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My life story's mostly just about teaching myself...basically everything.

Note: I sorely apologize for the unnecessarily long post. You'd probably do better by not reading it.

I wasn't good at math until I got to 8th grade...I had horrible teachers before then, and couldn't even multiply or divide fractions or do long division. But I learned algebra that year, and then went on to high school.

Freshman year of high school I had a really good geometry teacher, but that was about it. She gave me a book - Zero, by Charles Seiffer (sp?) - which I read religiously. In the back, it had the formula for the derivative of a function. I spent the summer learning what a function was, how to do limits, and applying the derivative formula to *every* function I could come up with.

Sophomore year I took Alg. II and precalc, as well as AP chem, and took the AP calc BC test on my own (since my school didn't have any calculus class). By then I had learned that you don't have to do *everything* from the definition of the derivative, which was nice.

Junior year, I took AP physics B (all my school offered), but I took the AP stats and physics C (Mech and EM) tests. I started studying differential equations that year, too.

Senior year, I just kinda coasted, as far as classes go. But when it came to the AP tests, I took bio, enviro. sci, comp sci AB, english language, and english lit. My school didn't offer enviro sci or comp sci. I also took 3 courses at the community college senior year: intro philosophy, east asian religion and philosophy, and partial differential equations.

So, during high school, I taught myself a great number of subjects...'cos that works in high school. That, and I had an absolutely horrible high school: 80% dropout rate, 5% of all students go to college, 75% under the poverty line. So, coming to Princeton was a totally different experience.

When I got here, I was at the bottom of the pack in *all* subjects...and I still didn't know if I wanted to do math or physics. So, in the past two years, I've had
5 physics courses (Newton mech, EM, lagrange and hamilton mech, grad quantum I, and experimental)
6 math courses (single-var analysis, linear algebra, multivar analysis, algebra with Galois theory, Fourier analysis, and grad course in noncommutative algebra)

And my grades have been mediocre, until recently. Almost everyone in my math classes had introductions to analysis very early on, or at least didn't have to teach themselves the prerequisites. I had never been in a math or science competition, my school didn't have a math club, wah wah wah. Point is, I'm finally getting to the point where my peers don't have several more years of experience in the subject than I do.

Upcoming courses: complex analysis, differential geometry, political game theory (my "humanities" course), grad course in QFT, and independent work in knot theory (a seminar).

I should think you would be ahead of your classmates just of how you taught yourself everything. Not a lot of people do that. and I'm taking complex analysis in the spring term too!

Where i'm from you can legally drink from the age 18. Not that I've actually gotten drunk yet. Just something about putting all those chemiclas iny our body, that do all sorts of crazy things. Same reason i don't drink coffee.

Oh, and my current calculus professor is probably the reason I am studying maths. his wife taught at my primary (elementary) school and he used to give the school supplementary material for the bright students (ie me). He even taught me the guitar for two years.

Though that supplementary material is probably the reason i was so bored the first year of highschool (I knew it all already) i still wish the school had let me skip that maths and go to the next level up. And when i was 15 i spent most of the time in maths teaching everyone else what the teacher was trying to teach them
(she was one of those super smart people who has problems teaching the really basic stuff, as it just seems so basic to her)

You're a kitty! Yes you are! And you're sitting there! Hi, kitty!

Yeah, that differential geometry/GTR course I took was definitely a highlight of my college career so far. GTR is just so beautiful.

Oh joy, life stories.

Born in Germany, moved around a lot, etc, etc, I eventually found myself in a selective high school in Sydney, Australia.
The NSW HSC doesn't have much in the way of advanced courses. There is no AP physics or equivalent, etc. Eventually I graduated after doing next to no work all throughout high school, with enough marks to get into the course I wanted, and not much more.
This is a trend that has continued through Uni so far, with most of my time going into co-corricular activities, such as the circus society, and sitting around being bored. I still haven't failed anything from doing no work, which is likely what I'd need to make me start actually putting effort in.
I am lazy.

Near the end of that I found out about the various Olympiads, and ended up getting into the scholar schools for informatics and physics. Informatics I couldn't go to, physics was good fun, and you ended up being taught basically the entire first year physics course in two weeks.


I'm currently an undergraduate studying a combined Computer Engineering/Science degree, and I'm planning on majoring in physics for the science.
Yay for five year degrees.
So far however, it's been all computer engineering except for the engineering physics.

On a personal side, I like physics, but have done very little self-study in the area, so my knowledge is basic Uni level, ditto maths.
Programming I am very interested in, and have been competing in programming competitions for many years, as well as the whole degree thing.

And they let you into Princeton? ;P
But seriously, how did you not see any proofs if you taught yourself calculus?

Green's Theorem, Stokes's Theorem, Schwarz's (Clairaut's) Theorem? All of those involve proofs, and there are a number of exercises in calculus books that involve proofs besides epsilon-delta derivative proofs. And let's not mention the fact that most of elementary calculus could be taught with proofs integrated right into the curriculum (believe it or not, sometimes it is). And what do you mean "wouldn't stand up to rigorous inquiry"? Are you saying it's invalid or false? Theorems, formulae, and other content in any calculus class is most likely just as valid as what you get in a more advanced math class, and would stand just as much "rigourous inquiry."