Is it necessary to be precocious?

[TheUnbeliever]

First post -- hi, board!

I'd be hoping to go into academia in maths, but I'm slightly worried about something -- is it necessary to be precocious?; i.e. is it standard for entrants to university courses to already know some (significant?) part of the course they're about to take?

I ask because I would, from the research and knowledge I do have, like to take the Pure Mathematics master's at Edinburgh but I'm concerned because whilst I am quite capable in maths, and have never had any problem with course contents at school at any level, am placed in a very good top set, love maths, etc., I haven't actually got a great deal of knowledge beyond what I've been taught. I've taught myself bits and pieces of formal set theory, some linear algebra (although fairly limited -- just the basics needed to construct some basic view/world/projection/transformation matrices for some 3D rendering) and some calculus (differentiation, integration -- I'm guessing probably equivalent to a Calc-I course in the States; Higher in Scotland/AS level in England/Wales).

I compare this to my other strength, Computer Science, and realize that I know absolutely nothing in comparison (where I have studied significant parts of full under-grad courses and have a fairly decent knowledge of the formalisms and more abstract mathematics-based stuff involved) and wonder if I should be better than I am in maths.

I can sort of reason and say probably not -- surely it can't be the case that only the very relatively few that are not only capable in maths, but have had the time to expend on vastly forwarding their knowledge can succeed in the field?

Sorry -- this is a bit rambling. In short: how much general maths knowledge should I have as I start to head up the ladder?

EDIT: Oh, stage -- I'm 15, going into fifth year at high school.

 

[mathwonk]

don't worry, precociousness is only a temporary condition.

 

[chroot]

If you're doing calculus at age 15, you're going to have no problems at all in higher education. Being precocious is always nice, but your work ethic is much more critical. If you go to class, do your homework, and study effectively, you'll do fine.

- Warren

 

[arunma]

What Warren said has been my experience too. In either science or math, intelligence isn't quite as important as plain old hard work. It certainly doesn't hurt to be a child prodigy, but I know plenty of "smart" people who failed out because they didn't have the work ethic. I also know people of average or slightly above average intelligence who work hard, and advance quite far.

 

[mathwonk]

precocious means ahead of ones age. better to be competent, regardless of age. in calculus this means competent at the level of books by courant, or courant and john, or spivak, or apostol. best wishes.

 

[G01]

You don't need to be a child prodigy, don't worry!

 

[J77]

Just go with the flow -- if you're finding it easy, nice; however, don't push or overexert yourself at a young age -- let it come naturally.

 

[Terilien]

No it really isn't. I'm "precocious" but look at where I've ended up . Better to have a strong work ethic, combined with somewhat high intelligence. Also precocity is not necessarily synonymous with high intellect, just look at me!

Oh and you seem fairly precocious to me anyway!

 

[Ki Man]

You don't need to be a child prodigy, don't worry!

he already is

 

[G01]

he already is

I wouldn't say doing calculus at 15 makes him a "child" prodigy.

Maybe a better word would be an adolescent prodigy!
(I know, I know, that was bad, I'm sorry!)

 

[Terilien]

A child prodigy would do calc before he's eleven, quantum theory and general relativity when he's 13.

He is however, rather precocious. Maybe I have very high standards when it comes to mathematical prodigies. Alot of youngsters do calc and such when they're fifteen.

Again you probably won't have any issues...

 

[Werg22]

Precocious is a relative term. You can only be precocious if you compare yourself to others. I find it better to not care about your rank among others because mathematics is much like an art; every mathematician has his own unique view of things and ways of understanding, making comparison absurd. At the lower levels, one could be seen as "very good" in math by his peers yet have a very shallow and grotesque understanding of its substance.

 

[Terilien]

At the lower levels, one could be seen as "very good" in math by his peers yet have a very shallow and grotesque understanding of its substance.

Very well said. It unfortunate that high school is full of people like that!

 

[mathwonk]

ask yourself what it takes to be precocious at 65?

 

[Math Is Hard]

ask yourself what it takes to be precocious at 65?

hey, stop that! You're hurting my brain.

 

[G01]

hey, stop that! You're hurting my brain.

Your brain is a squeaky toy, Meatwad. It can't hurt!

 

[Math Is Hard]

Your brain is a squeaky toy, Meatwad. It can't hurt!

ha ha.. oh, yeah.. right, I forgot.