If you are interested in deepening your education in the mathematical sciences beyond the fundamentals provided by a bachelor's degree in mathematics, then you should consider graduate school. This page and the resources it links to address key issues about graduate school in mathematics. Your adviser and other members of St. Bonaventure's Mathematics faculty would be happy to guide you as you contemplate these issues.
Graduate Degrees
There are three graduate degrees available in the mathematical sciences: the master's degree, the professional science master's degree, and the Ph.D.
A Ph.D., or doctorate, typically takes four or five years and prepares the student for research. The path to a Ph.D. includes taking classes, passing qualifying exams, and completing a dissertation. Matt Might, professor of Computer Science at the University of Utah, has a wonderful pictorial description of a doctorate in computer science, which applies equally well to a doctorate in mathematics.
A master's degree typically takes about two years and does not require passing qualifying exams nor completing a dissertation.
The professional science master's (PSM) is a relatively recent innovation in graduate degrees. According to the Professional Science Master's website, the PSM is “designed to allow students to pursue advanced training in science or mathematics, while simultaneously developing workplace skills highly valued by employers.”
Differences Between a Graduate and an Undergraduate Program
The are two main differences between an undergraduate education and a graduate education. First, a bachelor's degree in mathematics from St. Bonaventure provides you with a foundation in mathematics as part of of a liberal arts education. You take Clare courses, language courses, and other courses in addition to math courses. By contrast, in graduate school, you'll focus entirely on mathematics. Second, most students pay for their undergraduate education. However, most graduate students in the mathematical sciences do not pay for their education, because they have teaching assistantships or research fellowships which include full tuition.
Preparing for Graduate School: Inside and Outside the Classroom
The pillars of the math major at SBU are Abstract Algebra I (MATH 341) and Introduction to Real Analysis I (MATH 351). These pillars rest on the foundation provided by the three-semester calculus sequence (MATH 151, 152, 251), Discrete Mathematics I (MATH 207), and Linear Algebra (MATH 241). All of these courses are required of any student majoring in mathematics.
A major in mathematics also includes nine credits of math electives numbered 252 or higher. For the student bound for graduate school, Complex Variables (MATH 453), Topology (MATH 486), Abstract Algebra II (MATH 342), and Introduction to Analysis II (MATH 352) are all highly recommended. Taking all four of these courses would fulfill the math electives requirement and three credits of free electives. If you're unable to fit all of these courses into your schedules while at Bona's, it's not a big deal—you can simply take the ones you miss during your first year of graduate school.)
Participation in a summer Research Experience for Undergraduates (REU) would give you a taste of graduate school while you're an undergraduate and looks great on a resumé.
The Senior Comprehensive Project, the capstone requirement for the major in mathematics, provides superb preparation for graduate school. To get the most from your project, choose a topic that relates to more than one course. Your faculty mentor can help you select such a topic.
Resources
Each year the Math Department receives ads for several graduate programs in mathematics and allied disciplines, which we place in a wall-mounted binder just outside of the Math Suite. For a complete list of graduate programs, consult the book Fellowships and Assistantships in the Mathematical Sciences. This annual publication lists graduate programs by state, and for each program, provides the number of teaching/research assistantships it gave last year, the stipends for the assistantships, and the number of PhD's the program produced in each of eleven topics over the past three years. We keep the most recent editions among the student resources in the Math Suite.
The SBU Career and Professional Readiness Center has a wealth of resources about graduate school.
The Mathematical Association of America provides the following valuable online resources about graduate school in the mathematical sciences.