|Photo: Ricardo Cortez|
You are about to start an unforgettable part of your life. What you will soon realize is that the first year of graduate school is a time of important transitions in the way you study, the way you think about mathematics, the way you think about yourself and the way you think of your professors. Below I offer some suggestions of what you can do this summer in order to be better prepared for the transition to grad school.
Review what you learned in your Real Analysis course: Regardless of the area of mathematics you end up choosing for your dissertation, Real Analysis will play a key role. This is why the great majority of PhD programs will require that you pass an Analysis exam. Don’t just rely on the fact that you took an Analysis course as an undergrad. Review this material during the summer before you take a graduate Analysis course.
Understand the requirements of your program: Most PhD programs have requirements that include written exams (Qualifying exams or Preliminary exams), an oral exam, a specific number of course credits, and a dissertation. Your program has a list of such requirements and the times by when they must be satisfied. For example, the written exams must be passed typically during your second year, sometimes sooner. Make sure you know exactly the requirements of your program and when each must be satisfied. Verify your understanding with the graduate coordinator or chair of the department...
The most significant transition that you will make in graduate school is to go from being the student who is good at solving problems you are asked to solve to becoming the researcher who understands what the next problem that needs to be solved is. This requires understanding the bigger picture of where the problems fit. It helps to get comfortable talking to your professors about math. As a professor I am constantly looking for graduate students that are making this transition.
Source: AMS Blogs