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I am a Graduate student in Mathematics and in second Year. I have three qualifying exams in topics Abstract algebra, Real and Complex Analysis and Algebraic and differential topology.I already appeared for two times, but I didn't clear even a single subject and got very low grades. I will have a one more attempt and final attempt in January. Since I want to do research in Mathematics, but I failed in qualifiers I lost my hope completely now. Can any one suggest ideas so that I can improve myself and help me to prepare for the next qualifiers?

Thanks in advance.

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Although questions change, the topics examined tend to be pretty stable. So a deep familiarity with past qualifying exams at your university is very useful. –  André Nicolas Aug 20 '12 at 7:11
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I think the best people to ask for advice are the math faculty at your university. They know you, and they know their exams, far better than anyone here does. –  Gerry Myerson Aug 20 '12 at 7:22
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I do not know if this helps you, but I have found that the work which got me furthest was to try to write accounts of parts of mathematics which were as clear as possible to myself, and which explained what the subjects were about. The composer Ravel suggested: "Copy: if you some originality, this may come out in your copying. If not, never mind." You may have to write or copy several times before the real ideas get over to you. Also you can try explaining to others, if you can find someone who will listen. These are some ways of getting the wheels of the brain turning! –  Ronnie Brown Aug 20 '12 at 9:38

2 Answers 2

As Gerry Myerson said, it is probably best to talk to your professors, as they are (hopefully) personally acquainted with you and write the exams. A source of guidance I have been using when I don't have someone to ask is Steven G. Krantz's book A Mathematician's Survival Guide: Graduate School and Early Career Development. The book has a few chapters which concern the topic of qualifying exams, so perhaps there is some bit of information in there which might be of use to you.

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That's a very nice book. –  Siminore Aug 20 '12 at 8:09

Another thing to do is to figure out why you did poorly on the exams. I had a friend in grad school who was very able, but did not put in the preparation necessary to pass the exams. Each time, she simply put in less time than was necessary to make sure that she understood the material at the level needed for the exams. (She went on to another university, passed the exams, and is on her way to a Ph.D.)

I would ask the other students that have passed the exams about their preparation. You should see if you are putting in the same amount of effort and studying the right content.

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