Questions tagged [graduate-education]

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

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15
votes
6answers
5k views

How do I learn advanced mathematics without forgetting?

I am pursuing mathematics through distance education and I find that it takes me a long time to understand the concepts (e.g. sigma fields, measure theory, connected topological spaces, etc.). After I ...
7
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2answers
390 views

How much more skilled in the topic should you be in order to teach the topic?

For sake of argument, consider that skill of a topic is spectrum from "new and learner" to "experienced and expert." Where should you relatively be in order to teach the topic ...
3
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1answer
87 views

Is SQL relevant to statisticians' work?

I hope this is the right place for posting this, but if not, please let me know! I recently took a second class in Python programming which, toward the end, also taught a little bit of SQL. As it ...
7
votes
2answers
199 views

A Question about Theodore Frankel's “The Geometry of Physics”

Locked up in my self-distancing isolation in NYC, I'm reminded of how much I really like Frankel's book, which contains a wealth of beautiful geometry and topology from the standpoint of a ...
6
votes
1answer
94 views

Data on textbook adoptions in universities (math/science)

Does anybody know if there is a website/database/... on textbooks adoption in the US or some other country? (math/science textbooks) It would be interesting to see which textbooks are (and have been) ...
8
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3answers
194 views

Evaluating textbooks in math and physics

I’m currently interested in textbooks, especially the ones in math and physics that are used at the high school, undergraduate and graduate levels and, given the experience of the people on this ...
2
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2answers
246 views

What does one full year of calculus mean?

If a masters program (Fordham in math education) requires "at least one full year of calculus" does that mean just calc one or more than that?
2
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0answers
134 views

Why are a.e. defined functions rarely mentioned in elementary books?

In any standard development of measure theory in several well-known textbooks, the use of almost everywhere (a.e.) defined functions are first seen in the statement of Fubini's theorem, which states, ...
1
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0answers
61 views

How can I make a shift to applied mathematics? [closed]

I have done dual degree with bachelors in computer science. I am currently a software developer (India). I always have had interest in mathematics. But once was I got into college I did not work ...
9
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3answers
642 views

MacLane-Birkhoff's “Algebra” vs Jacobson's “Basic Algebra I,II” vs Lang's “Algebra”

(Cross-posted at Math.Stackexchange) I'm searching for an apt textbook(s) on Abstract Algebra for a very advanced undergraduate/graduate level course in Algebra, and would be grateful for any help. ...
2
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0answers
157 views

Online open-course-ware that uses Maclane's book “Algebra”

I am struggling with that book which I find to be more of second-guessing type than a book for self-study: it has cryptically written sections, no examples (and those given, and rarely, are even more ...
4
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3answers
250 views

Geometry textbook with an abstract algebra emphasis

I'm teaching a variety of undergraduate and graduate geometry classes (mostly for in-service teachers) which range from elementary axiomatic geometry to more advanced transformational geometry. I'm ...
10
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3answers
2k views

Are students majoring in pure mathematics expected to know classical results in mathematics very well by their graduation?

For example, I am confident that very few students majoring in pure mathematics can write a complete proof to the Abel–Ruffini theorem (there is no algebraic solution to general polynomial equations ...
3
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0answers
164 views

Succinct description of situations where naively obvious is correct, but for far more complicated reasons?

What is the name for a situation where the obvious thing turns out to be true, but the reasoning is more complicated? In abstract algebra we can say the rational numbers - the fractions, $\mathbb{Q}...
3
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0answers
112 views

On concentration inequalities [closed]

I would like suggestions for a good text on concentration inequalities (examples here https://en.wikipedia.org/wiki/Concentration_inequality). I am looking for sources (texts) that can give strong ...
3
votes
1answer
187 views

Better strategy on math graduate school [closed]

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 ...
12
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3answers
228 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 ...
2
votes
1answer
403 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, ...
2
votes
1answer
147 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 ...
8
votes
2answers
165 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
343 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
900 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
239 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 ...
13
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1answer
197 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
65 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
169 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: ...
13
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2answers
1k 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 ...
9
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3answers
1k 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
86 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'...
3
votes
0answers
113 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 ...
7
votes
3answers
195 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 ...
7
votes
1answer
169 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
452 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
votes
6answers
4k 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
73 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. ...
8
votes
0answers
467 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
124 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
135 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 ...
7
votes
3answers
177 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
607 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
162 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
197 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
189 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 ...
14
votes
3answers
617 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
788 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
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3answers
1k 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 ...
9
votes
7answers
2k 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
votes
5answers
451 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 ...