# AoPS or EPGY number theory?

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Does anyone know how EPGY's number theory class stacks up to AoPS's intermediate number theory class?

Or based on the course descriptions here, could you weigh in on which one might be a better bet for a kid who is at about the end of AoPS's Intro to NT level and will have about 4-5 months of algebra 2/trig (with very, very minimal calculus, just introductory material that might be covered in the first chapter of a good calc text) behind him?

http://epgy.stanford.edu/courses/math/M152/

http://www.artofproblemsolving.com/School/classlist.php#cd_intermediate:numbertheory (to answer the "do you need this?" question, kiddo says both courses have the "yes, I need this, it's so cool!" factor)

He has dabbled frequently in "number theory using algebraic techniques, multiplicative functions, modular arithmetic" (from the AoPS description) but not so much in Fermat's/Euler's Theorem, and primitive roots.

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Dd took all three courses! Good stuff, all. Number theory really is one subject whose prerequisite is just 'mathematical maturity.'  There isn't a need for any calculus or geometry or whatever first, just basic algebra. But though it can seem easy, it's one of the more devilish math subjects once you start in on Euler's and Fermat's theorems, Diophantine equations, primitive roots, quadratic residues, etc...but SO beautiful, too!

Dd took the classes in the following order:

AoPS Intro Number Theory, AoPS Intermediate Number Theory, and EPGY college number theory. They built nicely upon each other in this order, and she was happy with this plan at the end.

When dd took the AoPS intermediate course, it was seminar style (classes & message boards, but no graded homework) & only 8 weeks long. Now it's a regular course (so I assume that means graded hw) & they've extended it to 12 weeks with extra topics at the end.

The AoPS class has no textbook, but lots of hard problem solving (as always!). EPGY has a college level text (Stark), required lessons and quizzes on the computer, regular homework sets (dd wrote them up in LaTeX) which must be turned in for a grade, and a lengthy take-home midterm and final.

Dd definitely put more time into the EPGY course, and it took just over a full semester in high school. While it covered some of the same topics as AoPS, it went further in depth and also covered material that was brand new to her. But AoPS is no cakewalk...all of their online classes have VERY challenging homework problems (more so than the textbooks even)!

EPGY is undergoing some changes this year (I just answered a long parent survey about it; they're collecting data as they attempt to determine what to change). So I'd be tempted to hold off and do that one later on. There were some kinks when dd took it, and hopefully they'll be resolved.  I'd suggest AoPS first. Since there isn't a book & since you can drop before the third class w/o penalty, you wouldn't be out anything if it turns out not to be a good fit.

have fun!

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Kathy, what a lovely, detailed review. Thank you!

With EPGY, I am trying to gauge how much time it will take. My worry is that he is not a speed demon. He will take a long time to really think through the problems. So was it difficult for your DD to finish the EPGY class in a semester? If we wait and do AoPS first he should be older too so that might work out best. I don't mind if kiddo takes longer, just trying to work out the \$\$ issue. They charge another quarter's worth each time we extend right?

Thanks Kathy, will present your thoughts to DS and DH!

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EPGY gives an estimate of 5 to 10 hours per week, which we found to be accurate. It parallels an actual Stanford math class, except that EPGY kids get 24 weeks to accomplish what the college kids do in 12 weeks. Dd was a busy kid that year with plenty of extracurriculars that required travel, so she worked on the course more some weeks than others. It ended up taking her the full time period to finish.

When dd took this, her info sheet said that she was required to finish in 24 weeks, or else she'd be withdrawn from the class.  I'd recommend checking to see whether that rule still applies. If they are more flexible about the time now, I'd still expect them to charge another full tuition for any addition 24 week period - no fun!!

The homework and two exams were definitely at a college level, and took time to reason out. No plug & chug problems, just mind benders for the most part, and plenty of proofs. The software took a good chunk of time, too, and there's no way to short cut that part if you prefer to read the text instead --quizzes are built into the software & must be passed in order to move on. The homework write ups can be tedious & time consuming to get into good shape, too. You need to budget time for that, at whatever level your student's output speed is.

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DS will be taking AoPS intermediate Number Theory from Dec-March.  Yours and mine could be in the same class!

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EPGY gives an estimate of 5 to 10 hours per week, which we found to be accurate. It parallels an actual Stanford math class, except that EPGY kids get 24 weeks to accomplish what the college kids do in 12 weeks. Dd was a busy kid that year with plenty of extracurriculars that required travel, so she worked on the course more some weeks than others. It ended up taking her the full time period to finish.

When dd took this, her info sheet said that she was required to finish in 24 weeks, or else she'd be withdrawn from the class.  I'd recommend checking to see whether that rule still applies. If they are more flexible about the time now, I'd still expect them to charge another full tuition for any addition 24 week period - no fun!!

The homework and two exams were definitely at a college level, and took time to reason out. No plug & chug problems, just mind benders for the most part, and plenty of proofs. The software took a good chunk of time, too, and there's no way to short cut that part if you prefer to read the text instead --quizzes are built into the software & must be passed in order to move on. The homework write ups can be tedious & time consuming to get into good shape, too. You need to budget time for that, at whatever level your student's output speed is.

Kudos to your DD for working so hard Kathy. Awesome! Aiyee, I don't see kiddo having this level of stamina yet...but he really loves the subject and wants a class and his tutor is not into number theory as much as kiddo is. Gotta mull over this some more. Thank you Kathy. Really, really helpful info.

DS will be taking AoPS intermediate Number Theory from Dec-March.  Yours and mine could be in the same class!

Ruth, that would be so cool! I might have to set more time aside for him if we sign up. So many other things on his plate right now. Off to think some more about this.

Thank you both!

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