Note that college mathematics and “highest level” high school math camps are quite different topics.
If you’re truly interested in competitive math camps, they all cover similar material to AIME/AMO/etc., which as defined as high school math topics (algebra, geometry, number theory, counting), not including Calculus. Look at the camp material and none/few study linear algebra, MVC, DiffEq, etc. As mentioned above, they explore deep topics associated with the defined four topics. Olympiad-level geometry (mass point, barycentric, cyclic quadrilaterals anyone?), sophisticated counting/combinatorics (totient function?), algebraics/inequalities (Chebyshev?)
Iirc, the captain of D22’s math team when she first joined, a 2x IMO Gold medalist and recent Putnam Fellow, didn’t take beyond Calc in high school. AoPS and similar resources drove his learning.
I agree with the above - this should be driven by a passion for, and enjoyment of, math, not “looks good for college admissions”. I’m fortunate that D22 shares my love of competitive math, and it’s certainly something we’ve bonded over, through the years.
My son, a junior, did calc AB in 10th grade and is now in calc BC. We didn’t rush him, he chose to take certain classes at a slightly accelerated pace and we supported him. For senior year we will have him take something at the local community college.
Will it help with college admissions? I think only to the extent it shows serious interest in the subject and showcases a strength. Agree with some of the other posters here that getting into competitions like IMO will definitely be a differentiator and look good on the college app.
Such is the nature of these forums that reaching calculus three grade levels ahead and finishing calculus two grade levels ahead is seen as “slightly” accelerated.
As a general comment, the users on College Confidential are by no means a statistically representative subject of college-bound students and their parents.
Hi @mathkids! One other thought I had for the OP is do you think it would be a good use of time to start playing around with LaTeX? I think my S22 used that at MathILy and then for his PROMYS entrance exam and I think it could have helped him get in? Was that used at MathCamp?
Knowing LaTeX is definitely a useful skill, and OP’s son may like playing around with it. S22 was actually required to use LaTeX for homework assignments for one of his college classes. He too wrote the solutions to the Mathcamp entrance problem set in LaTeX. It wasn’t needed for Mathcamp itself unless one wanted to participate in the student run LaTeX competitions
Thank you for mentioning this. He has not learned LaTeX yet, but he has started to look at it. It hasn’t been essential yet, but yes that’s a question (maybe an easy question) - do other people find that LaTeX is expected (or at least helpful) for those things?
Funny you should mention that. My S22 does his math homework on a white board, sends a photo to the teacher and then erases it. It is a whole new world.
LaTeX is useful only if you major in Math in college, and writing proofs etc. Not otherwise. Poor use of time in high school. Also what kind of math your student should do, and how fast would depend on their end goal. Is Math itself the intended major? Or is Math just a tool for an engineering or an economics major?
Don’t think that’s true anymore particularly if the student is interested in any type of research in fields as diverse as economics and biology. Write any paper based on any sort of research where any mathematics is involved and LaTeX is liable to come in handy.
LaTeX has been around since the 80s. It’s a tool one uses if s/he needed to produce a document with lots of formulae/equations to be more professional looking than Microsoft Word Equation Editor (or the discontinued Aldus/Adobe PageMaker in those days) could. Desktop publishing was in vogue then. LaTeX was useful for submissions of articles/papers to professional journals, but it wasn’t required. These days, there’re a lot of “self-publishing” (including submissions to places like arXiv) and LaTeX is the default tool for many. However, LaTeX has nothing to do with learning mathematics!
As someone who wrote their PhD thesis in LaTeX back in the dark ages (late 80s/early 90s), there really weren’t any good alternatives back then. The ability to use equations in Word was drastically less sophisticated and didn’t allow for appropriate justification and line spacing. So you really had no choice other than to use LaTeX for a math PhD, I don’t know anyone who didn’t.
You’re right that theses (not just in math, but also in other quantitative sciences) were often produced in LaTeX then. And they still are today. For submissions to professional journals, the use of LaTeX was encouraged but not required (and I believe it’s still the case today). The professional journals have people who can help with editing and typesetting. A lot of submissions these days don’t have (at least initially) professional editing/typesetting, so the use of LaTeX becomes more widespread.
My son was in an advanced math track and is now a Math major at college. Took Calc AB in 10th, BC in 11th and did Linear Algebra and an independent Advanced Math class in 12th. He tried to place out of AB in 10th, but looking back it was a good thing that he didn’t. At the time, it felt like he was rushing through concepts just to skip ahead. By not skipping (and he was already on a fast track), he lay down a better foundation.
He didn’t do math camps (we live abroad), but did participate in national math olympic competitions for several years. IIRC, you dont necessarily need advanced calculus for those competitions (I would even argue that solid geometry and Trig background are more useful).
When he got to college, he placed into Honor level classes for Math majors and was able to place out of Intro level, though there are plenty of others in his major that started with the Intro level courses. While he’s ahead of some of his math cohorts, I haven’t seen a huge benefit yet…though I’m guessing he might have better access to research opportunities.
It is a whole new world.