Recent content by IGU

What you mention maybe doing pretty much describes what my son did. I pulled him out of school after 7th grade and he home-schooled until he went off to Cambridge to do maths. I've posted a number of times about various relevant things (search for Cambridge in posts I've made if you're...

Attending pre-frosh weekend at Caltech will make it completely obvious to you whether it's the right place for you. I'll be curious as to how you react to it. In any case, the experience is nothing like Berkeley or Stanford. Caltech is extreme, and populated by many extreme people. The...

Don't let all these responses that are suggesting you limit yourself get you down. You're young. You don't know where you're going to end up. If you have the time, as you seem to do, seek breadth to discover interests and depth to be sure of them. Don't choose classes so much for what the...

Yup, internalizing and automating the good parts of your parents is a large part of growing up. Good luck! You'll do fine wherever you decide to go.

No, this is spot on. This is what math is. Mathematicians spend most of their time lost, wandering in the wilderness. If you come away from hours working on a problem with no solution but perhaps understanding a bit more about the problem, that's mathematics. If you come away with a...

I'm a Techer, although from too long ago (mid 1970s) to have specific knowledge of what things are like now. But I've kept in touch and have met recent graduates, so I'm not completely ignorant. You've gotten some good advice. Be aware that Caltech doesn't admit students who can't handle the...

Calculus only has a couple of basic ideas, so you're unlikely to be missing much. Are you thinking you want to learn calculus as a mathematician, or to use it as a tool like a physicist? If the former, you'll learn what you need when you learn analysis; the calculus is just a warm-up to get...

ALEKS is useful for review, to check if students have any obvious holes in their knowledge, but it's not actually useful for learning anything well. If you want the best courses for students who love math and are good at it, check out Art of Problem Solving. My kid preferred the books to the...

Sure, it can be done. You have to be quite good at math though, as well as disciplined. My son started down this path, home schooling math from 8th grade on. He studied on his own, then branched out to taking an Art of Problem Solving class, then using their books, then auditing classes at...

Well, much depends on what you mean by understand. If you want to understand like a mathematician, then you'll have to spend your time figuring out proofs. Understanding consists of being able to prove everything forwards and backwards. You'll want to be able to do things like understand how...

Congratulations on taking control of your education! That's a big deal. Those are pretty good for taking real college courses. However you might want to look at Art of Problem Solving too as a good way to get a solid start on number theory, probability, and combinatorics. You see to have...

From my experience at Caltech (many years ago): many. From what I've read on the TSR forums from Cambridge mathematics students, many there too. Sure. It's always best to study material at your leisure in your preferred way. Lectures are a terrible way to encounter material for the first...

You didn't ask me, but I'll stick in my opinion anyway (hope you don't mind!). I think people learn best in different ways, highly dependent on the individual. Such a person as you describe is clearly not learning well from lectures. Indeed lectures are not a particularly good way to learn...

If you are going to avoid being "well rounded" then you're much more likely to get into a "not American" school. Cambridge gets quite a few Aussies.

I'll offer my son as an example. He self-studied starting in 8th grade when I pulled him out of public school in California. After five years of studying only math (much self-study, plus auditing (mostly graduate) classes at local universities) he went to Cambridge. He is now about to start...