There exists something called the Harvard College Mathematics Review, which "is a semiannual journal of expository mathematical articles written and edited by undergraduates." I learned about this from Vishal Lama's blog. (Conveniently, the how to link to a blog question is almost irrelevant here.)
The faculty feature article by Noam Elkies which was in their first issue, about the abc conjecture, is quite interesting. (I especially like the heuristics given therein for the number of rational points lying on certain curves and other solutions to diophantine equations -- concerning such questions as Mordell's conjecture and Fermat's last theorem -- which shouldn't surprise longtime readers.)
There have been two issues so far: the first issue and the second issue.
You know it's got to be good -- or at least it looks good from the table of contents and the few links I clicked on -- because I went to MIT for undergrad and I'm now a grad student at Penn and I'm still telling you about it. And you've got to love any publication which includes an article entitled Dunking Donuts: Culinary Calculations of the Euler Characteristic. I mean, who hasn't gotten hungry while doing topology? All those tori look like donuts.
And the editor-in-chief of the HCMR is Scott Kominers, who I've previously mentioned as one of the authors of a paper about whether or not you should wait for the bus.