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For questions on general considerations and problems of teaching mathematics, such as issues specific to teaching mathematics that are relevant in various contexts or courses.

13 votes
4 answers
3k views

Pedagogy, mathematics and Dieudonné's Foundations of Modern Analysis

I've heard from a friend of mine that Dieudonné's Foundations of Modern Analysis is "painful reading" and "a little outdated"; however, my teacher actually suggested it to me, describing it as a "wond …
Dal's user avatar
  • 1,131
5 votes
4 answers
519 views

Teaching number theory: geometric approach

Are there any books that are substantially based on a geometric approach to explain topics in number theory (elementary and more advanced)? If so, is such approach -- judging from your teaching (or …
Dal's user avatar
  • 1,131
11 votes
4 answers
2k views

Topics that should be in an undergraduate math programme

According to your experience as students and professors, what are (and why) the courses that should be part of a math undergraduate degree, but that are missing in most institutions?
Dal's user avatar
  • 1,131
6 votes
0 answers
315 views

Links between mathematical folklore and educational success

I would like to ask if, in the research field of mathematical education, some work has been done to investigate the relationship between 1) and 2): mathematical education and student motivation the …
Dal's user avatar
  • 1,131
5 votes
2 answers
301 views

Real analysis: why usually first limits of sequences and then limits of functions?

I notice that all of the analysis books that I've studied start from dealing with limits of sequences and only then move on to limits of functions. Does this kind of approach have any particular adv …
Dal's user avatar
  • 1,131
6 votes
4 answers
425 views

Intuition behind $\zeta(2) = \frac{\pi^2}{6}$

The result $$\zeta(2) = \frac{\pi^2}{6},$$ tends to amaze young students because of its beauty. However, although in literature there are many proofs of this result, I find that none is suitable for …
Dal's user avatar
  • 1,131
4 votes
2 answers
297 views

Promoting intuition (for undergraduate students): visual thinking, geometic approaches, etc....

Note: This question is ment to extend the scope of some related questions of mine. I would appreciate very much any suggestion to improve the way the question is posed. I would like to ask what is …
Dal's user avatar
  • 1,131
20 votes
11 answers
3k views

Books that every aspirant mathematician should read

I am a student and I would love to become a research mathematician one day. So I would like to ask you---experts in mathematics but also in education---what are some influential ($\star$) books that …
Dal's user avatar
  • 1,131