Hi i’m currently a high school freshman who is interested in going to Swarthmore. Right now i’m thinking of double majoring in math & econ. I had a few fears and anxieties that I wanted to talk with you about. So like I said before i’m interested in double majoring in math&econ but am worried because well currently I’ve already finished algebra 1 and 2 and am halfway through geometry(on khan academy) and am also taking AP calculus BC(also on khan academy). My anxieties are mainly about AP calc BC. So i’m currently learning about limits and continuity(for about a week) and am finding it a bit difficult. I could barely understand the concept of a limit and even when I thought I did I was wrong. I mean Khan Academy has great videos that are very easy to understand(apparently not for me). So my question is to everybody who majored/is majoring in math at Swarthmore. Should I be worried? Have you ever had this problem? What advice would you give me?
Thank you.
BTW: Sorry if my writing is unintelligible and sorry if my questions are a bit stupid.
Hey ultraboss101, please try not to worry too much about this right now. You are only just starting high school, and you have a long math road still ahead of you. You may be finding the concepts of limits and continuity difficult to grasp simply because you don’t yet have the proper foundations to understand them. Try not to be too discouraged, but rather try to diagnose the problem.
You say you have already finished Algebra 1 and 2, but believe me if you have simply worked through Khan Academy for those subjects you really haven’t finished them. Khan is great for a breezy, general overview, and I think his emphasis on intuition is great. However, it would be very difficult to gain a true grounding in any mathematics topic from Khan alone. You really need to work through some decent textbooks at the least, or at least online courses that are more rigorous.
I am a huge advocate of the idea that kids who have talent and are interested should advance on their own because I believe the curricula at most elementary and high schools are very weak. Tell us what you have done so far, and which materials you have used, and I am sure some of us can provide some more pointed advice!
Taking it on faith that this is a legitimate post, and you aren’t just messing around.
Worried about what? what “problem”? that you aren’t getting a math concept after a week of online videos?
My advice is to slow down.
What level math are you in at school? Have you done Trigonometry?
Counting this year (as it’s only Sept), you are SIX years away from declaring a math major at any college and 2 years away from when most future math majors will be doing Calc BC. Many students who end up as math majors don’t do BC until Grade 12 - or college, depending on what their school offers. And yet you are in a panic b/c, in Grade 9, after a week of online math videos you don’t understand a concept?
Calc is a conceptual leap from Alg/Geo/Trig. Think of the math skills you learn in those subjects as tools in a tool kit. You get to know how/when to use the hammer/screwdriver/wrench/etc.You get good at those skills (you know when to use a Philips head or a flat head). Calc is bringing the whole toolkit to bear on a complicated problem- first, you use this tool for this part of the problem, then a different tool for the next part of the problem, etc. It’s a different way of thinking, and for many kids- even really mathy ones- it is a push to re-orient how you approach a problem. This is not something to panic about.
Protip #1: the main thing about math is getting the foundation right. All teachers/teaching platforms will teach the same concepts and modules- but they can do it in different orders, laying out the path of understanding differently. If you jump between teachers and platforms you can end up with gaps that later come back to bite you- even if you are innately really strong at math (as my physics collegekid, who went to 3 schools in 2 countries between grades 8 & 10 discovered the hard way).
Protip #2: Swarthmore admissions will only be very mildly interested in your proposed major when you apply- they know that a third or more of students end up majoring in something completely different once they get to college. And they will pay 0 attention to your Kahn Academy coursework: it is your overall academic performance in school (and other objective achievements, such as IMO or AIME) that they will care about.
The reason why i’m worried is because students in top colleges learn things faster than average students. And here’s me wanting to go to Swarthmore and major in mathematics and I can’t learn a simple concept on Khan Academy. That’s the main reason why i’m panicking.
Guessing that you don’t see the paradox here: you see yourself as smart enough to know what is ‘simple’ in Calc BC - but are panicked that you are not smart enough to do it.
The collegekid I mentioned above had a melt down in Calc AB a lot like the one you are having. I strong-armed her into going to a tutor (which she interpreted as meaning that she wasn’t good enough in math- you can imagine how fun that conversation was for me…). The tutor spent about 45 minutes with her and came out and said that he had identified 3 specific elements that she simply didn’t know (probably from having had different learning sequences) and there was a conceptual leap she needed to make (he used the tool kit example that I posted above). She had one further session with him, and that was enough- she was fine, finished the course well, went on to major in Physics and minor in Math in college, and is now doing a PhD at Cornell.
You really don’t need to panic. It really will not help you to set up imaginary tests for yourself (“I can show that I can learn faster than ‘average’ students by doing lots of math online”). If you are having FUN doing Kahn Academy classes- do it. Don’t do it to prove anything to anybody. And if it isn’t fun, or if you aren’t getting it, don’t take it as a sign of failure. Put it aside and do something that is fun for you.
I didn’t study algebra 1 and 2 through Khan Academy. I actually studied them on a website called gifted and talented(I was neither). I think it was created by Stanford. Yeah so basically I just wanted to tackle some more advanced topics in math and see how I would do in them. I did a bit of precalculus(also on khan academy). My main fear is that well because it took me a week to learn limits(which is a basic concept in calculus) i’m not intelligent enough to study at Swarthmore. It was my assumption that students at these top schools learned much quicker than their peers. Is there anything else you would like to know?
To-may-to / To-mah-to. And just reinforces my point about math being a bad choice for doing randomly. Dipping into random advanced math topics to see how you do is NOT a good way to see if you are ‘intelligent’ enough for any school.
Imo, your assumptions are more wrong than right. Testing yourself to see if you learn random topics at a younger age than is typical, or trying to figure out if you learn faster than average doesn’t say anything about your overall capabilities- much less your suitability for Swarthmore.
Read these from MIT:
http://mitadmissions.org/blogs/entry/applying_sideways
http://mitadmissions.org/blogs/entry/being-qualified-for-mit
Like, MIT, Swarthmore looks for students who are learners- people who really enjoy getting stuck into learning about whatever they are interested in- and who tend to be very interested in things. If you have the stats (test scores, grades) for Swarthmore you are plenty intelligent enough to go there- but that won’t be what gets you in.
Please don’t ruin HS for yourself this way. Stop panicking about your ability to teach yourself a random bit of math online. If you love math, find ways to do it: clubs, summer courses, math competitions, whatever. Just don’t do it as a proxy intelligence test. The results- no matter what they are!- will not be meaningful.
@ultraboss101 - Just FYI, limits and continuity are actually some of the most subtle and difficult concepts in elementary calculus. A real understanding of the concepts - which you will not get in a typical high school or even college calculus class - requires an understanding of the construction of the real numbers. Continuity and limits at the conceptual level took over 2000 years to figure out (starting with Zeno and probably earlier ~500 BC)!
I am guessing that the Stanford GT program is what the old EPGY was, and if so that should have been a decent coverage of basic algebra. What math course are you taking in high school right now?
If you are curious about your aptitude for mathematics and you enjoy solving problems, I would suggest abandoning Khan for geometry (and for BC calculus) and convincing your parents to pay for the online course on geometry from AoPS (www.artofproblemsolving.com). My own kid is very advanced in mathematics, and took the AoPS course after having completed AP Calculus (in elementary school) and still found the AoPS course challenging and super fun. It might be worth looking into.
If you want to read a good introduction to limits and continuity that might pique your interest in “real” mathematics, borrow the Spivak Calculus textbook from a library and start working through the first chapters. Spivak builds up the treatment from first principles (similar to how it would be done in an Analysis class), so you really don’t need any particular prerequisites. The first few chapters of Abbott’s “Understanding Analysis” might also be helpful (the book will probably get too advanced though after that).
Good luck!