# When did your DC do AoPS Number Theory?

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My son is taking the AoPS pre-alg class right now. I have been doing poorly on the number theory problems at AoPS Alcumus. :blushing: So I bought the text and I just starting working through it myself. The beginning is very easy but it does ramp up. I'm not sure now where in the sequence Number Theory goes? My son could do parts of this now but I was thinking it was after AoPS Intro to Alg1? Where in the sequence did your DC do this book? What about Counting and Probability? If there is a thread addressing my question, feel free to just point me in that direction as I have shamefully, not done a search prior to asking. :lol:

Capt Uhura

Edited by Capt_Uhura
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My daughter greatly enjoyed the Intro to Number Theory course at age 13 (grade 8). Now, that was back in the days before AoPS had textbooks, so she took it as an online class, and it moved pretty fast. She'd already taken algebra and geometry at home with me at that point using a combination of Jacobs and Singapore NEM (AoPS didn't have algebra or geometry classes or books then!).

Number theory is one of those courses that only has a little bit of algebra as a prerequisite, but takes a mature sort of thinking process. The problems do start out easy (most kids learn about LCM, GCF, prime factors, different bases, etc, regardless of which curriculum you choose), but concepts such as modular arithmetic (which has different 'rules' from regular arithmetic), Diophantine equations, linear congruences, Euler's theorem, and so on, take lots of time and effort to think through. I find it deep and challenging in a theoretical sense; it's one area of math where I can always learn something new by playing with it some more.

Counting and probability is another subject that's quite different from algebra. Instead of set procedures for solving problems, you sometimes have to be really creative to come up with solutions. There is a constant search for patterns, and a sense of experimentation as you try to come up with a method that works.

I'm probably not making myself very clear here.:glare: But what I'm trying to say is that while neither of these courses requires more than some algebra one, they both require different ways of looking at math.

There is no real sequence of courses that must be followed. You can insert number theory or counting and probability at any point at which your student (or yourself!) feels comfortable with basic algebra. Some kids will be more suited to this "discrete" math and take off with it early. Some of us (myself included) won't even see this kind of math before college or even later.

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Thanks Kathy! I've been reading your older posts about your DCs math/science sequence at the high school board. Thank you so much for posting those! My boys are similar to your DD, I think, they love science but also humanities. It's hard to figure out where to focus. DH and I are both scientists so you think this would be easy lol but time does seem to get away from me especially since right now in 6th grade we're focusing on writing. DS is 11 in 6th grade. He's really enjoying the AoPS pre-alg class. He absolutely hated MM and somewhere along the way his love of math faded. I'm trying to get that back. I see that spark coming back w/ the AoPS methodology.

OH I was even worse w/ Counting and Probability problems at Alcumus than I was with Number theory. :D I'll work through that one at some point. I was good in math, enjoyed algebra, really enjoyed Calculus but I have so many light bulb moments when doing AoPS!!!!

So from your post, you'd recommend NT and C&P after AoPS Intro to Alg? I think someone here did half of NT and when it got tough moved into AoPS Intro to Alg and will later return to NT. The poster has black hair....her username is escaping me. :lol:

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I think someone here did half of NT and when it got tough moved into AoPS Intro to Alg and will later return to NT. The poster has black hair....her username is escaping me. :lol:

at first I wondered whether you were thinking of this thread, but they were using C&P

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Thanks Kathy! I've been reading your older posts about your DCs math/science sequence at the high school board. Thank you so much for posting those! My boys are similar to your DD, I think, they love science but also humanities. It's hard to figure out where to focus. DH and I are both scientists so you think this would be easy lol but time does seem to get away from me especially since right now in 6th grade we're focusing on writing. DS is 11 in 6th grade. He's really enjoying the AoPS pre-alg class. He absolutely hated MM and somewhere along the way his love of math faded. I'm trying to get that back. I see that spark coming back w/ the AoPS methodology.

You're welcome. Hey, it was difficult for me to figure out, too, even as a mathematician. My dd liked Singapore math, but it was true love when she was introduced to AoPS.:001_smile: Btw, she had writing-focused years along the way, too. It's tricky when their interests are so broad; she still can't choose what she likes best.

OH I was even worse w/ Counting and Probability problems at Alcumus than I was with Number theory. :D I'll work through that one at some point. I was good in math, enjoyed algebra, really enjoyed Calculus but I have so many light bulb moments when doing AoPS!!!!

I have them, too, believe me. I was trained as an applied mathematician studying engineering physics; i.e., mostly straight calculus/analysis track math. I've learned most of what I know about number theory and counting/probability along with my kids. I didn't know what I was missing all those years - it's so much fun!

So from your post, you'd recommend NT and C&P after AoPS Intro to Alg? I think someone here did half of NT and when it got tough moved into AoPS Intro to Alg and will later return to NT. The poster has black hair....her username is escaping me. :lol:

Ooh, I remember that thread, too; in fact, I think that I posted on it. She had pretty good luck doing some of the NT book over the summer and then moved into algebra the next year. Let me think...I think it might have been matroyshka? Are these the threads (here and here) that you're remembering? (you're in them, too!)

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Ah yes, it was Matroyshka!!!! THanks! That's a tough name to roll off the tongue but her beautiful face any sunny countenance (yes, we're doing MCT CE :lol:) remains in my brain.

Oh no doubt I posted in that thread. I was posting in a thread at the HS board about chem texts when I scrolled up and found that I had already asked the same question when the thread was first posted. Ha Ha Ha.

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I'm not sure whether DS could have done it earlier or not - possibly... As Kathy says, it's not the other math that's the prerequisite, but the serious thought. I hesitate to say "maturity" because it sounds like Piaget and age cutoffs... but more like being willing to hack at a problem for a bit and to be able to "see" the elegant solution without brute forcing it all the way through. And to apply one idea to another situation that has no obvious similarity...

Mathematically, DS had done Algebra 1, most of Algebra 2 (in bits and pieces along the way), Geometry, and Statistics. Other than the statistics it was mostly Singapore NEM (books 1 and 2, parts of book 3). Also MathCounts, Math Olympiad (MOEMS), and AMC 8 and 10 exams. So quite a bit of challenging math of different sorts.

One thing I wanted to throw in... although I wouldn't recommend it in general, there was a distinct benefit to doing Counting & Probability simultaneously with Number Theory. DS did them both as online classes (his first AoPS experience) and that was an intense workload... but they complement each other extremely well. Ideas that came up in one were applicable to the other later (in both directions), and some of the beauty of one would only become really apparent when it was applied to the other. I can't think of examples off the top of my head, but there were times when a technique seemed a little "parlor trick"-y until a week or two later when you realize that the other class could use it to solve something, and the lightbulb went off that these things were actually incredibly powerful tools. But... really really intense to do both classes together.

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Erica - Thank you so much for your feedback! I will see how i do with it but it's nice to know there is something down the road for DS!!!

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