student_advice - Some advice to undergraduate math majors 1...

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Some advice to undergraduate math majors August 22, 2011 1 Introduction The advice below is sort of a list of suggestions of do’s and don’t’s that I thought I would write, to rectify what I think are unwise decisions that I see undergraduate math majors make all the time. Opinions may vary, so you should take what I write with a grain of salt – by all means, seek out other opinions. 2 The advice Math is a difficult subject, especially when you get to the senior-level and graduate-level courses. You have to have a capacity for abstract reasoning, patience, an ability to write proofs, creativity, and a strong work ethic. Furthermore, reading and working homework problems is not really what math is all about; those are meerly to train you to do “the real stuff”. Research math is mainly about being creative and discovering new truths, just like in the sciences; it is about proving new theorems, and initiating new research programs. Were it just about “knowing things” and “being able to work homework problems”, the field of mathematics would have long ago died away and become a subject for technicians. It is not about “teaching”, as most people unfamiliar with research math- ematics seem to think; though, teaching is certainly very important in the progression of the field – training new minds to become full-fledged mathematicians. 1
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How are mathematicians rated? They are rated by research, teaching, and service, in that order. Research is rated based on the quality of research papers, the journals in which they appear, the number and size of research grants one receives, and patents. Teaching is based on class evaluations, working with REU students, working with thesis students, and in some cases “outreach” (e.g. educating the larger community outside GT in some capacity). Service is mostly about “committee work”, but also includes such things as working with REU and graduate students. This is directed to the student who thinks they don’t need to attend any lectures, and think they only need to take exams and to turn in homework: If you miss the lecture, and if you are fairly bright, you may still get a good grade. This is because I cannot make the exams
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