Questions tagged [graduate-education]

For questions related to studies for graduate or more-advanced students and courses.

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20
votes
2answers
252 views

Pressure vs. Laissez-faire: Literature dealing with balance in university-classes

I am seeking for some pedagogical literature dealing with the following question: Imaging you have an average class in college/university: What is a good balance between Laissez-faire and pressure? ...
32
votes
3answers
3k views

What happened to the Moore method?

I always read about the Moore method with great enthusiasm. Somehow I always felt that it should be how we do it in an ideal world, but it is impossible to use because of time and other constrains. ...
9
votes
1answer
164 views

Learning modulo sticking points, or “fluid study” in mathematics

In graduate school I once tried to rapidly learn mathematics by working through a text and collecting (and precisely remembering) where I had been stuck, and what parts of arguments or computations I ...
9
votes
1answer
200 views

What courses should be a part of a Mathematics Education degree program?

I had asked the title question in an answer here, but it didn't get any recognition, so I'm posing it formally. The key word in the question is should. In my Mathematics Education degree education, I ...
2
votes
1answer
190 views

Can I be a Maths Teacher? [closed]

I'm 26 and hold a 2.2 degree in Biomedical Science from a British university. I took my A Levels in Biology and Chemistry but only got an AS Level in Maths and Art. My work background is that I have ...
6
votes
1answer
258 views

How to propose subjects for bachelor's theses?

I have recently ended up in a position where I can supervise bachelor's and master's theses, and there has been some discussion in my research group of organizing thesis supervision within the group. ...
2
votes
0answers
170 views

How to choose a good PhD student in pure mathematics? [closed]

I have some personal criterion to choose my graduate students including PhDs. Here I would like to know what my colleagues' criterion are to choose their math PhD/MSc students. I hope this may help me ...
24
votes
4answers
2k views

What are some good examples to motivate the implicit function theorem?

I always had problems when teaching the implicite function theorem in advanced analysis courses. This result is motivated by later applications, but it would be great to be able to provide easily ...
9
votes
5answers
453 views

What to do if there is a disagreement on fundamentals, e.g. axioms or inference rules?

Sometimes it happens that a person doesn't want to accept your argument, because he claims not all the inferences are valid. There's a famous example of Lewis Carroll, namely What the Tortoise Said to ...
12
votes
3answers
396 views

Should one ask questions directly to specific students in a lecture or exercise group?

In the question Encouraging class participation there are some answers how to encourage class participation in general. Sometimes, there are some smaller lectures (in particular in graduate courses) ...
17
votes
2answers
688 views

Flipping (or not) a large graduate class

I teach a graduate class in algorithms. Students take this class primarily as a breadth requirement in grad school, and they are a mix of MS and Ph.D students in computer science. Most students taking ...
22
votes
2answers
1k views

Teaching and “The Two Cultures”

This is a rather broad (and perhaps too philosophical) question about undergraduate and graduate mathematics education. Gowers, in his article "the two cultures of mathematics", observes differences ...
14
votes
2answers
486 views

Is there any research on the correlation between a professor's research ability and their ability to teach graduate level courses?

In most universities that I am aware of, graduate courses in Mathematics are taught almost exclusively by research mathematicians. My question has two parts: What is the justification for this ...
13
votes
3answers
753 views

How to design a fair oral exam for >10 students?

Oral exams take place at two different points in during their study: As final examination to end their study (i.e., when the students have finished all necessary courses, they have an oral exam ...
11
votes
3answers
212 views

Introducing (Borel) measures via Riesz representation theorem

I think, the most standard way is to introduce measures in real analysis is to define them via the usual properties like $\sigma$-additivity, etc. However, if the students are familiar with ...
5
votes
2answers
136 views

How can one deal with classes split up (in terms of previous knowledge)?

Imagine a class which is split completey regarding previous knowledge which is in some way needed for the class. How can you deal with such a class? How can you - without giving too much workload to ...
4
votes
0answers
134 views

How fast must one teach category theory? [closed]

For a postgraduate class on category theory, how fast must one teach category theory? What is the pace one must take? Also, what must one assume that the students know? Thanks!
15
votes
2answers
194 views

How to choose/test future tutors?

When I have to give a big lecture with a lot of exercise groups, I have to choose the tutors who are grading the student's homework and explaining the lecture to the students. How can I find out if ...
5
votes
2answers
58 views

How to schedule a seminar (weekly based vs. one big meeting) to maximize learning?

You want to host a seminar where students will present either a chapter from a book, or a (part of a) scientific article. What is the best way (=such that the students learn as much as possible from ...

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