Reminder that CC is not a debate society. A number of posts hidden. Please get back to the OP, move it to PM, or start a new thread.
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Hopefully also helpful to OP, MIT does publish a list of summer programs where “If you’re the kind of student who’d like to spend your summer learning as much hands-on math, science, and engineering as you can, you might be a good fit for MIT!.. that offer compelling intellectual content and a rigorous educational approach”
Again to avoid any debate, it is for OP to decide whether these programs constitute spending your summer doing more academics.
Another point is that OP’s question was if this level of math were “good for MIT” and not only “good for MIT admission”. Let’s hope that OP’s child is admitted. Is there no disadvantage to being in an environment where a large fraction of your fellow students are more advanced in a discipline that is intrinsic to your interest (ostensibly math, engineering or CS)? Wouldn’t OP’s child have an easier, more enriched experience having access to more than the most basic Calculus 1 course, and an easier time meeting the curve against the brightest tech students in the world? We’re talking about a tech school here, and if it were my child, I’d want them to have access to the top that MIT could offer including access to the most rigorous classes and the biggest fish.
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Parent of a child admitted to MIT (but who chose to go elsewhere). The students admitted to MIT from our high school (typically 1-3 students each year) invariably have taken the highest level of math that the high school allowed.
For a number of years that meant BC in junior year, followed by MVC and Linear Algebra at a nearby college. Now it is BC in senior year. Nothing more is needed.
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These summer programs are a far better use of the summer than taking a class past Calc BC.
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Just in terms of understanding your post, exactly which of the recommended math camps would be accessible to someone who doesn’t have a trajectory past Calc BC? My understanding that Linear Algebra with Proofs, Discrete Math and the other co-requisites or pre-requisites for all of these programs are “past Calc BC”.
Not sure how all of these programs that stress “taking math beyond the classroom” jive with the argument that we need to keep math in the high school?
There are two ways to answer this question.
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If a student is stretching their math ability to the limit in high school, to the point that Calc is a challenge, then few of the camps are appropriate.
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If a student finds high school math easy, then any of the camps could be appropriate depending upon the skill of the student, even if the student doesn’t get beyond Calculus in high school.
Math camps tend to focus on topics not covered in high school, or covered only briefly. Topics typically include number theory, combinatorics, probability, advanced lessons in algebra, or contest prep for AMC 10/12, AIME, or USAMO.
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To clarify for OP, the MIT admissions website states that "MIT does not require applicants to take advanced courses beyond what is commonly available in high school. In the same light, Harvard states that AP classes are not mandatory, but can show interest in advanced fields. This is a bit different from what has been said here that MIT does not “expect” applicants to take advanced courses.
MIT admissions goes on to list 9 specific math camps and many other programs that are highly competitive and focus on “Exploring mathematics beyond the scope of what is typically taught in the classroom.”
OP is free to decide, if the top Technical school in the World is the target, whether their child wouldn’t benefit from a bit more than the high school curriculum lottery has provided them. My MIT friends, more than 3 decades after graduation, were up at 1am chatting about the different kinds of infinity and why Cantor’s diagonality theorem was incorrect. That’s the context I’m familiar with. If OP’s child really is a great fit for MIT, isn’t it plausible that they would want to take accelerated math?
Most of the programs listed on that page do not require Linear Algebra or MVC—many do not even require Calc BC prior to attending. My daughter was admitted to one of the mathematics ones but did not attend (it was COVID and virtual) in the year she was taking Calc BC. She attended another one of the science research ones and, although she had taken Calc BC by that point, it was not required. We also looked into several others on that list and were familiar with the requirements.
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I guess I was misled that we were talking about scooping ice cream and folding sweatpants for the summer so as not to be a one-dimensional academic wonk. If we’re talking about the choice between studying combinatorial proof vs. studying Calculus BC, both sound like what I’d expect for someone headed to MIT.
What isn’t being said is that no one jumps into AMC, AIME or USAMO without a pretty deep introduction to AoPS or the like. And that’s not exactly “only what the high school offers” either. Both paths (acceleration or competitive math) that are part and parcel of every program on the MIT list require substantial commitment to extra math. Outside of the classroom. Outside of the high school curriculum.
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You introduced the point that MIT does value math extracurriculars. That has long been true.
I believe the reason that MIT values the math camps over something like MVC is that quite frankly, the math camps listed are much more of a challenge than MVC. A child competing for USAMO can likely handle MVC by sixth grade. The extraordinary math skill is demonstrated to MIT through these math camps and the AMC exams, not MVC.
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But not everyone is interested in competitive math. My nephew is in 6th grade and is completing Linear algebra after getting an A in Differential Equations and a 5 on the BC calc in 5th Grade. We know some gold medalists with special prizes at the IMO and IPhO. They liken the preparation to the spelling bee or a varsity sport. My nephew isn’t that interested in that aspect of math at this point. He is interested in analysis, and he’s using the MIT Opencourseware to supplement his graded linear algebra college class to make sure he has exposure to proofs, but competitive math and the training involved is not an interest. He’d rather play baseball and chill with friends for those 3-4 hours a day.
He wants to major in applied math and “become one of the astronauts that stays in Houston” for NASA. Pure math beyond analysis is just largely irrelevant for that. He probably doesn’t want to go to MIT, but I’m not sure it’d be a bad fit. For students like my nephew, acceleration is the sensible approach. How many times does one have trouble grasping a concept all semester and the summer after, it all becomes clear? For anyone who doesn’t want to solve the Collatz conjecture or spend 7 years in isolation to come up with a 600 page proof of Fermat’s last theorem, acceleration seems quite rational. No?
My son estimated he knew 40+ math kids entering MIT one year. It was certainly a skewed group, but it wasn’t all math contest kids. The others were kids who had published research in math or kids who did math camps like Ross, PROMYS, Mathily or HCSSiM, which don’t focus on contest math. It’s likely that MIT accepted some extraordinary kids like your nephew, but he didn’t mention any like that.
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Please stay on the topic that the OP asked about.
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I think we agree. All the types of kids you mentioned make total sense for MIT. And I know some kids at MIT like my nephew including one recently admitted from our area. The data shows that most of those AIME / USAMO and PROMYS kids are also pretty darn accelerated as well.
All good data points for OP to consider in making a choice with their child. I guess my point was just that in a situation where a child is already going into Junior year to start precalculus, the ship has sailed for programs like USAMO and probably for PROMYS. So is trying to accelerate a bit such a bad thing to demonstrate a passion for and commitment to math? Especially if it’s above and beyond the norm for their school?
I asked that posters focus on responding to the OP’s query, not on continuing side discussions. If posters want to discuss other matters, they are invited to start their own threads on these matter.
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Greatly appreciate the discussion and your (and others) comments on this topic. I am in a similar position as OP in terms of what the school offers. My son is excited about taking advanced math, but has shown no interest/ excitement for competition math.
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I am not aware of us admitting a student who did not demonstrate mastery of at least some calculus in high school since I started working in our office in 2009 This is definitely something that has changed since @DadTwoGirls was an undergrad; it’s not clear that 18.01 can really be taken these days by students who are coming in with zero calc.
Right, the way I would describe it is:
- we effectively require some form of calculus in high school (or testing equivalent, e.g. those who self-study for AB or BC and take the tests without ever enrolling in the class, international students with olympiad performance demonstrating mastery, etc)
- once you have that, we don’t require any more advanced math than what you’d encounter in your high school, but we do typically like to see students who are pursuing the most challenging math curriculum available to them at their school, because 1. it advances preparation and 2. it may (depending) demonstrate that they really want to keep learning hard math and science (and be a good fit for MIT)
Well and it may indicate match, i.e., if you are the kind of kid who likes spending your summer at nerd camp (complimentary), you might like MIT.
We have no expectation of competition math. As @hebegebe said, competition math is one way that students can demonstrate a particular kind of national or international talent in a certain kind of mathematics, but it is only one way and only in a certain kind of mathematics.
You say that juniors are automatically assigned to precalc and then AB or BC as a senior, and your daughter might attempt to accelerate a year. What would she then do as a senior?
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