Undergrad High schooler Develops new Integration Technique

[glennbruda]

Hey, that's me haha! Thank you everybody for the constructive criticism and kind words, I really appreciate it. If I had a chance to rewrite the paper now, I would make a lot of changes, but I suppose that is what revisions are for.

Honestly, I'm a little surprised he's going to U of Florida. Nothing wrong with it, but he would probably have no problem getting into CalTech, MIT or Princeton, and would benefit from having more brilliant peers at schools like those.

Both of my parents are UF alums, I already know a few professors there from the process of writing this paper, I've been a Gator all my life (sports aren't the most important to me but it is a plus), and the cost of those colleges is extremely high. It just made sense for me to go to UF; perhaps I'll go to one of those colleges for grad school.

Maclaurin Integration's formula is too big and lengthy, but computer scientists can make an algorithm based on it to find the integrals of functions that can't be integrated by other techniques.

Nice job Glenn Bruda!

I concur. Perhaps a powerful mathematical engine such as Mathematica or WolframAlpha could incorporate such an algorithm in their database. Thank you!

 

[jedishrfu]

Welcome to PF!

Its impressive for one so young to have a published math paper. It seems the first paper is always the toughest one.

Have you taken the MAA tests or the Putnam yet?

Often young math talent take them as part of their education into challenging problems with twists and turns.

 

[glennbruda]

Welcome to PF!

Its impressive for one so young to have a published math paper. It seems the first paper is always the toughest one.

Have you taken the MAA tests or the Putnam yet?

Often young math talent take them as part of their education into challenging problems with twists and turns.

Thank you! I'm writing my second right now and I agree that it is significantly easier.

I have not; I never was a big fan of competition in math in general. I find that such a discipline is more elegant when people work together rather than against each other. Additionally, I don't like the time pressure aspect of such competitions usually. Perhaps I'll try the Putnam competition though, having a limited amount of very challenging questions given a lot of time seems palatable. Thanks for the suggestions.

 

[jedishrfu]

Yes so true on the competitions. They can never delve deeply into some problem and instead rely on the student noticing some insight above and beyond what they learned in traditional math courses. I took the MAA once and was lucky to get a single problem right.

My friend on the other was quite talented and became an MAA champion and was on a team that competed internationally with England and Russia. They failed miserably mostly due to the test structure. The US MAA was a multiple choice affair where you could strike out some non-answers and focus on the reduced set and make an educated guess. The international test was fill in the blanks for which the English and Russian teams routinely tested on.

The English in particular have the Tripos tests which students study for like crazy often using experienced tutor coaches. These tests dictated where in the hierarchy of academia you stood. The math tripos was the oldest of these tests.

https://en.wikipedia.org/wiki/Mathematical_Tripos

I think it was GH Hardy who lobbied for changes in these tests as he felt that they had held England back a hundred years or more in mathematics as compared to Europe. Basically the English were focused on applied math (tripos type problems) and Europe was into rigorous proofs and pure math.

https://en.wikipedia.org/wiki/G._H._Hardy

 

[ergospherical]

The English in particular have the Tripos tests which students study for like crazy often using experienced tutor coaches. These tests dictated where in the hierarchy of academia you stood. The math tripos was the oldest of these tests.

Tripos isn't competition maths but rather the name given to end-of-year exams at undergrad level. Nonetheless there are still a few oddities (if you top the maths tripos then you're designated the senior wrangler).

 

[glennbruda]

Yes so true on the competitions. They can never delve deeply into some problem and instead rely on the student noticing some insight above and beyond what they learned in traditional math courses. I took the MAA once and was lucky to get a single problem right.

My friend on the other was quite talented and became an MAA champion and was on a team that competed internationally with England and Russia. They failed miserably mostly due to the test structure. The US MAA was a multiple choice affair where you could strike out some non-answers and focus on the reduced set and make an educated guess. The international test was fill in the blanks for which the English and Russian teams routinely tested on.

The English in particular have the Tripos tests which students study for like crazy often using experienced tutor coaches. These tests dictated where in the hierarchy of academia you stood. The math tripos was the oldest of these tests.

https://en.wikipedia.org/wiki/Mathematical_Tripos

I think it was GH Hardy who lobbied for changes in these tests as he felt that had held England back a hundred years or more in mathematics as compared to Europe. Basically the English were focused on appplied math (tripos type problems) and Europe was into rigorous proofs and pure math.

https://en.wikipedia.org/wiki/G._H._Hardy

That's another thing that irks me about mathematics competitions as you alluded to in this post; the style of the test greatly influences the score of a participant. If the competitions were focused purely on mathematical skill, then theoretically each participant would do just as well regardless of format, but this is not the case.

Thanks for the links for the reading, I found them quite interesting.

 

[jedishrfu]

Tripos isn't competition maths but rather the name given to end-of-year exams at undergrad level. Nonetheless there are still a few oddities (if you top the maths tripos then you're designated the senior wrangler).

Quite true, I was thinking of the senior wrangler title too but then decided that it wasn’t germane to the discussion.

 

[MevsEinstein]

The style of the test greatly influences the score of a participant. If the competitions were focused purely on mathematical skill, then theoretically each participant would do just as well regardless of format, but this is not the case.

I very much agree. I don't really like math competitions, but that's the only fun math activity at my school, so I decided to join the school math competition. This is the same thing for many other people.

 

[nuuskur]

If the competitions were focused purely on mathematical skill, then theoretically each participant would do just as well regardless of format, but this is not the case.

Perhaps, it is not correct to assume that pure focus on technique implies uniform results. Math competitions are certainly focused on technique.

 

[MATHSTATMARXLENIN]

I found the paper meaningless,,,I Don't know how this Intimidating formula containing 3 different dummy variables is avoiding " calculation nuisance ",,,,I still would have accepted it if he could use that formula to evaluate the exact values of integrate 0toinf e^(x^2),,,which is pi/2,,,,but he leaves the answer as the intimidating series