How Can I Best Spend Summer 2010 to Prepare for Future REUs and Grad School?

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Sophomores interested in pure math are exploring research opportunities, particularly REUs, but many are uncertain about acceptance. Alternative plans include seeking research positions at their home institutions or engaging in independent study to strengthen their math foundations. Some are considering contacting professors for potential projects or forming study groups with peers. There is also discussion about the value of summer courses, though concerns about cost and the effectiveness of self-study are prevalent. Overall, participants are seeking strategies to enhance their qualifications for future research opportunities and graduate school.
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I'm a sophomore interested in pure math who's been looking at an applying for REU's for the last 2 months (in fact, I discovered this forum while looking for REU advice), but I'm not going to be surprised if I'm not accepted into any of the programs.

My plan B is to try and get a research position at my home institution (which starts taking applicants after they know which majors were able to find REU positions) but that's not a sure thing by any means either.

In the event I find myself with no research opportunities how should I best spend my time this summer to get in a better position for 2011 REUs / grad school?

I was considering getting some textbooks and self teaching myself about an area of mathematics I'm interested in, or going back and filling any gaps in my understanding of foundation courses like linear algebra and calculus if I find myself with 3 months of time to fill.
 
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Hey!

I'm in the same situation as you.

I'd say my plan B will be to contact professors at my own university and see if any have a potential research project for me or if they know any other professors who could act as a sort of mentor.

Alternatively, yeah I guess I'll do some independent study, or try and form a study group with other friends who didn't get into research programs.

If anyone has any ideas, do share!
 
Are there any classes you could take over the summer that would be worth your time? A number of schools will let outside students take courses over the summer, so if you look around you may be able to find something.

Of course, the huge disadvantage to this is that it will be expensive probably, so I don't know if it'd be worth it.

I haven't heard back from any of the REUs I've applied to either, so I too am bracing myself for the possibility that I won't get into any of them.
 
I'm thinking about taking courses, but my department is pretty awesome at really getting me to understand the material completely, and it's not like I don't have enough time to take all the math I want from them (I'm done with distribution, so I have 14 to 16 courses left since I'll probably take a few courses off to write my thesis). So I guess I'm having trouble justifying the price of summer courses given the risk that I might end up with shaky understanding of the subject.

I suppose I could take the summer to reinforce my linear algebra and multi-variable in preparation for the GRE. Anyone have other idea's?
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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