Questions tagged [graduate-education]

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

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Conferences dealing w/challenges of teaching higher level math to STEM audiences

I'm interested in knowing whether there are conferences that have, among other topics, the difficulty of teaching higher level mathematical concepts to folks with prior established skills in STEM, e.g....
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-4 votes
1 answer
119 views

Is it weird for an undergrad or grad quant/applied maths(/even pure maths) programme to not teach that probabilities of 0 or 1 will never change? [closed]

Edit: i didn't mean it like this programme should do this or that. i mean other people are accusing me like 'your programme should've had this or that' (actually they're saying that i should know this ...
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1 vote
0 answers
170 views

Mental Health in Mathematics

I am not sure if my question is relative to this meta but I still want to put forth my thoughts and concerns and questions because I think its not just me but others too who have similar issues. My ...
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3 votes
1 answer
166 views

To what degree can the legally blind, with computer induced medical problems, study statistics?

My son graduates from secondary school in 2022. But he shall attend university in Australia or UK — where you must apply for ONE major — not liberal arts in the USA. He wants to pick BSc Math with ...
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8 votes
1 answer
551 views

What famous graduate math textbooks use color?

I know that undergrad math books use colors, like Gilbert Strang in his undergrad Linear Algebra textbooks and Measure, Integration & Real Analysis by Sheldon Axler. Many first year calculus ...
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21 votes
8 answers
6k 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 ...
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8 votes
2 answers
434 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 ...
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3 votes
1 answer
114 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 ...
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8 votes
2 answers
924 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 ...
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6 votes
1 answer
107 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) ...
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9 votes
3 answers
264 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 ...
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  • 251
2 votes
2 answers
824 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?
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2 votes
0 answers
148 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, ...
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9 votes
3 answers
1k 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. ...
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2 votes
0 answers
231 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 ...
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4 votes
3 answers
320 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 ...
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10 votes
3 answers
3k 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 ...
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3 votes
2 answers
294 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}...
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3 votes
0 answers
116 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 ...
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3 votes
1 answer
231 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 ...
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13 votes
3 answers
258 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 ...
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2 votes
1 answer
512 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, ...
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2 votes
1 answer
170 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 ...
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9 votes
2 answers
192 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 ...
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5 votes
3 answers
389 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 ...
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  • 59
9 votes
3 answers
1k 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 ...
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16 votes
1 answer
264 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 ...
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13 votes
1 answer
203 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 ...
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0 votes
2 answers
72 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 ...
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11 votes
2 answers
184 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: ...
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14 votes
2 answers
2k 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 ...
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9 votes
3 answers
2k 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 ...
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8 votes
1 answer
98 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'...
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3 votes
0 answers
121 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 ...
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6 votes
3 answers
211 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 ...
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7 votes
1 answer
206 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 ...
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7 votes
1 answer
696 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 ...
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39 votes
6 answers
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....
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0 votes
1 answer
82 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. ...
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8 votes
0 answers
566 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 ...
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3 votes
0 answers
127 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 ...
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3 votes
1 answer
142 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 ...
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7 votes
3 answers
197 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 ...
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20 votes
3 answers
685 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 ...
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9 votes
1 answer
190 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 ...
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9 votes
1 answer
222 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 ...
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2 votes
1 answer
194 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 ...
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6 votes
1 answer
269 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. ...
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2 votes
0 answers
174 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 ...
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14 votes
3 answers
676 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 ...
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