Hey, I'm actually curious about this question in regards to other top science/math/engineering schools, like Caltech, Olin, and the like, if anybody can answer it for them. I chose MIT specifically because I thought it might be an extreme example. Anyway, I want to know on average, what the highest level math course is that people who are accepted to MIT completed in high school.
There was a local college fair that I went to with over 200 schools, and I asked a lot of the top schools' representatives this questions. Few, if any, could even give me an idea, haha. Yale's guy said that when he went, most had taken Calculus, but he was about 50, so I assume things have at least changed a little bit.
Personally, my school doesn't offer Calculus, so I've gone to the local community college to take Calculus 1 (differential) and Calculus 2 (integral). In the fall, which is my senior year, I'll be taking Linear Algebra there, and I'm not sure about what I'll take the spring semester (all that's left is differential equations and Calc 3, but those classes are scheduled very badly for a HS student). And I don't think I'll be able to specify what I'm taking during the spring semester on college apps anyway.
Also, what math have those in the top 10 percent in this category at MIT (this somewhat unquantifiable category) taken? Thanks!
On average, people probably finished single variable calculus (AP calc BC).
Somewhere in between top 5 and 10% probably have seen a significant amount of college math beyond calculus (e.g., number theory, analysis, etc.). Top 10% have taken multivariable calculus for sure. Sometimes people take linear algebra instead like you did.
I would say that most people have definitely taken calculus, many of them multivar.
Not sure what you mean by the top 10%, but some people come in with differential equations, some with higher. I knew a guy who came in already having completed the undergraduate math curriculum and started with grad-level classes.
Taking multivariable calculus or linear algebra is definitely common, but I doubt if over 50% of people have done it.
Most of the time, the highest track in school is to take calculus senior year. If you are advanced on your own, you might end up taking it a year early and thus have a year to spend on multi-variable calculus or linear algebra at a local community college. If people have gone to special schools or have physicist parents, maybe you are beyond that, but you sure as hell aren't going to get it in the public school system.
For that reason, I suspect that the median entering freshman has taken multivariable calculus.
One thing - not all understandings of multivariable calculus and linear algebra are the same. There's a difference between thinking of the former as a small extension of calculus + the latter as bunch of rules about some nonsense, and actually coming in having internalized them both. Those who have done so, I would wager, are probably visibly small in number.
Why do I bring this up? The actual tracks you can take through college math are very varied, and you'll find that regardless of what random facts you know, it's hard to progress far rapidly unless you have what they call "mathematical maturity", which is certainly beyond just writing proofs. This maturity can be acquired in a hard class on something like MVC or Lin. Algebra or in something beyond, and I think what matters is when you get it.
There's a good number of people I know at my own school who did multivariable calculus and linear algebra in some form...but with such shallow understanding and so little mathematical maturity that they might as well just have taken calculus.
I will have taken AB and BC (I know at some schools you take either or, but at my school AB is a prereq for BC) but this summer I am teaching myself Calc so I will proably have a few years above that (if all goes well), since there are so many diffeent subjects in math that one can do after calc, I would assume that this varies from person to person and depends on what types of educational reasources they have avalible to them.
This depends pretty heavily on the school someone attends too, but ignoring that, probably the average amount of math that most people come with credit for is 18.01, or the equivalent of AP Calculus BC. So, most people take 18.02, or some other version of multivariable calculus. Though there are a lot of people that have experience with multivariable calculus, linear algebra, or differential equations, but for some reason do not receive credit for what they've taken - maybe they forgot the material, or don't want to take ASE's during orientation, or want an easier freshman year.
Except in very special circumstances we require calculus of all of our applicants.
Beyond that, I don't think there is a meaningful "average." I've seen everything from basic calculus to "i've already taken every single undergraduate math course offered at my state university."
I think the mean would probably be AP Calc AB / BC, to be completely honest. If you're taking AP Calc AB, you're fine - we won't look down on you for not being good enough at math, but it also won't make me go "woah, look at their curriculum", eh?
Thanks for the replies guys, particularly from MITChris; I was hoping to get something straight from the horse's mouth.
Also I now realize I didn't phrase this well enough, since its hard to gauge how "high level" a math course is. I guess I figured Calc BC was probably the mean, but how about: How many people take a course /after/ Calc AB/BC?
And I guess while we're all here..lol... I've been wondering how some CC'ers manage to take math courses at their local universities, rather than community colleges? Do you have to take some sort of entrance exam, or just have some weird hook up?
Michaelwiggins, some universities have specific extension-like programs. I am from California, and in a circle of friends among whom it wasn't uncommon to take some summer classes at Stanford after junior year, during the summer - these aren't hookups or anything, I think these are classes made available over the summer. You may have to apply in order to do it and everything, but I think it was quite easily available, and certainly should be no problem if you're MIT caliber. I can't offer much more info than that, because I didn't choose to attend such a program.
So look into programs like this close to you, if you like, and only if you like.
Note that paying and taking classes may not help you much at all with admissions anywhere, so don't do it except for the enrichment and preparation.
Haha, yea, I wouldn't give up my decent-quality, paid-for-by-my-high-school, community college classes for marginally better, 1000 dollar university ones. I guess I was just kind of curious.
For a minute I thought that post said that 50% of MIT freshmen start in differential equations or higher. But thankfully there was no percent sign... that would be ridiculous
Students have all different sorts of options. Some high schools offer dual enrollment with a nearby community college/college/university for those who 'run out of math'. A very few high schools offer math in limited amounts past BC calc. Some students self-study (not generally a great idea), hire a tutor, or take summer courses. At least some colleges will let high schoolers take their normal summer courses,while others will only let them into courses intended only for high school students. A few even go the evening school route, although there isn't much advanced math there.
But the vast majority will not get any farther than calc - either AB or BC.
If you are aiming for top math/science schools, you will probably find that at least some math past calc will not transfer. You will have to sit a placement test of some sort at which point you may learn, somewhat painfully, that community college linear algebra is not equal to MIT linear algebra.
I don't know that a spring semester past linear at the CC will be very worthwhile. How about AP stat?
Replies to: On average, what is the highest-level math course that MIT students took in HS?
Somewhere in between top 5 and 10% probably have seen a significant amount of college math beyond calculus (e.g., number theory, analysis, etc.). Top 10% have taken multivariable calculus for sure. Sometimes people take linear algebra instead like you did.
Not sure what you mean by the top 10%, but some people come in with differential equations, some with higher. I knew a guy who came in already having completed the undergraduate math curriculum and started with grad-level classes.
Most of the time, the highest track in school is to take calculus senior year. If you are advanced on your own, you might end up taking it a year early and thus have a year to spend on multi-variable calculus or linear algebra at a local community college. If people have gone to special schools or have physicist parents, maybe you are beyond that, but you sure as hell aren't going to get it in the public school system.
For that reason, I suspect that the median entering freshman has taken multivariable calculus.
Why do I bring this up? The actual tracks you can take through college math are very varied, and you'll find that regardless of what random facts you know, it's hard to progress far rapidly unless you have what they call "mathematical maturity", which is certainly beyond just writing proofs. This maturity can be acquired in a hard class on something like MVC or Lin. Algebra or in something beyond, and I think what matters is when you get it.
There's a good number of people I know at my own school who did multivariable calculus and linear algebra in some form...but with such shallow understanding and so little mathematical maturity that they might as well just have taken calculus.
For top-ten percent, according to geomom's post here - http://talk.collegeconfidential.com/massachusetts-institute-technology/843128-mit-vs-caltech-admitted-both.html#post1063859093, I guess it would still be Calc BC, but they're more likely to have experience with like, math past single-variable stuff.
But as long as you're ready to take calculus by your freshman year in college, you'll be fine at MIT.
Beyond that, I don't think there is a meaningful "average." I've seen everything from basic calculus to "i've already taken every single undergraduate math course offered at my state university."
I think the mean would probably be AP Calc AB / BC, to be completely honest. If you're taking AP Calc AB, you're fine - we won't look down on you for not being good enough at math, but it also won't make me go "woah, look at their curriculum", eh?
Also I now realize I didn't phrase this well enough, since its hard to gauge how "high level" a math course is. I guess I figured Calc BC was probably the mean, but how about: How many people take a course /after/ Calc AB/BC?
And I guess while we're all here..lol... I've been wondering how some CC'ers manage to take math courses at their local universities, rather than community colleges? Do you have to take some sort of entrance exam, or just have some weird hook up?
Thanks again!
So look into programs like this close to you, if you like, and only if you like.
Note that paying and taking classes may not help you much at all with admissions anywhere, so don't do it except for the enrichment and preparation.
Comment: this may be because it wasn't taught and/or understood properly, which I find is notoriously the case quite often.
Note: These classes also tend to be expensive (~$1000)
But again, thanks everyone for your responses.
But the vast majority will not get any farther than calc - either AB or BC.
If you are aiming for top math/science schools, you will probably find that at least some math past calc will not transfer. You will have to sit a placement test of some sort at which point you may learn, somewhat painfully, that community college linear algebra is not equal to MIT linear algebra.
I don't know that a spring semester past linear at the CC will be very worthwhile. How about AP stat?