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Would it be bad for a prospective Computer Science major to skip calculus? DS's plan all along has been to take calculus next fall but he just realized that AOPS has an Intermediate Number Theory class and really wants to take that. He says he needs it for his actual programs that he's working on. To make a full credit, he'd also take Intermediate Counting and Probability. 

He took Algebra and Intro Number Theory/Counting in middle school, and geometry, Alg 2, and Precal in HS so far. I'm concerned that admissions people won't understand number theory on a transcript and that it will look less impressive. I'm also concerned that he will have a large gap between taking Precal and Calculus if he spends a year doing other math before taking it as a freshman. 

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13 minutes ago, square_25 said:

If he wants computer science, I would say that the intermediate number theory and counting classes are going to be just as useful as calculus. He'll want calculus eventually, though, I think. 

Is he getting grade reports for his AoPS classes? If he gets a good grade report from the class, I think that would be quite meaningful on a transcript. 

Thanks for that. I really had no clue but he's convinced that number theory is more important and that calculus will always be there. How hard would it be to jump into intermediate number theory when intro was 4 years ago? 

He didn't get grade reports for his classes in middle school. I mean maybe he did? I didn't really look or pay attention much because I wasn't putting them on a transcript. Do you have to do anything different when you sign up for an online class to get a grade? His other HS classes were taken at public school.

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2 hours ago, Paige said:

Would it be bad for a prospective Computer Science major to skip calculus? DS's plan all along has been to take calculus next fall but he just realized that AOPS has an Intermediate Number Theory class and really wants to take that. He says he needs it for his actual programs that he's working on. 

. I'm also concerned that he will have a large gap between taking Precal and Calculus if he spends a year doing other math before taking it as a freshman. 

1) no idea about how admissions would think since both my kids wants to try to finish all the community college requirements for computer science to get an associate before graduating high school. So no BTDT experience 

2) DS14 took precalculus, AP Statistics then AP Calculus BC. So he had a year gap between precalculus and calculus. He had to review and ask DS15 for pointers. He did AP calculus BC as a summer intensive last summer and took the AP exam in May. 

3) DS15 took the AoPS  intermediate number theory class since there is no textbook to self study. I do think the class comes in useful as a foundation for discrete math (computer science requirement) later. 

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Does he have time in his schedule to take both simultaneously?  (Just offering that as a possibility since sometimes the idea of taking 2 courses in the same subject area gets overlooked as an option.  My kids have done it quite a bit and people often seem perplexed that they could do that.  😉 )  He could take AoPS's NT and then something like Thinkwell cal so that both don't have the same level of time commitment.

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4 hours ago, 8FillTheHeart said:

Does he have time in his schedule to take both simultaneously?  (Just offering that as a possibility since sometimes the idea of taking 2 courses in the same subject area gets overlooked as an option.  My kids have done it quite a bit and people often seem perplexed that they could do that.  😉 )  He could take AoPS's NT and then something like Thinkwell cal so that both don't have the same level of time commitment.

I asked him if he wanted to do that but he really likes AOPS and wants to stay with it. I think taking both at the same time would be far too time consuming.

1 hour ago, square_25 said:

That’s a really good solution. Especially since I’m not a huge fan of the AoPS calculus class.

Can you tell me why you don't like the calculus class? I'd be happy to talk him out of it! One draw for aops classes is that they are text based chats instead of videos.

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31 minutes ago, square_25 said:

It goes REALLY quickly. And as usual, they try to dig deep, but there's so much there that digging deep sometimes just means you don't get enough practice. 

I taught the class a little while ago and my impression was that a lot of kids were riding on having seen the ideas before, because they had taken the class at school. I might recommend at least reading over a basic calculus textbook and making some headway first before doing AoPS. 


how would you compare difficulty if AoPS calculus to Intermediate NT? 

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From a purely academic standpoint, it is no problem to skip calculus in high school.  You just take it in college.

But from a college admissions perspective, if he plans to apply to competitive colleges/programs, not having calculus in high school may put him at a disadvantage.

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15 minutes ago, EKS said:

From a purely academic standpoint, it is no problem to skip calculus in high school.  You just take it in college.

But from a college admissions perspective, if he plans to apply to competitive colleges/programs, not having calculus in high school may put him at a disadvantage.

Ugh. That's what I was thinking. IMO, the classes he wants to take are no bunny classes like consumer math or even most statistics, but I doubt the people looking at applications will all understand it. I think it will be as difficult as the average calculus class. He doesn't plan to attend especially selective schools, however- at least not as an undergrad. He wants to stay nearby where he has a good internship lined up because for what he wants fancy degrees don't add enough value to justify the expense, but the connections he'll make with the internship would be extremely valuable. 

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2 hours ago, EKS said:

From a purely academic standpoint, it is no problem to skip calculus in high school.  You just take it in college.

But from a college admissions perspective, if he plans to apply to competitive colleges/programs, not having calculus in high school may put him at a disadvantage.

My oldest son just graduated (woo hoo!) and applied as a CS major this last year. CS is INSANELY competitive nowadays. My dh and I were both CS majors years ago, and we were really surprised at just how many people apply for CS now. It's had large popularity spike which results in a lot more competition for space in the various programs. 

My ds did dual enrollment Calculus I and Calculus II and then took the Calculus BC AP exam. (We were big on covering all the bases we could through both DE coursework and AP/standardized testing where possible to "validate" his homeschool grades because he applied to very competitive programs). In looking at the stats of kids accepted to various programs (private schools as well as state schools), I think calculus was taken almost universally. Lots of kids, in fact, went on to take linear algebra and multivariable calculus and other advanced math courses beyond calculus I and II. 

I used to think that taking calculus was more just to "check a box" and "show rigor," but my son has actually used his calculus A LOT in his CS coursework. Machine Learning classes and AI applications rely HEAVILY on calculus. That wasn't the case back in my day, so I kind of "pooh poohed" the utility of calculus for CS, but in modern applications it can be pretty essential, depending on what you want to study. ML and AI are hot subfields at the moment. 

I would think, based on the extreme competitiveness of the major, that not having calculus at all when it could have been taken (kids at schools where it isn't offered would be exempt from this expectation to some degree) might be a red flag for admissions. The course you are looking at may indeed be more rigorous and awesome, but I wonder how many admissions officers would look into your course descriptions enough to figure it out. Even if they do, they really probably want to see calculus because it's what they are familiar with to check the "math rigor" box in their heads. It's tough when they are sorting thousands of apps!

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2 hours ago, Paige said:

Ugh. That's what I was thinking. IMO, the classes he wants to take are no bunny classes like consumer math or even most statistics, but I doubt the people looking at applications will all understand it. I think it will be as difficult as the average calculus class. He doesn't plan to attend especially selective schools, however- at least not as an undergrad. He wants to stay nearby where he has a good internship lined up because for what he wants fancy degrees don't add enough value to justify the expense, but the connections he'll make with the internship would be extremely valuable. 

I just saw this. I don't know how many schools are nearby that you are considering, but having a narrowed down list will definitely make it easier for you to see what admissions for CS at those specific schools looks like. If his overall stats look good in comparison to the average for these schools and you feel that those are also a good financial safety, then you can probably disregard my calculus advice (lol) and just take whatever math he wants. My advice was more based on the overall competitive admissions process assuming big state schools or more competitive private schools. We didn't have a narrowed down list (we were all over the map!), so we tried to check lots of different boxes for different schools. This year really was a shock for our family about how state schools (we always kind of thought these were "safe") have become so competitive with regards to admission. I guess I'm getting old! 🤣

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There are several issues here. The first, mentioned in the OP, is the concern the OP has if there's a large gap in time, between the end of Pre Calc and the beginning of a Calc course. My DD had Pre Calc in high school and then based on her ACT Math score she placed into Calc 2. But the first semester, she wasn't able to get into Calc 2, so she took it the 2nd semester.  After the first Calc 2 class, she reduced the hours she was working for Work-Study by 50%   She did very well, finishing Calc 2 with an "A-", but I am certain she had to work very hard to do that. It is normal that if one does not use the material, one is going to forget some of the material...

I believe/suspect that if he had Calc on his transcript that might possibly help with Admissions.

I believe that his Math placement in university will depend upon his SAT Math score or his ACT Math score or some other qualifier, including possibly a Math Placement exam given by the Math or Engineering school in the university.

If the school my DD is in, which is NOT a STEM school, is typical of other state Flagships, yes, the demand for seats in C.S. is tremendous.

I believe that he should take Calculus in the university he wants to get a B.S.C.S. from. They will teach it the way they want it taught.

Good luck to him!

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9 hours ago, EKS said:

 

But from a college admissions perspective, if he plans to apply to competitive colleges/programs, not having calculus in high school may put him at a disadvantage.

Do you think it's important to have *proof* of calc by the time one applies? My DS as planned will have a Calc 1 (of 3) community college grade, and would be taking AP Calc BC (but, no score obv). 

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26 minutes ago, madteaparty said:

Do you think it's important to have *proof* of calc by the time one applies? My DS as planned will have a Calc 1 (of 3) community college grade, and would be taking AP Calc BC (but, no score obv). 

Many students take calculus during their senior year, so they don't have "proof" of calc until their final grades come in. As long as you are showing the calculus class on the transcript, you are fine. During the college admissions process, you submit first semester grades when they are available. You also have a list of spring semester courses on the transcript, so admissions officers know what classes are taken during the whole senior year.  

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22 minutes ago, madteaparty said:

Do you think it's important to have *proof* of calc by the time one applies? My DS as planned will have a Calc 1 (of 3) community college grade, and would be taking AP Calc BC (but, no score obv). 

I am not an expert, but I would think that having calculus taken during the senior year would be enough. 

That said, the only person I know who was a direct admit to a highly competitive CS program (University of Washington) skipped a grade in elementary and did AB in his junior year and BC in his senior year (at that time the school required that AB be taken prior to BC).  This was in a top performing district where very few seventh graders took Algebra 1.

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I agree you don't need proof.  But, I also agree that cal is pretty much not more than the standard math STEM kids are applying with having taken.  

What about taking Thinkwell's cal 1 course as a yr long course instead of a semester course?  It would be cal.  And the time commitment would be fairly low.  (My dd completed both this yr.  It is planned as a 38 week sequence.  She spent on avg a little more than an hr to an hr and a half per day.  Some days were longer if there were a lot of videos.  But the sequences chpt in cal 2 was by far created the longest days.  Just completing cal 1 would probably take 45ish mins max per day.

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3 minutes ago, square_25 said:

@EKS: do you think having a grade report on a hard AOPS class would be enough to make up for lack of calc or no?

It is really going to depend on the U.  Most admissions officers don't know AoPS or math courses any more than the man on the street.  They know what they are used to seeing and that would be cal.

1 minute ago, square_25 said:

To be fair, AoPS precalc isn’t great preparation for calculus to begin with!! I’d definitely review all the relevant functions before calculus, because precalc only does trig functions.

Just as another perspective, the only precal and cal my ds took were AoPS.  Both were great fits for him.  For pre-cal though he worked directly with Kathy and no online course.  Cal he took online.  He really liked both courses.  But, he is a strong math student who can make connections and fill in gaps on his own without any explicit teaching.  (Definitely not a skill a lot of students have, most of my kids included.)

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9 minutes ago, 8FillTheHeart said:

I agree you don't need proof.  But, I also agree that cal is pretty much not more than the standard math STEM kids are applying with having taken.  

Yep. Completely agree with this. When my ds changed his mind about desired major during his junior year (from chem to CS), my main concern was that our math wasn't quite up to par with others applying for CS. He had started out ahead, and did calc with thinkwell his junior year (he was using the cc for advanced chemistry classes instead of math). However, the community college wouldn't let him test to place out of Calc 1 his senior year(it was a co-req for his CS classes), so he redid it there at the cc again 🙄

It was a "first kid learning moment" for us, because I didn't realize that they would be picky about calc being their own class (with no option to test out), and we ended up "wasting" a year. In the end, he knows calc really well now, lol, and I learned from this mistake for my next two! 

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57 minutes ago, square_25 said:

@EKS: do you think having a grade report on a hard AOPS class would be enough to make up for lack of calc or no?

I have no idea.  I don't know how familiar the admissions folks are with the various AoPS courses.  That said, if the student is going to be applying for direct admission to a competitive CS program, I'd probably go the conservative route and encourage them to take calculus.  With my kids my strategy was to go rogue on top of expectations (either explicit or implicit) rather than in place of expectations.   If that makes sense.

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2 hours ago, square_25 said:

Oh, yeah, absolutely. That's why I thought a less demanding calculus in the fall would be a good idea, to combine with a harder AoPS class. 

By the way, I've written quite a few recommendation letters for kids in AoPS classes... if you have a child do really well (I mean an A or above) in a hard AoPS class, I absolutely think it's a good idea to get a recommendation letter from the teacher. 


there has been debate in the past here over what is an A in AoPS class. Blue bar is an A, but what about a green bar? Somebody here said green bar was also an A. 

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12 minutes ago, square_25 said:

They've started providing actual percentages for people to go by when assigning grades, so I would guess that nowadays only a blue bar is an A. 

And what would that make the green bar, a B or a C?

Then, of course, you have to factor in the assigned problems which I don't recall being related to any bars. 

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11 minutes ago, Paige said:

And what would that make the green bar, a B or a C?

Then, of course, you have to factor in the assigned problems which I don't recall being related to any bars. 


I think this varies from class to class. The craziest example would be Calculus, where one proof per week accounts for the majority (if I remember correctly 65%+) of the grade. That’s scary to know your grade hangs on one problem per week more or less. I think for other classes it’s more even handed. And you certainly can get to blue without having to solve everything. Calculus, another ballgame.

 

I think for PS kids who are taking these classes for enrichment, it’s less risky. For homeschooled kids taking these classes for real grade in high school, so stressful.

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29 minutes ago, Roadrunner said:


I think this varies from class to class. The craziest example would be Calculus, where one proof per week accounts for the majority (if I remember correctly 65%+) of the grade. That’s scary to know your grade hangs on one problem per week more or less. I think for other classes it’s more even handed. And you certainly can get to blue without having to solve everything. Calculus, another ballgame.

 

I think for PS kids who are taking these classes for enrichment, it’s less risky. For homeschooled kids taking these classes for real grade in high school, so stressful.

So weird to read. When ds took the class, no work was completed online. He was sent a page of problems to solve and scan in.

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When DS had class he had some questions that were different than alcumus with the bars. These questions were graded personally by the teacher and I don't think there was any automatic grading for those. It's been about 4 years, however, so my memory is fuzzy. He had alcumus sets and additional written problems for each week. 

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Yes, Alcumus, auto graded problems, and then one proof problem that is graded by the teacher. Alcumus didn't exist when my kid took Intermediate Algebra and precalculus (it did for lower level courses), so it was auto graded problems and then one proof problem with extensive teacher feedback. The relative balance between those three components I can't exactly remember.  Calculus doesn't have alcumus, so it has auto graded problems, and then one proof per week. I believe that proof is about 65% of the weekly grade. Now how well you need to solve it to get a blue bar, I don't know. They tend to take into account the difficulty. 
 

just adding. Found a detailed page on grading. It looks like they still maintain green as A:

https://artofproblemsolving.com/school/handbook/current/documentation

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FWIW, applications usually have a place for planned senior classes, and both DD's high school and college transcripts list classes that are in progress or have been registered for so far, but have not yet been begun.  So whatever math is planned for senior year will be visible, even though there won't be a grade yet (and my guess is that there won't be substantial change for most students during senior year). 

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I would advise him to take calculus. Like the pp mentioned, cs is one of the most competitive majors and he needs to get admitted. Calculus can be used as a barrier just because most schools have such high performing students vying for few slots.

my dd took AOPS number theory and also a selective school Number theory class and the AOPS Was about 2/3rd of what was covered in the college class. If possible he can try to take both I think calculus starts late in the fall. If there is a number theory class in the summer, he can take that. 

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Oldest DS is currently doing CS at Purdue and he's taking lots of math, including number theory and probability. He loves math and has extra time to take more upper level math courses because he tested out of 2 semester's of calc with AoPS in high school.

If your son takes NT and prob now he might have to retake them in college (since they don't have test outs for those, typically) in addition to requiring calc.

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He’s not concerned about testing out of classes in college. He wants number theory for practical reasons right now to help him make his programs better. He’s doing cryptography programs. He isn’t the type to think practically about checking boxes or planning ahead- he wants the math because he wants to use the math. 
 

They don’t offer number theory until the spring however. 
 

I emailed Thinkwell to see if they are accessible but haven’t heard back. If he could do that and just take number theory as a one semester class that might be better. He could pick up counting and probability in the summer if he really wanted. 
 

If he gets his foot in the door with this one company he’s talking to he won’t have to worry much about selectivity. He’d do his basic classes at the community college and then the company has an arrangement to send employees to a really great program with funding. I’m not even sure if CS is an accurate description of the major he wants. Are cryptography or security specializations under CS still or their own programs?

 

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42 minutes ago, Paige said:

He’s not concerned about testing out of classes in college. He wants number theory for practical reasons right now to help him make his programs better. He’s doing cryptography programs. He isn’t the type to think practically about checking boxes or planning ahead- he wants the math because he wants to use the math. 
 

They don’t offer number theory until the spring however. 
 

I emailed Thinkwell to see if they are accessible but haven’t heard back. If he could do that and just take number theory as a one semester class that might be better. He could pick up counting and probability in the summer if he really wanted. 
 

If he gets his foot in the door with this one company he’s talking to he won’t have to worry much about selectivity. He’d do his basic classes at the community college and then the company has an arrangement to send employees to a really great program with funding. I’m not even sure if CS is an accurate description of the major he wants. Are cryptography or security specializations under CS still or their own programs?

 

What do you mean by accessible? FWIW, their courses are going on sale 45% off June 25.

https://www.homeschoolbuyersco-op.org/thinkwell-math/#mobile

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46 minutes ago, 8FillTheHeart said:

What do you mean by accessible? FWIW, their courses are going on sale 45% off June 25.

https://www.homeschoolbuyersco-op.org/thinkwell-math/#mobile

The videos must be accessible for the hearing impaired by having subtitles or a transcript. The subtitles can’t be like the automatic YouTube ones but actually accurate. 

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@Paige Are you thinking of using Thinkwell for calculus?  If so, I'd recommend that you also take a look at Derek Owens.  I've used both, and prefer DO.  That said, Thinkwell covers more ground if you do the whole thing.  It's also cheaper.

He could easily get through the DO course in a semester.

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22 minutes ago, EKS said:

@Paige Are you thinking of using Thinkwell for calculus?  If so, I'd recommend that you also take a look at Derek Owens.  I've used both, and prefer DO.  That said, Thinkwell covers more ground if you do the whole thing.  It's also cheaper.

He could easily get through the DO course in a semester.

We have already looked at DO and can't do it because of the audio. 

Thinkwell says they have subtitles and transcripts, so I think I'll go with them and then probably hire a tutor as needed if he runs into any issues. Then, if things are going well, he can add NT as an elective. That's assuming he agrees to my plan...

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8 hours ago, Paige said:

He’s not concerned about testing out of classes in college. He wants number theory for practical reasons right now to help him make his programs better. He’s doing cryptography programs. He isn’t the type to think practically about checking boxes or planning ahead- he wants the math because he wants to use the math. 
 

 

 

I'm not familiar with cryptography, except I watched a lecture by Arthur Benjamin RSM RSA cryptography in a Great Courses class.  If that's what he's stuck on, this is an excellent explanation.  If he needs to learn about mods, that's pretty straightforward, and in fact, makes solving problems very easy.  He could probably self study that in a short period of time.  

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10 minutes ago, daijobu said:

 

I'm not familiar with cryptography, except I watched a lecture by Arthur Benjamin RSM cryptography in a Great Courses class.  If that's what he's stuck on, this is an excellent explanation.  If he needs to learn about mods, that's pretty straightforward, and in fact, makes solving problems very easy.  He could probably self study that in a short period of time.  

I think what he wants is more tools for making his own secure systems? It's hard for me to talk intelligently about it because I don't know what he's doing, but he's trying to write something better than what he sees out there. 

He'd probably really like that Great Courses series. Do you know if he'd need to already have calculus to follow along?

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44 minutes ago, Paige said:

I think what he wants is more tools for making his own secure systems? It's hard for me to talk intelligently about it because I don't know what he's doing, but he's trying to write something better than what he sees out there

He'd probably really like that Great Courses series. Do you know if he'd need to already have calculus to follow along?

 

I'm curious too about what he needs to know.  You don't need calculus for discrete math.  What I liked about the course and the lecture in particular was that it doesn't shy away from the math.  So he'll get a solid understanding of why RSA works.  It's pretty cool actually.  This is a great explanation.  

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22 minutes ago, square_25 said:

 Hmmmmm. What does he see out there that's a problem? That's a pretty strong judgment. 

He'll probably need a LOT of math if he wants to do better than the current levels of security, which are mostly not constrained by math but by human error and computing speed... but to understand them all well, you do need a fair amount of number theory. 

I don't know. Imperfection? A puzzle or challenge to attempt? He's just interested in that area.

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10 hours ago, Paige said:

I don't know. Imperfection? A puzzle or challenge to attempt? He's just interested in that area.

This sounds like my oldest DS! He wrote what he acknowledged was a completely impractical chess program because "the math was so much more elegant". I have no idea what he was doing, but it was something to do with having the program go through every single possibility instead of abbreviating it like most chess programs do, and he said he would have needed a computer as big as our house to make it actually run, but he was so stinking excited about that program 🤣

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1 hour ago, square_25 said:

Oh, goodness, that sounds impractical!!

Oh, yes! He was in 10th grade when he did it, and he ended up writing a college app essay all about how even though he knew ahead of time it wouldn't work in the real world, he went ahead and wrote the program anyway because the math was so cool and because he wanted something "pure" and not corrupted by expediency. And how even though other smarter peope than him had already solved these problems, he wanted to grapple with them himself and come to his own conclusions. I'm pretty sure that essay is what got him accepted to Rose Hulman with maximum merit aid, even though he ended up choosing Purdue instead 🙂

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Anyway, OP, my point with that story about my D'S was not to brag on him (although I happily do that too lol) but to point out that if your DS is similarly driven to explore higher math, he might prefer to go ahead and get Calc "out of the way". I know you said he wasn't really worrying about future credits and whatnot right now, but if he's that self motivated he might go ahead and learn cryptography himself in his free time and then he could do calc for "school".

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This might not help you at all but I figure it won’t hurt. 

My rising senior is a likely math major. We’ve used AOPS all along, he self-studies and doesn’t do the classes. What we are doing this year is having him self-study and hiring a tutor to meet with him on a regular basis (maybe weekly or biweekly) to go over questions. Also, to have her go over proofs as I can’t do that anymore at the Calculus level. We haven’t used the classes in the past due to the timing of them. He’s also going to take Statistics and Intro Number Theory from WTMA. He’s also taking Physics and Econ which seems like a very math-heavy year. But then I realized it’s what he wants to be doing and what he ultimately wants to be doing all the time. 

 

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21 hours ago, square_25 said:

@Paige: DH was wondering if your son has done any abstract algebra. That is, groups, rings, fields, that kind of thing. (He said that if not, he'd probably need to study that before getting seriously into cryptography, although he could give him a place to start without that, too.) 

Not officially. I don’t know what he’s studied on his own. Probably not much. He’s been deep into programming and network security  so I doubt he’s learning math beyond something specific he runs into here or there.

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