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One of my acquaintance who is a math major undergraduate once told me that most students at his level focus on problem solving and ignored understanding proofs of major theorems, for example understanding the details of the proofs of Sylow theorems. He told me that the professors sometimes explain these kind of proofs but most undergraduate don't remember much of those. He told me that students have a better chance of acing their exams if they concentrate on solving/proving problems(with understanding) and forget about understanding difficult technical proofs because most are not needed for exams and there's not enough time to do both. How true is this? Thank you.

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closed as off-topic by user416281, Namaste, Badam Baplan, jvdhooft, José Carlos Santos Jun 12 '18 at 20:15

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  • $\begingroup$ Is this a question about mathematics? Maybe your question is more appropriate in Mathematics Educators. $\endgroup$ – Taroccoesbrocco Jun 12 '18 at 10:14
  • $\begingroup$ Oh I'm sorry. I didn't know there's a math educator stack-exchange. $\endgroup$ – QuirkyCat Jun 12 '18 at 11:01
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    $\begingroup$ Agreed that this probably belongs on matheducators forum, since the question is very broad and depends on the curriculum, teacher's expectations, and academic environment. $\endgroup$ – Badam Baplan Jun 12 '18 at 14:44
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This depends a lot on the student and also the exam/professor, but also the country in which you study. Usually in an exam you will have to solve problems, but also prove some major theorems.

I have heard that in the UK problem solving is usually typical for exams, while in Germany no matter how hard a proof is, you still have to know it for the exam.

If it is a written exam solving exercises will be the main part of the exam. If you however have an oral exam then you will have to do little to no problem solving and only understand concepts/theories, their theorems and you will have to be able to prove pretty much everything, no matter how long or difficult the proof is.

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  • $\begingroup$ Thank you for sharing it. I didn't know there's such a thing as oral exams for math. So I was wondering what this oral exam is like? Do you know before hand what proofs to concentrate on? And do you actually prove the required theorems in-front of your professor on the blackboard and demonstrate your understanding to them verbally? $\endgroup$ – QuirkyCat Jun 12 '18 at 10:58
  • $\begingroup$ You usually don't know which proofs to concentrate on, thus to be safe you should know the most/all of them. In general you would only learn the "important" proofs, a good indicator is when a theorem has its own name. You would prove the theorem in front of the professor unless it is a proof which is several pages long, then a rough proof with all the main ideas and concepts often suffices. The main idea being, that your professor sees that you understand the theorem and proof. $\endgroup$ – user564337 Jun 12 '18 at 12:39

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