For mathematicians who are admitted to a Ph.D. program, some (like myself) are treated to a strong dose of humility. The universities' math departments quickly proceed to screen their Ph.D. students in such a way that- within a few years- about 1/2 of them ultimately drop out of the program. The method of screening such students is the qualifying exams, which the graduate students dreadingly refer to as "the quals." Students must pass courses, but professors usually pass most of the students in their courses; "the quals" are the main obstacle students must overcome. Most of the problems on the quals are of the form "Prove that..." or "Show that ...." Preparation for the quals requires incredible memory capacity- memorizing all of the proofs that might potentially be covered, and incredible devotion to spending sufficient hours studying them. Ph.D. students are usually offered 4 years of "funding", which consists of a small salary (about $13,000 back in 1997) and free tuition as payment for TAing undergraduate math courses. TAing involves leading about 4 discussion sections per week, holding 2-4 office hours per week, and grading tests and quizzes. I remember TAing as the most enjoyable part of the program. However, "funding" is contingent on following the timeline for passing "quals"; once a student falls behind (which happens to most), they are subject to losing funding, being bumped down to the master's program, and ultimately removed from the program. The Ph.D. program is described in the universities' catalogs as a 4-year program, of which the first 2 years are spent passing qualifying exams, and the last 2 years focus on completing the dissertation. Very few (if any) of the Ph.D. students- even the successful ones- ultimately follow this timeline. Most of those who complete the program require 3 to 4 years to pass all of the quals. Only then are they allowed to begin work on the dissertation, which takes another 2 to 3 years. Those who ultimately complete the program typically do so in 5 to 7 years; thus, they are lucky to be done with school by the age of 28 or 29.
Whereas college allows for a healthy balance between studying and participating in the social and cultural life on campus, successful completion of the Ph.D. program requires intense immersion in mathematics and self-isolation that is excessive to some of us (like myself). Here is where I must diverge from those who completed the program and will ultimately become leading researchers in mathematics. This blog is for mathematicians who- like myself- left or chose not to enter the "ivory tower" so to speak, and realize they must function in the "real world."
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I am an undergrad who is on ur way to the world of math. I am in my third year and i just switched my major from bio to math. any suggestions for me?
ReplyDeleteMy suggestion- based on my own experiences and current philosophy concerning lifestyle, etc.- would be to ideally secure an entry level position after graduating college, and delay graduate school until after your career direction is becoming clearer. I personally would not pursue a graduate degree in mathematics, having found that graduate-level math is not valued outside of academia and perhaps a handful of government positions in the DC area. A graduate degree in a related area (MBA, engineering, computer), perhaps obtained while working, is probably valuable.
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