Expectations in Graduate Level

[Sudharaka]

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? :)

 

[Dustinsfl]

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.

 

[alyafey22]

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.

 

[Petrus]

After taking some courses on proofs

Thanks this post made me think! After doing some research I think I find a book I have to read in summer!
How to Prove It: A Structured Approach:Amazon:Books

Regards,
\(\displaystyle |\pi\rangle\)

 

[Matrix0]

I understand the frustration and confusion that can come with transitioning from undergraduate to graduate level assignments. In graduate level studies, the expectations are higher as we are expected to have a deeper understanding and mastery of our field of study. This often includes the ability to not only solve problems computationally but also to prove theorems and concepts.

The reason for this shift in expectations is due to the fact that in graduate level studies, we are expected to contribute to the advancement of our field. This requires us to have a deep understanding of the underlying principles and theories, which can only be achieved through rigorous proofs and critical thinking.

While it may seem daunting at first, I believe that this shift in expectations is necessary for our growth as scientists. It challenges us to think beyond just solving problems and pushes us to understand the fundamental concepts and their applications.

So, to answer your question, I do not believe that the perfect grad student needs to be able to prove every theorem in the book. However, it is important for us to have a strong understanding of the core principles and be able to apply them in our research. With practice and perseverance, we can all improve our ability to prove theorems and contribute to the advancement of our field. So don't be discouraged, embrace the challenge and keep pushing yourself to become a better scientist. :)