- #1

brushman

- 113

- 1

Right at the beginning of your freshman year? After your first semester? Beginning of sophmore year...?

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- Thread starter brushman
- Start date

- #1

brushman

- 113

- 1

Right at the beginning of your freshman year? After your first semester? Beginning of sophmore year...?

- #2

story645

- 675

- 2

- #3

eri

- 1,034

- 20

- #4

chiro

Science Advisor

- 4,815

- 134

Right at the beginning of your freshman year? After your first semester? Beginning of sophmore year...?

If while you're studying you see a problem and think you have a novel way to solve it then go ask your professors for guidance and they can steer you in the right direction and hopefully get you started.

You'll more than likely develop specific interests in a particular area. The lecturers will (hopefully) have the experience in what they are teaching and you can always get ideas for further reading which will hopefully generate ideas for possible further research.

It definitely in my mind takes a long time to see the forest from the trees. When I started doing math I had commercial experience in programming with computational geometry, AI, computer graphics and related areas. It took me a while to realize that most of mathematics could be boiled down to one thing: transforms.

When I thought in that manner, everything from proofs, to group theory, to calculus and analysis, topology etc made sense in a unified view of mathematics. Its not to say that everything is all about transforms but it has helped me see what the goal of what in my view most mathematics is about (ie starting with a representation, axioms, linear system etc and using specific transforms to end up at some point where an analysis can be made to solve the particular problem in some context).

Its probably going to be unusual for anyone to see the forest from the trees in their freshman year, but if your curious and take two step forwards and one step back, talk to your lecturers and fellow classmates, read the literature, and have some end goal in mind, you will most likely come across a problem, or generate an idea that directs you to something more specific. Typically though for this to happen we have to know a lot of math and then bring everything together of which our knowledge and reflect on it.

For me personally I'm researching a specific integral transform that relates discrete sum series with z being an element of the integers [ie Sigma f(z)] in both a finite and infinite domain to the integral representation where the domain is the real number (ie Integral f(x)dx where x is an element of the reals).

I wish you all the best.

- #5

jtbell

Mentor

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This probably depends on what field you're in: physics, math, computer science, basket weaving?

- #6

Chetlin

- 36

- 0

- #7

Gib Z

Homework Helper

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I've been allowed to accelerate some classes, one being Sophomore Real and Complex Analysis. Should I do well, they will allow me to do Senior Complex Analysis in the second semester. Say I go well in that as well, will I be able to do any research?

If I pushed myself and learned about Metric Spaces by the end of the year, then would I be able to do research?

- #8

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If you have strong grades by the end of your 2nd year and can devote extra time for research work or experience, then by all means, go find something to do. It will also give you plenty of time to know who's who in your department and who's doing what, rather than just blindly looking for something to do when you are new there.

Zz.

- #9

Vanadium 50

Staff Emeritus

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2021 Award

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- #10

jtbell

Mentor

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How exceptional is exceptional?

Surely someone in your department would be able to answer that better than us all out here?

Based on what you're taking now, I think you'd be considered "exceptional" for a freshman at most American universities, but things may be different where you are.

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