Hi all!

I've posted here a few times before and remember these forums as being immensely helpful. Here's my situation. I've finished my first year of college as a pure math major. Technically I also am a computer science major, but I've recently come to the final decision to put all my focus on math, which means I'll probably be dropping the CS major at some point (whenever it keeps me from taking as many math classes as I please

). I definitely plan on going to graduate school in math.

I love math, and I really want to go to a math REU next summer. The one at Williams College is my top choice, but there are many that would be great.

I've done a lot of reading and studying in my spare time, so my knowledge isn't well represented by the classes I've taken. Nevertheless, the courses I've taken so far are calculus I-III, differential equations, and linear algebra. Next semester I'm signed up for analysis and abstract algebra. The semester after that I plan on taking complex analysis, topology, and hopefully another class, either number theory or abstract linear algebra.

Since I've got a year before applying, though, this schedule is malleable, but I'll have to finalize it soon (especially next semester's schedule). I thought I'd therefore ask here for advice on my schedule for next year.

I've spoken with my advisor about this, and he didn't seem totally knowledgeable about the REUs. However, he will also be the teacher for abstract algebra next semester, so I have my target set on him for a possible letter of recommendation.

So I'm basically looking for advice on what would be good to do with my schedule next year with the goal of getting into the best summer REUs.

I also have another specific question. My calculus III instructor (from last semester) was for some reason unusually impressed with me and even had the director of the Honors College here write me a personal letter congratulating me. Would a letter of recommendation from her be good for the REUs even though she taught calculus III (and not a higher course)? I'm asking now because she won't be here next year. In fact, she's not here right now, but she will be back for a bit in July, so that'll be my only chance; I'd have to have her write the letter this summer even though I won't be applying for a year.

But that also would pose another problem. I don't know how many or which REUs specifically I'll be applying to, so I'm not sure how I'd have her write the letter now.

I also have some general questions. Like I said, I love math. It's why I'm here. I know for a fact that I want to go to graduate school in math--there's no doubt about it. Honestly, I just want to learn as much about math as I can. If it was up to me I'd take nothing but math classes all four years.

That's not possible, though, since the math department requires a large number of non-math courses. I'd be in heaven if I could just take nothing but math classes, though. Perhaps this is asking too much, but would it be reasonable for me to request this possibility from the math department or at least request that I perhaps take extra math courses in place of the present requirement for non-math courses? I haven't spoken with the math department about this yet because I've been afraid that it could be considered "rude" or simply out of line or ridiculous. What do you guys think?

Finally, sorry for the length of this post and thanks for reading!