All Questions
Tagged with graduate-education undergraduate-education
49 questions
19
votes
1
answer
8k
views
Is MacLane and Birkoff's "Algebra" suitable today as either an undergraduate or graduate text in abstract algebra?
I'm going to review the 3rd edition of Saunders MacLane And Garrett Birkoff's Algebra at my blog soon and this is the first time I'm really carefully reading it. While I'm really enjoying the book,I'...
- 5,052
4
votes
2
answers
2k
views
Where can I find new types of problems regarding graduate level mathematics?
Though not an undergraduate student , I just wanted to know where can I find hard new types of problems regarding the problems in graduate level mathematics.
As per my information , standard books ...
- 221
6
votes
3
answers
393
views
Math programs in Russia and post-Soviet states - how do they compare to US?
I studied math in college and also took a few years of Russian. For a time, I was looking for a way of living in Russia post-graduation (well before the recent war) and I asked one of my professors, ...
25
votes
14
answers
17k
views
What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?
I have helped to TA and taught several courses with mixtures of advanced undergraduate and early graduate students in engineering/STEM. These courses are the classics: signal processing, control, ...
- 12.9k
6
votes
1
answer
474
views
Resources for designing math degree programs
I'd like to know where I can find resources which are helpful when one has to design or improve grad and undergrad degree programs in pure and applied mathematics.
In particular, I'm searching for up-...
- 237
-4
votes
1
answer
274
views
Are the standard of questions provided in reputed institutions like MIT, Stanford, Oxford, etc., as good as the problems of IMO?
I did not win the International Mathematics Olympiad, so I was very curious to know the standard of questions asked in the graduate and undergraduate courses of maths and computer science in ...
- 5,052
5
votes
1
answer
245
views
Strategies for Designing Challenging Yet Feasible Quiz Problems for Upper-Level Math Courses
In the past semester, I taught two 7-week courses: discrete math and algorithms designs (which is essentially still math) for undergraduate CS students. I implemented weekly 25-minute quizzes ...
- 8,093
1
vote
1
answer
151
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Summer or Semester Programs which bridge to Graduate Mathematics
A few years back I had a student attend the MASS semester at Penn State. It was a fantastic experience for my student and it certainly helped him find a place in graduate school and I would wager it ...
- 8,093
4
votes
1
answer
488
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 ...
- 2,248
3
votes
2
answers
394
views
Common mistakes in probability
$\DeclareMathOperator\Var{Var}\DeclareMathOperator\Bern{Bern}\DeclareMathOperator\Pois{Pois}$Question: What not-trivial mistakes do students often make when solving problems in probability theory, ...
- 1,852
14
votes
8
answers
2k
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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 ...
- 535
14
votes
8
answers
1k
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 ...
- 237
10
votes
3
answers
1k
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 ...
- 199
15
votes
11
answers
4k
views
What are some research-level opportunities in mathematics that do not focus on proofs?
The research level of mathematics (what is done by professors and upper-level graduate students) tends to be heavily portrayed as focused on writing proofs to the exclusion of most anything else math-...
- 1,005
4
votes
2
answers
1k
views
Is the Wronskian still assumed for graduate education?
About thirty years ago, in a practice GRE (Graduate Record Exam) math
test in the US,
a question assumed the student knew the definition of the Wronskian. I had never heard of this determinant
before.
...
- 11k
-4
votes
1
answer
178
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 ...
- 574
3
votes
1
answer
204
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 ...
- 66
3
votes
2
answers
308
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}...
CommunityBot
- 1
9
votes
7
answers
2k
views
Galois Theory: necessary?
I noticed the discussion of whether the teaching of Galois Theory is necessary on MathOverflow. Here at LSE, everything we teach in mathematics should have some application to the social side of life.
...
- 9,736
10
votes
2
answers
235
views
When to encourage students to read mathematical literature written in English (in non-English speaking countries)?
There is a lot of mathematical literature 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 ...
- 8,713
8
votes
2
answers
478
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 ...
- 8,713
9
votes
3
answers
360
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 ...
- 14.8k
6
votes
1
answer
133
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) ...
- 1,940
8
votes
3
answers
2k
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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. ...
- 878
4
votes
3
answers
438
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 ...
- 30.2k
9
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 ...
3
votes
1
answer
637
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, ...
- 183
13
votes
3
answers
451
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 ...
- 1,836
2
votes
1
answer
203
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 ...
- 1,836
9
votes
3
answers
2k
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 ...
- 65
13
votes
1
answer
219
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 ...
- 22.1k
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 ...
- 9,130
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 ...
- 67
7
votes
3
answers
220
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 ...
- 2,031
23
votes
3
answers
2k
views
What are the differences between graduate and undergraduate classes, relevant to course design and teaching?
I will be a postdoc in the fall and will be teaching my very first classes aimed at graduate students. One will be an intro class, and the other a topics class.
There are of course many differences ...
CommunityBot
- 1
13
votes
3
answers
2k
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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 ...
- 31
8
votes
0
answers
588
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 ...
CommunityBot
- 1
14
votes
3
answers
773
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 ...
CommunityBot
- 1
3
votes
1
answer
172
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 ...
CommunityBot
- 1
21
votes
2
answers
292
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?
...
- 7,752
35
votes
3
answers
4k
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.
...
- 1,723
9
votes
1
answer
210
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 ...
CommunityBot
- 1
6
votes
1
answer
287
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.
...
CommunityBot
- 1
9
votes
5
answers
549
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 ...
- 109
11
votes
3
answers
438
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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) ...
CommunityBot
- 1
23
votes
2
answers
2k
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 ...
- 6,213
13
votes
3
answers
1k
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 ...
- 12.4k
5
votes
2
answers
178
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 ...
- 9,468
15
votes
2
answers
278
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 ...
- 9,468