Dodging the Calculus Trap

Pre-College Topics High School Life
1

Hey, all!
So, I’ve gotten a couple steps ahead in math to the point where I’m set to take Calculus I next year. However, I’ve also read Richard Rusczyk’s (that Art of Problem Solving dude) calculus trap article (bam https://www.artofproblemsolving.com/articles/calculus-trap), and it’s given me a bit of the heebie-jeebies.

Have any of you guys figured a better path than devoting oneself totally to ‘The Calculus’ for your highschool career? Are there websites, resources, and other things that do what Rusczyk set out to do, but are less another class to spend your summer on and more of just a place to stretch your brain out, get you real comfortable with those foundational math tools we’re all supposed to have sooner or later?

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Well, I’m taking AP Stats next year and DE Pre-Calculus senior year so I don’t have to take AP Calc (I really just don’t like math that much so what’s the point lol)

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@OMPursuit AoPS, which Rusczyk himself created.

The point of the article is not that you shouldn’t take calculus (it’s a very useful and interesting subject). But if you want to study calculus or higher-level mathematics subjects, it’s good to have practice solving difficult, complex problems (often in simpler areas as the article emphasizes) since those skills can carry on when tackling research-level questions, for example.

4

$-)

Do you have the option of taking classes at a local university?

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@OMPursuit are there opportunities to participate in math competitions or a math circle at your school or in your community? If you search on the AOPs website you’ll find links to local and national contests. Does your school have a math club or Mu Alpha Theta? If not maybe you can start one.

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I’m a STEM student and I can think of a million things that would be more beneficial for both your sanity and the college admissions process than to think about calculus or any other subject over the summer. :slight_smile:

I think @halcyonheather quoted the wrong text above.

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@jakejake637 Heeh, you do you, man. AP Stats is supposed to be more helpful than calculus in most people’s lives, anyway!
I saw a TED talk on it once, whatever that means o.o’

@MITer94 Okay! Yes. I’m aware of the Art of Problem Solving, since I was looking at the guy’s website in the first place, but his classes all cost serious bank. It’s not a bad option, though! Thank you. :>

Doubtlessly, though, there should be places to find difficult, complex problems that aren’t tAoPS.

@halcyonheather The community college would let me dual enroll (that’s what’s happening next year), but I dunno how much better they’d be than anything else (or if I want to take moar classes). The university (bearer of shiny, proof-based math courses) is only open to rising juniors and past. o.o

@JasonMath My school is super small, and doesn’t have any math club! I’d start one, but interest is low and teacher sponsors are sparing. We didn’t have enough kids to do SciOly this year, which got me really sad. :<

There used to have a math club while I was in middle school (and I went! :D), but this math professor was running it out of his house and he stopped doing that. The university ran one a couple years before that, but that’s also done. Hark!

I did participate in the AMC 12 this year (nobody else from my school attended… </3), and it was super fun! Looking over the practice tests, too, got me sort of familiarized with what Rusczyk has to offer. Which is a lot. He seems like a cool guy. o.o

@skieurope Hehe, I think you misread me; I’d rather find some community to get the depth Rusczyk describes than take /another/ class over the summer. This is less an ‘OMG, college’ question and more a ‘where are the maths?!’ type of thing.

by the way- halcyonheather quoted the article itself, not my post XD

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What do you want to study in university? If you’re going to do engineering or physics, calculus and linear algebra are pretty important, and calculus is honestly 90% of the higher-level math you’ll do in engineering. Other than that it’s lots of trig and algebra. Perhaps it is different if you want to be a math major.

I don’t see how taking calculus is mutually exclusive from doing other math things though. I guess it depends on how developed you think your math skills are/how much time you may have to devote to it.

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@RMIBstudent I’m way into math, and definitely plan on taking calculus! I meant dodging the trap Rusczyk described- students coasting into Calc without really learning to problem solve- and not avoiding the subject.

My gripe is that once I start calculus, I’ll likely be taking calculus classes until university. :<
I’ve got Calc II and multivariable calc, then- bam! College.

Edit: Actually, I’m pretty sure the CC goes on a semester class schedule- which means it’d be Calc II/III in the same year, then… moving into diff. equations, advanced algebra? Eesh. o.o

That’ll still be a long period of just calc (maybe one of those classes occupies two semesters), and diff equations uses calculus heavily (if I recall correctly)!

Going so far as I can, as fast as I can might look cool on paper, but I dunno if it’ll do me a lick of good mathematically. My question was on other communities or resources (other than the already-named and pretty impressive-looking AoPS) to help build those problem solving skills.

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Okay! So!

In case anybody else is wondering about this in the future, I’ve found some stuff.

@MITer94 ‘s suggestion led me to check out AoPS’ forums, which led me to both the thriving math community on there and the Alcumnus math game.
It’s pretty rad.
Anyone in the same boat should definitely check these resources out.

MIT OCW also has a course on combinatorics! It seems pretty good, but seems to lack any actual video lectures on the subject or real instruction. :L
But the P-sets are free! <3

Brilliant.org also offers a fine set of problems (showy name aside), including some stuff that’s plain unsolved. Apparently a lot of their content is user-submitted, and some of it strikes me as quite hard.
They do want you to pay for things, though. :confused:

That’s all I’ve turned up, but seems like plenty to keep me occupied. I’ll try and drum up math interest in my school, too (as per @JasonMath 's suggestion), and suggest others do the same.

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Good luck! Starting a math club would also look great on your college applications.

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Does your community college have Discrete Math or Discrete Structures? It might be in the CS department, but it usually counts as math, but is off the Calc I > Calc II > MultiVar / LinearAlg > DiffEQ track, so can let you “slow down” by a semester and has applications to contest math type problems.

There are online math contests you can do as an individual, not as a team. I don’t know the names off hand, but AoPS and some other sites have lists of math contests.

If you also do CS, there are CS things to do with math. Look at Project Euler, for example.

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@OMPursuit what kind of stuff are you interested in? Then I could give some more specific recommendations.

The AoPS classes are great and well worth the money in my opinion. They are taught by top-notch folks, and even the TAs are very pro. But a another option is, buy the AoPS Volume 1 and 2 (and solution manuals). There are a lot of fun problems. If you like counting problems at all (and who wouldn’t), the Intermediate Counting book is great, just to give an example.

Also you might check out Prof. Poh Chen Loh’s Expii site. (He is the IMO coach for the US.)

I don’t know your specific situation, but another idea is to start some sort of math outreach to share your knowledge and enthusiasm with some younger and potentially less fortunate students. For example, you could offer to coach a local Mathcounts team at a middle school, or set up tutoring at a library (maybe in a economically downtrodden area).

Take a look at this article :slight_smile:
http://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/426855/

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@OMPursuit AoPS is pretty useful. I don’t use it much anymore now that I’m in college, although I occasionally look through past exams and check through AoPS forums.

I actually took the combinatorics course (18.314, but they renumbered a bunch of courses last year). There is also an algebraic combinatorics course. I can see how they didn’t record the lectures - it was a small class when I took it (~20 students).

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 I do Project Euler now and then, but I' a horrible programmer @Ynotgo  ;)

I’ve yet to pass problem five- although it’s taught me a couple things already, and inadvertently lead me to meet some cool people. XD

Discrete math seems pretty cool, too! I’ll need to look into it.

@inn0v8r I came in a couple times at our public library’s tutoring circle and helped some kids out! I had a blast and would still be doing it, but it ended up clashing hard with other things. I recommended starting a tutoring ring at my school a while ago, but nobody’s come forward yet and I haven’t met many other students in a good position to help (yet).

The summer should be good for that, though. :smiley:

@MITer94 Darn! Curse you, MIT, and your favorably small student-to-teacher ratio.
I have the first AoPS book from a while back, and I’ve only recently been able to take a whack at it. The problems are really good, so far!

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@OMPursuit On the contrary, most classes I’ve taken at MIT are fairly large.

Out of the classes I’ve taken, pretty much all GIRs and common course 6/18 classes are large, usually 50-200+ students. In fact 18.314 might’ve been the smallest of my classes (along with a couple math seminars and foreign languages).

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Huh! Cool beans.
I wonder how they keep their 8:1 ratio. Do professors double up for the large classes,
or do many just not really teach? o.O @MITer94
Taking a class with peers in the hundreds sounds awful strange, though I’ve heard the added independence is nice

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@OMPursuit Some professors don’t teach (or maybe only teach one course per term). A few of my classes had two or more professors. However most classes are taught lecture/recitation style, and recitations are usually smaller (10-20 students).

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Hi OM,

I don’t think calculus is a trap at all. On the contrary, you can learn calculus to reinforce your mathematical maturity, while supplementing it with proof-based math/discrete math on the side. There’s no reason for you to delay learning calculus just because you are scared it’s a trap.

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@tellmecombo Oh, no- I’m really very excited to take on calculus. It seems really interesting, and I’ve honestly been interested in rates of change for a loong time.

My fear is/was entering calculus (and exiting calculus) without getting much better at solving problems, or furthering my understanding of numbers, math- all that.
I think some really cool people have already contributed real good advice, and I’m optimistic that eventuality won’t happen. :smiley:

Hopefully, this thread will help others in my situation!