have more of a choice. Then I started thinking maybe I should get the Geometry set as a reference while I am at it. Then I found these sample pages in the Geometry book and I am not so sure. Okay, I will buy the Counting & Probability as well as Number Theory sets since these will fit our purposes.

What I mean is that I am not sure about the Geometry set. DS will take Geometry next year and he will be using whatever book the school provides - I don't know which one as I haven't look into it yet. I am rambling but I do have a question specifically about the Geometry book. I notices from the two pages that it is presented in very simple language, almost geared toward a younger audience, if that makes sense? It is very different from other Geomtery texts that I have seen. However, it is only 2 pages so perhaps that is not enough to make a judgment? I seem to recall very high opinions about the Geometry course itself, but what about the book? Is it a good comprehensive text? Will using this text cause any difficulties? Alcumus itself provides sophisticated problems so my inclination is to assume the book would be very good. Anyone who have actually used the text or can compare to other decent textbooks?

I can just buy the other two sets first, but I figure I might as well buy all three sets at the same time if I am going to do so.

I have not seen the AoPS geometry book. However, the tone of the books I do have is conversational, which might be what you're sensing when you say that the language is simple. I do know that the geometry book has a reputation for being the most difficult of the intro series.

It's an excellent book - the only reason to hesitate would be if you prefer to start with one AOPS book to see how your DS got on. In mathematics we are always striving to make things more understandable, so simple language is a virtue! There's no lack of content.

PS the excerpts here have more like 14 pages than 2 - if it was some other excerpt you found, maybe this will help?
http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:geometry

I think that the conversational tone is part of it. I can almost picture someone trying to teach a youngish kid in that manner. It may also be that the topic was very simple as well.

That's what I was trying to determine - that it is in fact an excellent book with comprehensive content. You are right, simple language can be a virtue as long as it communicates just as much and as well. I guess my concern is based on some of the "Algebra" media aimed at younger students that do not actually provide comphrehensive content.

If I remember correctly, you are one of the mathematicians so that is a strong endorsement for the book. I will go ahead and order it with the others. Thanks.

I just got the Counting & Probability and it does starts very simple as well but in this programs defense if one wants to teach such subjects correctly it's best to start thinking in the correct way at the beginning. Counting can seem deceptively simple but it really is a very complex problem mathematically. That is probably what is going on with the Geometry book.

The books do seem to have a 'Conversational' tone and that is why I perceive them as likely to work with young mathematicians. I have yet to see what my teen thinks about them yet. I don't as of yet have a good idea how they work.

I can only speak about the pre-algebra book but I love the conversational tone as it delivers rigour by example. I see this as training for mastery as opposed to mimicry. So far, so good. I am enjoying it myself too.

Well, I ordered all three sets but will be using the Counting & Probability one unless DS decides he would rather do number theory. It would be interesting to see DS' take on it (although he isn't a teen).

That's good to know. Since the Geometry one will likely only be used as a reference and/or source of challenging problems, I didn't want DS to have a problem transitioning between texts.

My son is 11 and is finishing chapter 12 of 15 in Number Theory. I also bought the other two sets. He will begin Counting next and then Geometry.

Number Theory started pretty easy for him but as he got into it he was definitely challenged. He covered a 2+ chapters a week at first but it has slowed down now to one chapter per week.

From a brief glance at the other sets I think they will challenge him too.

I just got the books. I didn't realize that the Counting & Probability and the Number Theory books are so thin although I supposed it makes sense since the course is only a couple of months long.

As for the challenge issue, I figured that we would be safe since DS can always do the Alcumus problems set at the difficult levels even if the books turn out easier than I expected. In any event, the books would be a good reference.