What does actually research mean

[sutupidmath]

I am going to be a freshman in the un of west texas this fall, i am going to study math, so i would really like to participate in any research project in calculus. But i do not really understand what this may look like. What for example could i be assigned to research as a freshman in calculus,(looks like impossible to me)??

thnx

 

[neurocomp2003]

- literary review or literary collection of a specific topic
- coding (more than likely)
- experimental work if applicable
- attempt to apply the knowledge you would get from the prof/references they provide on a specific topic.

 

[arunma]

I doubt it's possible to do research in calculus. Calculus has been a fully established branch of mathematics for more or less a century now. And while calculus is important to most areas of mathemathics, I doubt you could research it anymore than you could do research in algebra or trigonometry.

My research experience is almost exclusively in physics, but I can tell you a tad bit about what math research entails. From what I've seen, a good portion of mathematical research is computational. As Neurocomp said, this would mostly be coding work. I once did a theoretical physics project on analyzing electromagnetic wave propagation in the Earth's atmosphere, and basically I spend a couple semesters coding a program. I could see this as a project that could just as well be done in a math department. When I took a mathematical biology class, I also once had to write a research paper analyzing biochemical pathways in the cell cycle. Essentially I had to use Mathematica to numerically solve a series of differential equations, present graphs, and then qualitatively analyze what was going on.

So there are a couple types of research projects that you might find yourself doing as a math major.

 

[Data]

I doubt it's possible to do research in calculus. Calculus has been a fully established branch of mathematics for more or less a century now. And while calculus is important to most areas of mathemathics, I doubt you could research it anymore than you could do research in algebra or trigonometry.

Of course, to mathematicians algebra refers not to simple symbolic manipulation but to a huge class of subjects. You can divide mathematics roughly into three branches (though there's so much overlap and so many topics that don't quite fit that this is not a great guide): Analysis, algebra, and topology. There is a lot of current research going on in algebra! Calculus is part of analysis; while it'd probably be very difficult to find any ongoing research in calculus per se, there's obviously a lot of activity in analysis as a whole.

 

[fasterthanjoao]

And while calculus is important to most areas of mathemathics, I doubt you could research it anymore than you could do research in algebra or trigonometry.

Ouch, a large bunch of my lecturers just got belittled. Algebra is a tremendously huge area of research.

There is a lot of current research going on in algebra!

yep.

As for calculus, I don't think you're being nearly specific enough. Have you really even started calculus yet or just think the subject sounds interesting? For the calculus I've covered so far, it all reaches into applied mathematics (Physics-esque courses, etc.) whereas algebra and topology can be as abstract as you like. So if by 'research' in calculus you mean a potential undergraduate project, I'd consider something physical; say temperature distributions in a room or something.

 

[sutupidmath]

Ouch, a large bunch of my lecturers just got belittled. Algebra is a tremendously huge area of research.



yep.

As for calculus, I don't think you're being nearly specific enough. Have you really even started calculus yet or just think the subject sounds interesting? For the calculus I've covered so far, it all reaches into applied mathematics (Physics-esque courses, etc.) whereas algebra and topology can be as abstract as you like. So if by 'research' in calculus you mean a potential undergraduate project, I'd consider something physical; say temperature distributions in a room or something.

I have just self-taught calculus, as a means of getting prepared for college.

 

[arunma]

Of course, to mathematicians algebra refers not to simple symbolic manipulation but to a huge class of subjects. You can divide mathematics roughly into three branches (though there's so much overlap and so many topics that don't quite fit that this is not a great guide): Analysis, algebra, and topology. There is a lot of current research going on in algebra! Calculus is part of analysis; while it'd probably be very difficult to find any ongoing research in calculus per se, there's obviously a lot of activity in analysis as a whole.

Ouch, a large bunch of my lecturers just got belittled. Algebra is a tremendously huge area of research.

Heh, I guess I should have known to watch my mouth around you mathematicians. In my earlier post I made a rather glaring vocabulary mistake. By algebra, I was referring to arithmetic (i.e. high school algebra), in which there aren't any significant research areas.

But you are correct, rigorous algebra (the kind with fields, rings, etc.) is a heavily researched area in mathematics.

 

[gravenewworld]

when you copy from one source they call it plagiarism, when you copy from many resources they call it "research"

 

[J77]

Heh, I guess I should have known to watch my mouth around you mathematicians. In my earlier post I made a rather glaring vocabulary mistake. By algebra, I was referring to arithmetic (i.e. high school algebra), in which there aren't any significant research areas.

But you are correct, rigorous algebra (the kind with fields, rings, etc.) is a heavily researched area in mathematics.

Rigorous algebra?

A lot of research, which involves algebra, involves the use of simple concepts like addition and multiplication.

I don't think something qualifies as "rigorous" because it involves things which a smaller percentage have taken time to learn.

See http://www.elsevier.com/locate/laa for some examples of current research.

 

[mathwonk]

research is finding and solving problems. its like homework but the problems are harder, and you try to think of new questions yourself.

here is an exmple of a question that occurred to me a couple years ago while techig calculus. i knew that the indefinite integral of a continuous function was determined by its derivative nd one value.

but what about the indefinite inetegral of a riemann integrable funtion? a riemann integrable function f is continuous almost everywhere, so the indefinite integral would have derivative equal to f almost everywhere, and would be continuious.

question: does this determine the indefinite integral? it turns out not to. the indefinite integral is determined by being lipschitz continuious and hving derivative equal to f almost everywhere.

this turned out to be well known to analysts, but i still enjoyed discovering it.