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

3
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1answer
134 views

Better strategy on math graduate school

I'm just starting graduate school (master in mathematics) and there we have absolute freedom in choosing the number of courses that we can attend each term. In consequence, I'm wondering what is the ...
10
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3answers
193 views

Quizzes (with questions known in advance) instead of homework in a graduate mathematics class. Good Idea or Bad Idea? Pros and Cons?

I'm teaching a graduate course in mathematics next semester. I'm planning to have a midterm and a final exam. But I'm thinking about having weekly (or once-every-two-weeks) in-class quizzes instead of ...
3
votes
1answer
192 views

Why do the stages of rigorousness have specific timestamps?

This is a reduced quote from There’s more to mathematics than rigour and proofs of Terrence Tao (emphasis mine): The “pre-rigorous” stage, in which mathematics is taught in an informal, ...
3
votes
1answer
136 views

Effective computer lab layouts for a university math class

Many math classes benefit from occasionally being held in a computer lab. My question is about the pros and cons of different layouts and mechanics of a lab and "solutions" you have found to be ...
7
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2answers
152 views

How much prior math should I review in teaching a graduate-level course?

I am scheduled to teach a graduate-level course in engineering whose basis is in the solution of ODE’s and PDE’s, and thus is about halfway between a math course and an engineering course. We ...
5
votes
3answers
310 views

L'Hopital's Rule: Why do we need it?

I'm preparing a design/teaching experiment for my Curriculum Design Course right now. I've decided to cover L'Hopital's rule with a student I've been working with for a year, so skill wise he's ready ...
8
votes
3answers
231 views

A4 paper of notes in an exam

What are the effects of allowing students take one paper, say of A4 size, full of whatever they want, into an exam? It might be called a cheat sheet or something similar. Students might write it by ...
16
votes
1answer
213 views

How to improve atmosphere in male-dominated courses

I'm teaching a graduate applied mathematics qualifying exam review course this summer, and I have 9 males and 1 female. My co-instructor and I are also both male. While I don't necessarily see this ...
12
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1answer
177 views

Question about the process of creation of problems and exercises in Mathematics

I have a question about formulating problems and exercises in Mathematics. When attempting to create a problem of Number Theory or Real Analysis, for example, in this process, is the problem first ...
0
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2answers
57 views

Can I do a PhD after many years I've graduated and can I get funding? [closed]

I'm in my second year of Mathematics. I would like to take a PhD and if possible also a master. However, I was thinking to take a master in Machine Learning, work for a bit in that industry (5-10 ...
11
votes
2answers
159 views

Transitioning from 'Read textbook to learn' to 'Read original paper/Read paragraphs of textbooks'

I wanted to ask the following on Mathematics stack exchange, but checking the help centre, it appears that this site is more relevant: "Mathematical education, especially about teaching and pedagogy: ...
12
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2answers
429 views

Does learning classical approach to differential geometry before modern approach help or hinder?

To my mind, there seem to be two main paths to differential geometry. There is the classical approach, focusing on curves and surfaces in $\mathbb{R}^n$, especially $\mathbb{R}^3$. Prerequisites tend ...
10
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3answers
539 views

Mathematics in UK vs Central Europe

Is mathematical education better outside UK and USA? Studying in UK I noticed that the Uk syllabus of 3-4 modules per area of mathematics, is often easily covered by one module in central Europe, for ...
8
votes
1answer
74 views

Assessing the level of students in a class

Recently I've moved to another university and next semester I will have my first class there. The problem is that I don't know the level of the students that will be attending my class. Of course, I'...
0
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0answers
77 views

How to formulate math problems? [duplicate]

I always had doubts about how to formulate difficult problems (high-level problems) in mathematics? Is there any rule (a pattern) for this? Or is it a matter of level of knowledge and background? or ...
3
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0answers
109 views

Sketching paraboloids on paper

I have to teach sketching paraboloids on paper by looking at it's equation. Last year when I taught this topic no one was interested in learning this particular thing. They felt the topic difficult ...
6
votes
3answers
185 views

References for graduate education

A search in Google returns lots of studies and thinkings about teaching in undergraduate schools. Could anybody come up with any research/references about teaching in graduate schools (graduate ...
6
votes
1answer
134 views

The role of visualization and intuition in graduate and postgraduate math and developing it

[I am not an mathematics educator; but because the process of learning is educating yourself, I'm posting it here] In Visual Complex Analysis's preface, the author gives an analogy with pseudo-deaf ...
6
votes
1answer
311 views

Why is multivariable analysis often omitted?

Related but not duplicate: What courses require multivariable analysis? By multivariable analysis I mean the rigorous version of multivariable calculus (something equivalent to Ch.9-10 in baby Rudin ...
37
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6answers
3k views

What am I supposed to be learning with long proofs of the main theorems in class?

It seems like this is exclusively how (most) people teach graduate/upper div math classes. They go through the proof of some big theorem, sometimes it might take two lectures. It's obviously important....
0
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1answer
66 views

Algebra or Analysis [closed]

I am currently doing MS in Mathematics. As far as I know there are two approaches which anyone can take to do Mathematics- Analysis and Algebra. Choosing which area to work on seems difficult to me. ...
7
votes
0answers
364 views

Can Compare and Contrast be used in Mathematics Teaching and Research?

I happen to be a fan of the "theme and variations" approach to problem solving. In certain cases, a certain question had drawn enough to attention to generate dozens of solutions. Ways to Prove the ...
3
votes
0answers
116 views

How can I adequately prepare myself for a Master in Mathematics? [closed]

I am an undergraduate student, studying towards a Degree in Applied Mathematics and Statistics. I am studying at an online university specialised in distance learning and I am therefore developing ...
3
votes
1answer
131 views

Is it okay to post my own problem set solutions?

There is a set of lecture notes I would like to work through the exercises very carefully. Instead of having thousands of scrap pages lying around my desk - I considered typing them up on and posting ...
6
votes
3answers
166 views

References on British, German and French educational system

I'm writing a comparative study between mathematical teaching in my country (which sucks by the way) with others. However, I don't want to make it about today, globalization gives us a good notion of ...
18
votes
3answers
530 views

How can I discourage proof by patchwork?

I have a student who is working in their spare time on proving or disproving a conjecture of the form $$\exists x.\forall y.\phi(x,y).$$ Right now their strategy is to construct an $x$ and then show ...
9
votes
1answer
142 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
179 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
184 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
241 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
168 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 ...
13
votes
3answers
558 views

The interplay of memory and mathematical performance

As mathematicians and mathematics educators we very often see the Dunning-Kruger effect in action. Our calculus students are certain that they are masters of Calculus because they took the AP exam. To ...
14
votes
8answers
691 views

Teaching advanced math using books with cartoons

Could an effective and 'comprehensive' course on advanced math be taught through a series of fun comic books, say a fun and adventurous series of stories each exploring advanced math principles ...
13
votes
3answers
830 views

Mathematical Knowledge for Teaching

Does anyone know of any course called Mathematical Knowledge for Teaching? Where is this course taught? If it's not a course, is there any workshop about this? Or possible a book? It's not knowing ...
8
votes
6answers
1k views

Galois Theory: necessary?

I noticed the discussion of whether the teaching of Galois Theory is necessary on MathOverlflow. Here at LSE, everything we teach in mathematics should have some application to the social side of life....
9
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5answers
424 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 ...
16
votes
2answers
669 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 ...
19
votes
2answers
873 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 ...
12
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4answers
5k views

Mathematics Education Graduate Program List and Rankings

U.S. News and World Report publishes school rankings for many different disciplines, including mathematics. Is there any ranking for mathematics education graduate programs? Weaker question: Is there ...
12
votes
8answers
1k views

What is gratifying in being a mathematics teacher?

I think the title says it all, but in case it does not: Is being a math teacher gratifying? If yes, what is gratifying in being a math teacher? (If not, why...) Does the feeling lasts, or perhaps ...
14
votes
2answers
463 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 ...
12
votes
3answers
552 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 ...
12
votes
3answers
383 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) ...
11
votes
3answers
153 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 ...
12
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3answers
237 views

Using Several Textbooks in a Course

Sometimes a teacher prefers to use several textbooks in his/her courses because he/she thinks the arguments of each book is better in a part of course material or there is no comprehensive textbook in ...
10
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2answers
150 views

When to encourage students to read mathematical literature written in English (in non-English speaking countries)?

There is a lot of mathematical literatur in some non-English languages (French, German, Spanish, etc.) that students from these countries don't need to read English literature (at least) for their ...
31
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3answers
2k 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. ...
5
votes
2answers
123 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 ...
5
votes
2answers
49 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 ...
4
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0answers
124 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!