As a 2nd year undergraduate, what should I do to enhance my maths grad school application if I don't get into noteworthy summer programs?

Question

Sorry for the long title, but I just received some of my marks for the semester including a C+ in a programming course and F in a cell biology course) and am worried that have ruined all my chances at getting into summer program (I'm in Canada, so I'm looking at the few US REUs that accept foreign students on a limited basis).

What should I do if I don't get into any summer activity to help my graduate school application if I want to pursue mathematics? I'm in second year and haven't taken too many higher level maths courses, so I don't know how that would look when applying for NSERCs at my school.

I was thinking of maybe just doing some reading in mathematics and working on some personal projects that may help me look like I can actually do something on my own. I am also currently self-learning combinatorics and graph theory in the hopes of working with my discrete maths prof who does combinatorial optimization (and has asked and received my CV already).

If anyone has any advice as to what I can do to enhance my grad school application if I get rejected from everything I apply to? I feel ridiculous for doing badly this semester as it was just too much to handle and doesn't reflect my work ethic at all. I want to redeem myself but don't know how? Thanks in advance for the advice!

Answer 1

If you have one bad semester, particularly just a couple of bad grades in non-major courses, it's not going to torpedo your PhD application, though to show it's not a concern, you should do very well in your major courses, taking what advanced courses you can.

For the summer, programs such as REUs can help broaden your perspectives. These are also nice because they give you money and a chance to work with other interesting students. However, another common option is to find a professor, say at your university, willing to work with you over the summer on a reading course or a research project (possibly informally). Several of our faculty do this semi-regularly (I usually travel in the summer, though I've done it a couple of times), sometimes with a group of students, so try asking around in your department.

I personally think reading courses are just as good, if not better than, most undergrad research projects because at your stage the most important thing is to learn a lot of math. While you can just read things on your own, a professor's guidance can be quite valuable. Also it will provide an opportunity for you to get a more meaningful letter of recommendation, which is very helpful in applications.