Math after Calculus BC

[Black-eyed Suzan]

My son finishes AP Calc BC this year and needs 2 more years of math (probably a class or more each semester). I don't know what the best choice for a likely math major is. I would love your input, please!

Background:

He loves math and has enjoyed his AOPS classes/books so far. He did decently well on the AMC12 and AIME and is interested in continuing to participate in those competitions. He will probably major in something like applied math (or maybe finance?). He is not a future engineer and geometry was his least favorite math course. He is pretty apathetic about programming.

He has not had AOPS Intermediate C&P or Intermediate NT. He is interested in taking statistics, too.

We do have a free CC dual enrollment option, but I do not know how rigorous their math is. Other parents have noted that other classes are very easy, so that is not encouraging to me. My understanding is that taking major classes at a CC is not preferable anyway because the treatment will be richer and more rigorous at a 4 year university. But feel free to offer a different opinion if you have it!

Questions:

My research has shown that most students go on to take Multivariable Calculus and Linear Algebra after Calculus BC. But is this rushing through a standard curriculum? Is it better to explore other topics? Or is it preferable to keep continuing in the sequence so skills don't atrophy?

I had thought about a course each year in the sequence along with a course in another topic. Does that sound reasonable?

Other options I have found and have no idea how to evaluate:

AOSP C&P

AOPS NT

AOPS WOOT – can this be counted on the transcript as a course? Or is it considered extracurricular math competition preparation only?

AOPS group theory

IMACS mathematical logic 

CTY self-paced classes (on the expensive end for our budget) – Multivariable Calculus, etc.

MIT OCW Multivariable calculus 

EdX and Coursera also seem to have options

Statistics: BlueTent self-paced, CTY self-paced, CC, PAH

Thank you so much for your help! My background is no help in evaluating math paths at this level.

 

Note: Malam was kindly helping me with this question on the Accelerated board. Here's the link to that if you are interested:

https://forums.welltrainedmind.com/topic/712025-aops-group-theory-vs-linear-algebra-through-stanford-ulo/

[kokotg]

My oldest did BC in 11th grade and took linear algebra and "intro to logic, set theory, and proofs" (basically a proof-heavy discrete math course, as far as I can tell) at a local university in 12th grade. He's about to graduate with a degree in math from Macalester (a small LAC). This worked fine for him. He deliberately didn't take multivariable, partially because he wanted a break from calc and partially because we figured most of the other math majors would be taking it their first year at Mac and that it might be better to leave it for that. Linear algebra was interesting because he ended up TAing for a linear algebra class his 2nd year of college, and that kind of made him wish he'd waited because he'd forgotten a lot and the class he'd taken hadn't covered as much. But then he got to attend the classes since he was TAing, so it was a bit stressful but all worked out. He really enjoyed the proofs class, and I think it helped solidify that that was what he wanted to do in college. And, indeed, he hasn't strayed at all; he went to a LAC so he could take all kinds of classes, but almost all of his classes have been math, CS, stats, and GIS-based geography classes. He could have gotten credit for discrete math from the proofs class, but opted to take it at his college instead. 

So...what he did was fine, but I think other options would have been equally fine. What kinds of colleges is he looking at? There is some concern at smaller schools about running out of math to take, particularly since you're looking at 2 full years of college classes. I think this is a bit overblown in most cases, though, except perhaps at schools with extremely small math departments. My kid didn't have any trouble finding classes, and there are lots of options other than just whatever's on the course schedule that semester, too (he did a Budapest Semester in Mathematics, a summer REU, and is doing an honors project now; plus he had the option of doing other independent studies). 

[Mom_to3]

AoPS Intermediate C&P and Intermed. Number Theory are really quite excellent, especially if your son already likes their text-based program. You may be able to fit them in in one year...

[Black-eyed Suzan]

15 minutes ago, kokotg said:

My oldest did BC in 11th grade and took linear algebra and "intro to logic, set theory, and proofs" (basically a proof-heavy discrete math course, as far as I can tell) at a local university in 12th grade. He's about to graduate with a degree in math from Macalester (a small LAC). This worked fine for him. He deliberately didn't take multivariable, partially because he wanted a break from calc and partially because we figured most of the other math majors would be taking it their first year at Mac and that it might be better to leave it for that. Linear algebra was interesting because he ended up TAing for a linear algebra class his 2nd year of college, and that kind of made him wish he'd waited because he'd forgotten a lot and the class he'd taken hadn't covered as much. But then he got to attend the classes since he was TAing, so it was a bit stressful but all worked out. He really enjoyed the proofs class, and I think it helped solidify that that was what he wanted to do in college. And, indeed, he hasn't strayed at all; he went to a LAC so he could take all kinds of classes, but almost all of his classes have been math, CS, stats, and GIS-based geography classes. He could have gotten credit for discrete math from the proofs class, but opted to take it at his college instead. 

So...what he did was fine, but I think other options would have been equally fine. What kinds of colleges is he looking at? There is some concern at smaller schools about running out of math to take, particularly since you're looking at 2 full years of college classes. I think this is a bit overblown in most cases, though, except perhaps at schools with extremely small math departments. My kid didn't have any trouble finding classes, and there are lots of options other than just whatever's on the course schedule that semester, too (he did a Budapest Semester in Mathematics, a summer REU, and is doing an honors project now; plus he had the option of doing other independent studies). 

Oh, thank you for sharing! Those are interesting considerations.

Right now (as a 10th grader) he has no idea where he'd like to go to college. But looking to make sure there are enough math classes available seems like a great idea.

[EKS]

My son took two years of statistics at the high school (AP and post AP) after BC because that is all they had, and he loved it.  I know it was a less rigorous choice, but he's glad he did it that way.

[daijobu]

I vote for any of the AoPS classes, especially NT and CP.  You can definitely put WOOT on his transcript; I think it's very impressive if he can keep up with that class.  

Is he close to solving 10 problems on the AIME?  If he can grab an USAMO, he's in an elite group.  

The other options are also solid if that's what he prefers.  

[Atlas]

If he is really interested in doing finance, it will be better to do some finance related class and call it mathematical finance.

[8filltheheart]

My ds DE'ed at our local 4 yr university. For multivariable, diffEQ1&2, and linear alg. He also DE'ed physics. He is a physics geek, so his love was physics over math. For him, DEing was 100% positive. He won first place in a high school physics competition just by showing up (zero prep).  All of his credits transferred and he was able to use his scholarship $$ for grad classes that his U let him take as an undergrad.

[Malam]

Where/how did he decide he was pretty apathetic about programming?
If he can reliably score above 5 in AIME tests, then he's qualified for WOOT (although it does devote time to geometry)

How are his proof skills? If they're not good, then I would suggest taking int. counting and probability (assuming he can pass the prerequisite test), which would prepare him well for an advanced calculus-based (possibly bayesian) statistics class - although that would likely need to be DE or self-taught from lectures/textbook(s).

[Black-eyed Suzan]

On 2/23/2023 at 4:57 PM, daijobu said:

I vote for any of the AoPS classes, especially NT and CP.  You can definitely put WOOT on his transcript; I think it's very impressive if he can keep up with that class.  

Is he close to solving 10 problems on the AIME?  If he can grab an USAMO, he's in an elite group.  

The other options are also solid if that's what he prefers.  

 

On 2/23/2023 at 6:25 PM, Malam said:

Where/how did he decide he was pretty apathetic about programming?
If he can reliably score above 5 in AIME tests, then he's qualified for WOOT (although it does devote time to geometry)

How are his proof skills? If they're not good, then I would suggest taking int. counting and probability (assuming he can pass the prerequisite test), which would prepare him well for an advanced calculus-based (possibly bayesian) statistics class - although that would likely need to be DE or self-taught from lectures/textbook(s).

That's great news that WOOT can go on his transcript. Maybe he'll like the geometry portions more with a goal in mind. 😉 

He does qualify for WOOT.

I can't evaluate the proof skills myself, but he reliably gets good scores on his AOPS writing problems.

He's dabbled with scratch, python, and java. Maybe it's the way we went about it, but he's never been that interested. He does use LaTeX proficiently, so maybe it's just a question of having a goal and not just programming for programming's sake.

Thanks for the recommendation for the statistics class, too!

Edited March 25, 2023 by Black-eyed Suzan
privacy

[Black-eyed Suzan]

2 hours ago, 8filltheheart said:

My ds DE'ed at our local 4 yr university. For multivariable, diffEQ1&2, and linear alg. He also DE'ed physics. He is a physics geek, so his love was physics over math. For him, DEing was 100% positive. He won first place in a high school physics competition just by showing up (zero prep).  All of his credits transferred and he was able to use his scholarship $$ for grad classes that his U let him take as an undergrad.

I'm so glad the physics and math DE worked well for him! I need to check the specifics about high school students at our local 4 year. I don't think they allow DE, even if we pay for it, but I'm not 100% sure about that. It sounds like that may be a good option senior year if it's possible.

[8filltheheart]

3 hours ago, Black-eyed Suzan said:

I'm so glad the physics and math DE worked well for him! I need to check the specifics about high school students at our local 4 year. I don't think they allow DE, even if we pay for it, but I'm not 100% sure about that. It sounds like that may be a good option senior year if it's possible.

Our local Us didn't allow enrollment or limited class choices to classes we weren't interested in (we moved between his 1st and 2nd semester jr yr.)  For both schools I made an appointment with the registrar's office.  I took his test scores (for the first U I only had his ACT scores from 8th grade, but he was waiting for his AP scores for both BC and chem), a LOR from his AoPS cal teacher, his transcript, and ds himself.  Basically, I told them that referring him to the local CC would not work bc he would surpass their level of course offerings before he graduated from high school and he needed to be in an environment that would meet his academic needs.  They listened to my concerns quite seriously.  Both Us initially limited him to 2 courses/semester--1 math/1 physics--(except they did allow labs not count toward that limit).  By his sr yr (after having the highest grade in the classes he took), they allowed him to take 3.  He graduated from high school having completed almost the equivalent of a minor in both.

Edited February 24, 2023 by 8filltheheart

[Malam]

12 minutes ago, 8filltheheart said:

Our local Us didn't allow enrollment or limited class choices to classes we weren't interested in (we moved between his 1st and 2nd semester jr yr.)  For both schools I made an appointment with the registrar's office.  I took his test scores (for the first U I only had his ACT scores from 8th grade, but he was waiting for his AP scores for both BC and chem), a LOR from his AoPS cal teacher, his transcript, and ds himself.  Basically, I told them that referring him to the local CC would not work bc he would surpass their level of course offerings before he graduated from high school and he needed to be in an environment that would meet his academic needs.  They listened to my concerns quite seriously.  Both Us initially limited him to 2 courses/semester--1 math/1 physics--(except they did allow labs not count toward that limit).  By his sr yr (after having the highest grade in the classes he took), they allowed him to take 3.  He graduated from high school having completed almost the equivalent of a minor in both.

Did you pay tuition?

[8filltheheart]

5 minutes ago, Malam said:

Did you pay tuition?

Yes.  He ended up going to college full-ride+ scholarships,, so DE paid for itself multiple times over.

[RoundAbout]

Wow.  Following!

I feel like I could have written this post. We have the exact same issue - my 10th grader is finishing up AP Calc BC and AP Stat this year. He also is a contest kid and did well on the AMC 12 and got an 8 on the AIME this year so is thinking about WOOT. He also did well on the USAMTS and is applying to math camps for this summer. 

In a twist though - DS is mostly a foreign language guy and wants to major in linguistics. He's not interested in hard STEM careers but loves math just for fun. So I don't want it to become a grind for him and there's no need for him to race ahead.

All of the options you've listed are ones we're looking at. I was wondering how something like WOOT is perceived on a transcript?

[NittanyJen]

I teach the AP Stats course at PAH. You can ask anything you like.

[Kassia]

My kids who did DE did Linear Algebra, Differential Equations, and/or Discrete Math after Calculus 2.

My kids in ps who did AP Calculus BC just went on to AP Stats because the math teacher at the high school was lousy but the stats teacher was great.  All four ended up with STEM majors - 3 in engineering.  

 

 

[regentrude]

16 hours ago, Black-eyed Suzan said:

I'm so glad the physics and math DE worked well for him! I need to check the specifics about high school students at our local 4 year. I don't think they allow DE, even if we pay for it, but I'm not 100% sure about that. It sounds like that may be a good option senior year if it's possible.

They might call it something else. Maybe visiting student, or non-degree-seeking student?
I'd have a hard time imagining a uni refusing to take tuition money from anybody with a pulse.

[NittanyJen]

18 minutes ago, regentrude said:

They might call it something else. Maybe visiting student, or non-degree-seeking student?
I'd have a hard time imagining a uni refusing to take tuition money from anybody with a pulse.

Agreed. I specifically didn’t enroll my kids as DE, because that would have limited them to specific, generally lower level classes, often pitched at high schoolers instead of actual regular college classes. I had them enroll as Continuing Ed instead. They had ‘last priority’ registration (which I expected and agreed with, because they shouldn’t displace a kid trying to get a class to graduate on time) but had no trouble getting into the courses they wanted anyway. All they had to do was meet the prerequisites for a given class.

[SanDiegoMom]

I replied on the other thread, but just wanted to add that my son did Calc bc in ninth. AP stats in 10th, multivariable Calc during that summer after 10th, is in Linear Algebra rn, and will be taking Diff EQ during his senior year.  I am not sure what your son’s college plans are, but we decided here in California it was best to continue the math sequence through CC bc it seemed to be the new standard for the ps kids, and my son will be measured against his classmates (he is in brick and mortar school).  So for instance, he had about 4 other kids in his class last year, and 8 in his linear algebra class this year from his high school. 
 

If your son really is leaning more towards languages, I would encourage him to take the math classes that most interest him. If he wants challenging, then the Intermediate NT or Woot are great options. CC will not be anywhere near as challenging.  We would have done classes at our four year U if it were closer, but he is heavily involved in school clubs and this is the best option for him, time wise. 

 

[Black-eyed Suzan]

On 2/24/2023 at 12:13 PM, regentrude said:

They might call it something else. Maybe visiting student, or non-degree-seeking student?
I'd have a hard time imagining a uni refusing to take tuition money from anybody with a pulse.

I looked again and it is called visiting student! Thank you so much, regentrude!!

[SeaConquest]

I can't remember if you're in CA, but you can definitely enroll in math classes at UCs/CSUs as a high school student (either online or in-person). Also, if your son is enrolled at a CC, and is taking more than 6 units there, he can cross-enroll at a CSU/UC without paying tuition for one class. You just pay an administrative fees and any additional lab/materials fees specific to the class. That may not work if you aren't paying fees through free DE for HS students, so you have to check (my son takes CC classes, but is enrolled via his CHSPE, so we pay full CC tuition and he gets normal registration priority). With respect to CC math, there are excellent honors math classes to be found. You just have to dig. De Anza/Foothill come to mind immediately, but there are others. Some schools may only offer in-person honors, but with some digging, you can find online options, if that is your preference.

Another option is University Level Math/Physics at Stanford Online High School (SOHS). I know a few boardies have kids that have taken classes there.

My DS is finishing up AoPS Calculus at the moment, and we've explored several options for high school. We landed on him continuing post-AoPS math at SOHS, but of course, that is obviously fluid. He may decide that he would prefer to take AoPS Group Theory vs Analysis in a few years -- who knows? There are lots of very quantitative areas of finance to explore. You could spend a semester/year studying the material in the CFA exam and it would give him a huge leg up if he ultimately decided to go into finance. They don't necessarily have to stay on the standard math major path. 🙂   

[rzberrymom]

5 minutes ago, SeaConquest said:

Also, if your son is enrolled at a CC, and is taking more than 6 units there, he can cross-enroll at a CSU/UC without paying tuition for one class.

Wait, what??? Do you have more info on this? Our local CC caps DE units at 11.99, so we’ve been paying out of pocket for extra classes at the local CSU. I never heard of the free class thing!!

[SeaConquest]

1 minute ago, rzberrymom said:

Wait, what??? Do you have more info on this? Our local CC caps DE units at 11.99, so we’ve been paying out of pocket for extra classes at the local CSU. I never heard of the free class thing!!

Yes, google cross enrollment and your neighborhood UC/CSU. Most people don't know about it. But, I am not sure it would work if you're getting free DE. We pay the CC tuition, so double check with your CC and the CSU/UC about it.

[rzberrymom]

Oh my gosh, I found it! Inter-system cross-enrollment!?! It’s completely buried at the bottom of a lonnnnggg webpage about enrollment. CC is free for everyone in our county, so I can’t imagine that could disqualify someone.  I cannot believe I never knew about this and wasted so much...

[SeaConquest]

12 minutes ago, rzberrymom said:

Oh my gosh, I found it! Inter-system cross-enrollment!?! It’s completely buried at the bottom of a lonnnnggg webpage about enrollment. CC is free for everyone in our county, so I can’t imagine that could disqualify someone.  I cannot believe I never knew about this and wasted so much...

I need to make a specific post about it on some of the larger homeschooling FB groups. Too few people know this is an option. I just don't know if it applies in the case of special admit/DE HS students that aren't paying CC tuition. But yes, it does seem like most of CA CCs are free for everyone, so I'm not sure why there would be a distinction made. Sometimes, it's better not to ask the question and just apply. Lol.

[Meredith]

Been off WTM Boards for awhile and now getting reacquainted.

My three oldest kids finished AP Calc BC in 10th grade.  

DD (born 1999) dual enrolled in Multivarable Calc, Statistics, Computer Science - graduated from Univ of Michigan in Biomedical Engineering

DD (born 2001) dual enrolled in Multivariable Calc, Differential Equations, Statistics - graduated from Univ of Michigan in Biophysics and Spanish

DS (born 2003) dual enrolled in Multivariable Calc, Differential Equations, Statistics, Accounting, Computer Science x 2 - sophomore in chemical engineering at Univ of Michigan

My fifth kid (born 2008) is the mathlete in the family, went to National MathCounts, taking AMC10/12 and AIME. He has taken many AOPS courses including Intro and Int C&P and NT. All excellent. He also does OTIS for Olympiad training.

Years ago I was worried about them taking their Mutivariable and Diff Eq too early but my engineering students have not commented on it being a problem at all. At Michigan, the math classes are brutal so it's generally encouraged to get your Calc done not at Michigan. I think this is because math education is generally not great in high school and when they get to "real" math in college, they have not been taught to think. I do not think this is the fault of Michigan professors (like I used to) but rather the quality of math education. If kids learned through AOPS, I think they would do fine with college calc.

Also, I learned after a few years that it was best to dual enroll at the CC because they did the best job in making sure the courses could transfer easily to our nearby colleges.

My son thinks that the AOPS Int C&P will not be difficult for your son but it would be useful for him and he will learn some things. The AOPS Int NT class is harder than the Int C&P.

I think your plan of continuing with Multivairable Calc/Differential Eq with AOPS class on the side is perfect. Multivariable Calc is pretty easy relatively speaking. Diff Eq and Linear Algebra are harder. Evan Chen's OTIS is more Olympiad-focused than WOOT but they are are similar and draw from the same mathy students.

HTH!

 

Edited March 9, 2023 by Meredith

[Black-eyed Suzan]

25 minutes ago, Meredith said:

Been off WTM Boards for awhile and now getting reacquainted.

My three oldest kids finished AP Calc BC in 10th grade.  

DD (born 1999) dual enrolled in Multivarable Calc, Statistics, Computer Science - graduated from Univ of Michigan in Biomedical Engineering

DD (born 2001) dual enrolled in Multivariable Calc, Differential Equations, Statistics - graduated from Univ of Michigan in Biophysics and Spanish

DS (born 2003) dual enrolled in Multivariable Calc, Differential Equations, Statistics, Accounting, Computer Science x 2 - sophomore in chemical engineering at Univ of Michigan

My fifth kid (born 2008) is the mathlete in the family, went to National MathCounts, taking AMC10/12 and AIME. He has taken many AOPS courses including Intro and Int C&P and NT. All excellent. He also does OTIS for Olympiad training.

Years ago I was worried about them taking their Mutivariable and Diff Eq too early but my engineering students have not commented on it being a problem at all. At Michigan, the math classes are brutal so it's generally encouraged to get your Calc done not at Michigan. I think this is because math education is generally not great in high school and when they get to "real" math in college, they have not been taught to think. I do not think this is the fault of Michigan professors (like I used to) but rather the quality of math education. If kids learned through AOPS, I think they would do fine with college calc.

Also, I learned after a few years that it was best to dual enroll at the CC because they did the best job in making sure the courses could transfer easily to our nearby colleges.

My son thinks that the AOPS Int C&P will not be difficult for your son but it would be useful for him and he will learn some things. The AOPS Int NT class is harder than the Int C&P.

I think your plan of continuing with Multivairable Calc/Differential Eq with AOPS class on the side is perfect. Multivariable Calc is pretty easy relatively speaking. Diff Eq and Linear Algebra are harder. Evan Chen's OTIS is more Olympiad-focused than WOOT but they are are similar and draw from the same mathy students.

HTH!

 

So encouraging and helpful! Thank you!

[Meredith]

6 hours ago, Black-eyed Suzan said:

So encouraging and helpful! Thank you!

Oh also (I think I kind of said this but to expand a bit), different CC's are different in quality of instruction. After having my first two kids take dual enrolled classes at a four-year university close to home (because I thought it would be more rigorous than the CC) and then having some struggle with some of the classes not transferring to their college, we tried the CC and were pleasantly surprised with the quality and level of instruction and have stuck with CC ever since for the rest of my kids. So you need to look into the local CC's and universities to see what is the best fit and not make assumptions like I did.

Also - you probably know this - if he takes statistics, better to do it dual enrolled because it is only one semester rather than AP Statistics which is usually a year-long class for one semester of college credit. Just an efficiency issue from my point of view.

Edited March 10, 2023 by Meredith