Hello! Welcome to the Math Club website. We are a student organization for anyone interested in mathematics. We meet every Tuesday at 5pm in Innovation Building E327.
On December 6, I gave a presentation to the UVM Math Club on applying to graduate schools and REUs, and getting strong letters of recommendation. Here is a page collecting the links and information I presented.
A worthwhile pursuit during your undergraduate degree is to do some research with a faculty member. While you will be expected to contribute to the project, mostly with hard work and sweat, it is the job of the faculty member to help you find a project to work on and give you guidance on how to solve it. It is fine to go up to a professor, tell them you enjoy their work, their teaching style or their personality, and ask if they have any research opportunities! (Although if you do not know the professor well, you should expect to get no answer or an answer of no. Supervising undergraduate research is difficult work for us.)
Opportunities to do undergraduate research at UVM:
The National Science Foundation also funds programs called REUs (which stands for Research Experiences for Undergraduates). These are typically summer programs where the student is paid to work on a research project, possibly in a small group with other students, under the supervision of a faculty member. You can search the full list of funded REUs for opportunities that interest you. The typical deadline for a summer research experience is in March but can be as early as the beginning of February. The application typically requires a personal statement, so you should give yourself at least one month to complete this work.
If you generally enjoy school or you are not sure what to do after undergrad, you should ask yourself if you would like to go to graduate school. In most technical fields in the United States, you will apply for PhD programs right out of undergrad (without first getting a masters degree). Again in most technical fields in the United States, the degree will take 5 to 7 years, and you will be supported by a small stipend (tuition remission plus ~$15-20K salary per year) which should allow you to go to graduate school without depending on others financially or taking on any debt (but without becoming rich either). Going to graduate school can be some of the most fun you will have; you will be surrounded by other people who love your area of study as much as you do, you will have time to think and learn (if that does not sound like heaven, grad school is not for you!) and you will become an worldwide expert in a topic you and your advisor have chosen.
Note that this does not mean that you should go to graduate school. Despite being great, grad school is also terribly difficult. You will spend months or years (yes, years!) being stuck on a problem and feeling incredibly stupid. You might feel isolated from people you used to know, especially as they get jobs, buy houses and start families. You will need to be creative and self-directed; no one will know the answers to the problems you are thinking about. Completing graduate work requires intelligence and talent, but mostly hard work and perseverance.
Deadlines to apply can be as early as December 1. This means that you should be thinking of applying to graduate school throughout the fall semester of your senior year. Given how much we have to do during the semester, I would even amend this to say that you should be actively thinking about this in August before your senior year, with the possibility of even taking the GRE subject test in April of your junior year.
Here are a few resources with further reading, which will go a long way towards demystifying the process and giving you advice on how to put your best foot forward:
Typically a graduate school application will require some letters of recommendation, a personal statement, and your GRE scores. Sometimes a school will have more exotic requests, such as a list of courses you took, maybe with the textbook you used and/or the topics covered. Start keeping this list early.
For your personal statement, do not hesitate to reach out to a mentor or a letter writer for help and advice. I will quote Prof Daugherty here because her advice is great and worth emphasizing: "Be explicit, sincere, positive, and concise. Don't be self-deprecating. Be mindful of your audience (senior mathematicians evaluating your potential success in mathematics). Be professional, but not overly dry—let the reader know who you are, without inadvertently offending a stranger." and "Start early. Have your friends and mentors read your statement for you, and edit, edit, edit. Make an appointment (or several) with the UVM Undergraduate Writing Center." (At the UVM Undergraduate Writing Center you can get a one-on-one appointment with a writing tutor. If your statement cannot be read by a non-technical person, it needs to be edited!)
By now you will have noticed that to apply to everything you will need letters of recommendation from faculty members to support your application. A typical application will ask for three letters of recommendation.
Obtaining three letters of recommendation might seem daunting, which is why you should start thinking of this early. As early as your first year, make a habit of attending office hours, asking questions in class, and speaking to your instructors before or after class. No one will write for a student they do not know, and the longer the faculty member has known you, the better their letter should be. This advice goes double for any faculty member you especially get along with or for someone teaching a class you are doing well in. Those people are those who are most likely to write you a great letter, and you should cultivate your relationship with them meticulously. During office hours, try and ask some questions outside of the purview of the class: Ask about the person's research (their research interests are usually posted on their website), ask a question that is slightly outside of the scope of the class... Anything to get a scientific conversation rolling and show your interest and intellectual maturity.
An impportant point to keep in mind when emailing faculty members is to use the appropriate title in addressing them. Anyone who has a PhD should be addressed (at least) as "Doctor Lastname" in a first correspondence. Please please please refrain from using Mr., Mrs., Ms. or even worse, Miss! A professor is a doctor who also has a certain kind of faculty position at a university. A professor should be addressed as "Professor Lastname." Note that some faculty members here at UVM are professors and some are lecturers; most faculty members will list their title on their website. When in doubt, always use the highest possible title; this means that you should default to "Professor" if you are unsure.
When the time comes to ask for a letter of recommendation, do everything you can to make your letter-writer's life as easy as possible. Several people have written excellent pages on the information they require from students to write them a letter. Read a few of these and follow the spirit of their guidelines as much as possible. A strong letter comes from a content faculty member!
While the information below is specific to people interested in mathematics and statistics resources, there is a chance that your field has similar resources available. Please contact a faculty member in your area of interest to ask if anything similar is available. Another good option is to look up any professional societies in your field to see if they maintain any content directed at undergraduates (they almost certainly do!).
The math major at UVM is designed to be flexible so that you can use it to reach your goals. If your goal is to go to graduate school in pure mathematics, I will collect here whatever advice I can to help guide you and make the best out of your time here.
Many associations collect information of interest to undergraduate students interested in mathematics. Take advantage of their hard work!