Math education before University?

[Noxide]

On average, I would like to know how deeply some of the more mathematically inclined university students have delved into higher mathematics before attending university. I am in the top 5 for marks in my courses, but having talked to others in the top 5 I discovered that they had been doing the material covered in our courses many years prior to taking said courses. Am I at a disadvantage relative to those students even if our grades are the same? I only discovered the beauty of math at the beginning of the year. Is it too late to pursue attendance at a respectable graduate school given that I did not express an interest for mathematics prior to university? Please give me your thoughts and perhaps the level of mathematical knowledge you possessed before entering university.

 

[rs1n]

On average, I would like to know how deeply some of the more mathematically inclined university students have delved into higher mathematics before attending university. I am in the top 5 for marks in my courses, but having talked to others in the top 5 I discovered that they had been doing the material covered in our courses many years prior to taking said courses. Am I at a disadvantage relative to those students even if our grades are the same? I only discovered the beauty of math at the beginning of the year. Is it too late to pursue attendance at a respectable graduate school given that I did not express an interest for mathematics prior to university? Please give me your thoughts and perhaps the level of mathematical knowledge you possessed before entering university.

Unless these other students went to summer programs or did their studying in some sort of program (i.e. there is some paper trail documenting their mathematical endeavors at an early stage), I do not see how any university would know for certain that these students did math on their own without actually interviewing them. I think you're fine.

That said, there is no reason to not begin your own appreciation of mathematics by branching out on your own while still in high school.

 

[Gib Z]

If your marks are the same, then your performance is seen to be the same. This is despite whether or not a grad school somehow knows the other did some topics earlier. If you continue to get top marks, there is no problem. The only way a disadvantage may arise is with a difficult class where you may struggle to grasp all the concepts firmly in such a short amount of time, whilst the other student in that case has a better ability to get higher marks.

Most courses are designed so that you have the opportunity to get high marks even if it was your first time learning it, but some set the difficulty higher and get a lower average. In those cases, the person who knew the content already may find it easier to get the stellar marks. But note this doesn’t mean it’s impossible for you, perhaps just a bit harder. It’s never this extreme, but say you had an entire Calculus course crammed into 4 weeks for some reason (which is similar to how some Uni’s cram Abstract Algebra into a single semester in my opinion), then the student who hasn’t learned it before will have to step up to a large task of understanding such a load in such a short amount of time, whilst someone who knew it already will still quite easily get very high marks.

This is a minor issue to think about; the best you can do is to think about learning as much as you can from now on. Don’t let the focus to accelerate through topics, but to understand each solidly. That’s very important. Grad schools don’t look at who knew the content in some sort of fashion as quickly as possible; they look at who knows the content most solidly at the moment! (as well as research potential). It so happens that I am probably one of the students you are talking about, but unless it really interests you, I don’t think knowing how much other people knew will help you, especially in light of what I’ve just told you. Good luck in your studies, and wish me luck in mine! =]

 

[Sankaku]

Grad schools don't care about what you did in High School. If you do well at the material you are working on right now and have continuing motivation to work hard when you get to undergrad, you will be fine.

 

[Noxide]

I suppose I did not get my point across very clearly. I am in undergrad right now, and I've started doing some research on past great mathematicians out of interest and found that many of them had a passion for math from an early age. Since I did not have this passion until very recently, I am just wondering if it's too late to become one of the greats.

Thanks to all the posters so far.

 

[jeffasinger]

It is entirely possible that you are joining too late in the game to be the next Euler, but I would not let that discourage you. It is definitely not too late for you to learn a lot of mathematics, and help advance the front of human knowledge in some field of math a measurable amount. That is still a possibility, and a worthy goal.

From my understanding of it, if you take a lot of math as an undergrad, do well at it, and do some research, you will get into a PhD program in Math.

 

[Sankaku]

...I've started doing some research on past great mathematicians...

While it is good to enjoy the history of mathematics, NEVER compare yourself to people like Euler, Gauss, Poincare, or Riemann. You will only despair. The good thing is that you don't have to be Gauss in order to make meaningful contributions to any field (if that is what you really want). The cult of genius can be very damaging for healthy motivation.

 

[Gib Z]

In my opinion, whether you are going to join up with the greats isn't even decided by how early you get into math, but the brain you are born with. If you don't have their gift, you won't be at their level even if you apply yourself from the day you are born.

That said, does it really matter? It's not like you've spent your whole life thinking you were going to be one of the greatest contributers to mathematics, and you definitely shouldn't aim for that. Just aim to contribute the best you can, and if knowing that, yes you probably won't become one of the "greats", becomes some sort of deal breaker for you and depresses you continually, I'd suggest finding another field to work in.