Transitioning from undergrad to grad school

[~Death~]

hi
im a pure math major and going into my sr year next semester

im supposed to apply to grad schools sometime next year as well, but I have

a problem. I don't think id have a problem getting into a program my GPA is 4.0 in all

my math courses and I've taken quite a few including some in topology algebra number

theory analysis linear algebra complex analysis and logic and i think i have a good basic

understanding of these courses (a lot of which are prereqs for grad school level courses)

But, grad school is different ...youre moving from doing generic textbook problems to having

to choose and write a thesis topic

I find this really intimidating ...considering the greatest geniuses in human history have

been studying these subjects for centuries to think that I should be expected to come up

with something semioriginal myself is intimidating

And this isn't a small decision ...whether I should go to grad school or not, it costs money

takes time and what subject i choose to puruse after undergrad will determine my

future career choices! So I'm scared to say the least

So I've decided that my best option is to take this summer and see if i can write a mini

thesis. If I can at least write something down to my liking then I'll know that I have

the potential to go onto grad school, but if I can't I am not sure i want to risk it

and maybe ill choose a different subject to major in

The only problem with that is, I've never been told how to start a thesis, or even how to choose a topic...I googled and found undergraduate research experiences offered at various universities --mine does not have these unfortunately.

So I am basically wondering if someone could help me choose a topic and give me some suggestions/insights on where to start. I'm willing to read and research different papers and books in the topic area myself ...but as I've said i only have undergraduate level knowledge in these subjects

Thanks for any help

 

[MathematicalPhysicist]

Look at it this way, even Einstein, Bohr, Feynman, etc, were once freshsers like you, in writing scientific articles...

A good way to pick a subject is by reading survey articles (mostly popular and not overly technical because you still an UG) of experts in different areas, and see if the problems there seem interesting to you.

 

[davesface]

Where, specifically, would one go about finding such survey articles?

 

[MathematicalPhysicist]

You can check through google.

type something like: "A survey of open problems in combinatorics" or whatnot, and you get quite a lot of pages describing research and open problems.

Or otherwise you can check handbooks which cover open problems, such as one handbook on open problems in Topology, I forgot its title.

Or otherwise look at websites of leading researchers, they might have written some introductory notes on their research areas.

 

[RandomGuy88]

It sounds to me like you have no research experience which is really important for graduate school. I think instead of trying to write your own thesis you would be better off doing research with a professor at your university or through an REU. That way you would know what it is like and what you would be getting yourself into when you go to graduate school. I do not think it will be very productive for you to just try to pick a research topic when you have no experience and no one to guide you.