What to do during summer?

Question

So I just finished my 2nd year as an undergrad majoring in mathematics. I plan to continue on to a Ph.D afterwards, but only recently did I realize how behind I was... I haven't done any research, completed any projects or summer programs. I haven't done any outside reading so I don't really know much about any particular subject. Everyone I know in my program has at least something, so I'm worried that I'm really late in preparing for grad school.

I know I should probably consult a professor or advisor, but school's ended already... and admittedly, I've been a little apprehensive when talking with professors since, well, I don't really know anything in the first place, and I know they're very busy, so I eventually just awkwardly ask some questions and leave ASAP having not understood much.

In short, I'm just very confused and don't know what to do from here on out... so any advice would be great.

Answer 1

I haven't done any research, completed any projects or summer programs.

That's okay. You've only just finished your second year of undergraduate studies.

I haven't done any outside reading so I don't really know much about any particular subject.

That can be remedied! How about taking some summer classes in a community college, in a branch of science that intrigues you?

I've been a little apprehensive when talking with professors.

You're going to need a bit more chutzpah in order to get your money's worth out of college and graduate studies! Perhaps you could transition into feeling more comfortable with professors' office hour visits by focusing primarily on visiting the office hours held by grad student teaching assistants for the time being.

It is very common for second year students to be hit hard with an appreciation of how little they know. Try to ride this storm of self-doubt while reminding yourself of that fact.

It would be great if you could find one or more mentors, either on your own or through a matching-up program. The mentor might be a faculty member who serves as your undergraduate advisor -- the person who checks your proposed schedule and advises you about what courses to take next year, etc.

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Edit 5/20

There are several ways to break the ice.

Ask for some undergraduate advising -- s/he will check your unofficial transcript against your proposed schedule for next semester. Make sure you have this conversation in this person's office, not over email, because what we want to happen is for the professor's natural mentoring instincts to kick in, so that one thing leads to another.

In the experimental sciences, one can ask for a tour of his/her lab. You might want to ask your question over at Mathematics Education as well.

Spend some time reading the research descriptions of the faculty in your department, to see whose area intrigues you, then take a look at some of their papers. When you find one that gets you intellectually excited, make an appointment like this: Dear Professor So-and-so, I've been reading your "title of paper", and wonder if I could make an appointment to come in and talk with you about this area of research?" Or something like that. Researchers love to talk with people about their work.

To get matched up through a formal matching up program, you need to look closely at your department's website, or ask your department administration if there is such a thing.

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During the school year, attend lots of seminars. Be bold about chatting with grad students over cookies afterwards. If no one is bringing cookies, juice and paper cups, bring some!

Answer 2

If any of the other suggestions provided by excellent people here doesn't suit you, then a fallback option I would recommend is instead use the semester to plan your future strategies for next semester and prepare yourself to be more comfortable in implementing it come fall!

I would suggest picking a class/subject in your major that you will preferably be taking next semester. Then don't wait - start now! If you don't know what the course is really about (I know I rarely do in advance!), you can try to meet with a professor who will teach the class, with a department chair, or with your adviser, or you can write a short email. Let them know you want to get a jump on the next semester to prepare yourself for advanced studies/research in the future. If a general class schedule or syllabus is available, even better!

Then set yourself a nice schedule for the summer - giving yourself plenty of time to actually relax and recharge your batteries for the coming semester - and get cracking! Next semester you should be generally better prepared and be able to learn the subject deeper and more readily than others, rather than scrambling to learn what you need to keep up. You should hopefully be able to ask more insightful and interesting questions, participate in class, and maybe also go to office hours and ask even more advanced questions about the material to move towards mastery. With the extra prep you'll likely be able to also do better grade-wise.

All this extra contact and work will not only improve your education, but if you have been shy this can be your first deeper connection with a professor. After you've had time to work with them and become more comfortable, and if things are going well and they are recognizing you are a good and dedicated student who wants more than just a degree and to move on, then you will be in a great position to ask them about research options in the future - or for recommendations/introduction to another professor who you might want to work with.

You can also apply this same "show up, participate, ask questions, go to some office hours/meetings" strategy to other classes, and begin to make more contacts - naturally! It's much less stressful than it seems at first, and you might develop some valuable skills and meet some really cool people. You can then repeat all this strategy the following semester as well, and begin planning for doing research/independent study during a semester or over summer if that suits you.

Finding people you work well with and have more advanced connection to you beyond just class will also conveniently be able to help you with getting research, work with you when you hit more advanced topics, and as a bonus can also be the source of future reference letters which are actually useful because they know you outside of class!

Rather than panicking, I'd suggest you take a deep breath and instead work to prepare yourself so in the following semesters and next summer you will be ahead of the game rather than behind. And if you continue to follow through and put in the effort and use good strategy, you'll find yourself likely enjoying the process more, having better connections, being more prepared, and generally making the most of your education - and maybe even being in a better position for an advanced degree, too.