What Are the Expectations for Graduate Students?

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Discussion Overview

The discussion revolves around the expectations placed on graduate students, particularly in relation to the nature of assignments and the emphasis on proofs versus computational problems. Participants explore their experiences transitioning from undergraduate to graduate studies and the implications of these expectations on their learning and understanding of mathematics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether a perfect graduate student should be able to prove every theorem in the recommended textbooks, noting a shift from computational questions in undergraduate studies to a focus on proofs in graduate assignments.
  • Another participant shares their experience of being expected to prove major theorems for qualifying tests, citing specific examples like the orbit stabilizer theorem and Cauchy-Goursat theorem, which can require extensive proofs.
  • A different participant reflects on their initial dislike for proofs, attributing it to a lack of familiarity and skill in constructing formal proofs, but later expresses a newfound appreciation for them after taking relevant courses.
  • One participant mentions their intention to read a specific book on proofs, indicating a proactive approach to improving their skills in this area.

Areas of Agreement / Disagreement

Participants express varying views on the expectations for graduate students, with some agreeing on the necessity of proving theorems while others reflect on their personal journeys and challenges with proofs. The discussion does not reach a consensus on what the expectations should be.

Contextual Notes

Participants highlight the differences in assignment types between undergraduate and graduate levels, indicating that expectations may vary by institution and individual experiences. There is also mention of specific qualifying tests that may influence these expectations.

Who May Find This Useful

Graduate students in mathematics or related fields, educators in higher education, and individuals interested in the transition from undergraduate to graduate studies may find this discussion relevant.

Sudharaka
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Hi everyone, :)

Stuck in a terribly difficult assignment I came to think of the following. What is the expectancy level from a grad student? I mean in undergraduate assignments we were given more often computational type questions, if we are given proofs they aren't so difficult. Then in grad level I found that it's the other way around. Almost always we have to prove things. Some are in fact equivalent to theorems in the recommended textbooks. Is it that the perfect grad student need to be able to prove every theorem in the book? What is your idea about this? :)
 
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Sudharaka said:
Hi everyone, :)

Stuck in a terribly difficult assignment I came to think of the following. What is the expectancy level from a grad student? I mean in undergraduate assignments we were given more often computational type questions, if we are given proofs they aren't so difficult. Then in grad level I found that it's the other way around. Almost always we have to prove things. Some are in fact equivalent to theorems in the recommended textbooks. Is it that the perfect grad student need to be able to prove every theorem in the book? What is your idea about this? :)

I original was doing pure math in grad school until I realized I prefer applied. If have you qualifying or similar tests in your country, then yes you will be expected to prove major theorems in order to progress to candicacy or get your MS. At my school, for example, some of the old qualifiers would have prove the orbit stabilizer theorem on it as a question as well as Cauchy Goursat and some other big theorems. Those type proofs can be about 3 pages long.

My idea is to me it sounds about right.
 
Two years ago , I used to hate proofs. In the calculus book we were asked to prove simple results but I didn't like solving these types of questions. I think the reason is that I didn't get used to doing these stuff and I lacked the ability to analyze and construct formal proofs. After taking some courses on proofs , they are now may favorite questions. When you see the wording of a theorem in real or complex analysis you realize it is written with care.It has to follow the laws of logic .I believe that proofs are just like computational problems you have to get used to them and prove as many theorems as you can.
 

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