Any tips on getting into a top tier grad school from an average

Kick ass on the GRE.

>>17877764
>by the time I graduate will have math up to diff eqs and linear algebra under my belt
lol these are really childish stuffs, but maybe your program doesn't use much mathematics.

>how to become more appetizing to these schools
you had 500 hours in the lab???? you better have glowing recommendation from your professor(s)!

3 things to focus on: letter of recommendation, grade, GRE subject test. I guess this is covered under LoR but it would be an advantage to have nailed down a research focus in your undergrad and produced some results. Sure in grad school you might change your direction, or even your field, but for now, since your school is not quite up there, this is what they will judge you on.

As a person who moved from a school ranked in the 80s who moved to a school in the twenties:

I was in the 97 percentile for the GRE, 3.7 GPA, a year of research experience, an internship, and one of the people who wrote me a recommendation was friends with one of the people on the committee, which I'm sure helped.

They say your statement of purpose is also really important, but it's hard to give tips on that. Anyways, I'd say the research experience is probably most important, probably even before your recommendations, because Grad school is about learning how to research, so already having experience with that is a huge plus.

>>17877824
>I'd say the research experience is probably most important, probably even before your recommendations
...Those two could be put under the same category of letter of recommendation. How does one claim to have research experience on a topic without a good LoR? You could spend a lot of time at the lab but if the recommendation is so so, the admission committee would think the professor has final say on your whole research. If you have good LoR this means you did something with an expert and he has a good opinion of you, that means productive research experience. The weirdest case I could think of is guy doing independent research, and directly submit them to the admission committee. Then again, even in this case, realistically, they would at least give some professor in the field a look first to get their opinions i.e. a LoR.

>>17877764
Professor writing here.

I'm not in your field, but I've been on grad school acceptance committees.

Assuming you've got the grades, the single biggest piece of ammunition you've got is your letters of recommendation. Choose your letter-writers carefully. They have to be able to say more than a generic "He was in my class and got an A". You want the person whose lab you worked in to talk in specifics about your skills and dedication, and give examples of your independent thinking. You want one of the people on the paper you might get your name on to talk specifically about your contributions to the research. The more specific and detailed the letter, the better.

That said, you're right in thinking the competition for top-tier schools will be heavy. Go for it, but have a couple of second-tier applications out there as well. Good work is being done in some of the leading State universities, and remember that on the PhD level it can be more important what specific professors you'll be working with than what university they're at. Somebody doing cutting-edge work at the University of Midwestern State may have more to offer you than someone past his prime at MIT.