33
votes
1answer
2k views

Probability that a stick randomly broken in five places can form a tetrahedron

The following problem was brought to my attention by a doctoral dissertation on Mathematics Education, but - as far as I know - the solution remains unknown. I have already asked this question on ...
2
votes
3answers
298 views

Good Books on the history of Zero

I am looking for books that discuss the origins of the zero, specifically the differences in the use and concept of the zero number among different civilizations (considering also the Mesoamerican ...
23
votes
3answers
1k views

Is “problem solving” a subject to be taught?

I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all grades. The peoples involved has sent me the textbook for seven graders (13 ...
8
votes
2answers
778 views

Reference for a nice proof of “undetermined coefficients”

I'm teaching an honors differential equations class and have been using linear algebra heavily. I thought it would be interesting to include a proof of the method of undetermined coefficients along ...
19
votes
10answers
2k views

Learning through guided discovery

I have been working through Kenneth P. Bogart's "Combinatorics Through Guided Discovery". You can download it from this page: http://www.math.dartmouth.edu/news-resources/electronic/kpbogart/ I've ...
2
votes
2answers
212 views

learning sources about Ihara Coefficient

Do we have any good sources(lecture notes or books) for learning about $Ihara$ Coefficient? Is there any relation between $Ihara$ Coefficient and the eigenvalues of graphs? Thanks for any help.
12
votes
4answers
870 views

Simple groups with the same cardinality as PSL_2(Z/p)

In an undergrad honors algebra course it's sometimes shown that when $p$ is prime and $>3$ then $PSL_2(Z/p)$ is simple of of order $p(p-1)(p+1)/2$. But that this is the "only" simple group having ...
33
votes
5answers
4k views

Is the boundary $\partial S$ analogous to a derivative?

Without prethought, I mentioned in class once that the reason the symbol $\partial$ is used to represent the boundary operator in topology is that its behavior is akin to a derivative. But after ...
11
votes
3answers
1k views

Analysis from a categorical perspective

I have not studied category theory in extreme depth, so perhaps this question is a little naive, but I have always wondered if analysis could be taught naturally using categories. I ask this because ...
11
votes
2answers
1k views

The probabilistic method - reference to less challenging questions

I am teaching a course in combinatorics and large part of it is dedicated to the probabilistic method especially in the case of graphs. The course is an undergraduate level (almost none of the ...
1
vote
0answers
418 views

Good sources for linear algebra for convex optimization and graph analysis?

What are some good sources for linear algebra for convex optimization and graph analysis? In Particular, is Gilbert Strang's MIT course suitable, or some other online course? I prefer online courses ...
12
votes
6answers
2k views

Euclid with Birkhoff

I'm looking for an short and elementary book which does Euclidean geomety with Birkhoff's axioms. It would be best if it would also include some topics in projective (and/or) hyperbolic geometry. ...
11
votes
10answers
3k views

Math History books

I'm teaching a course over the summer (it's a sort of make-your-own course for non-majors) and I'm planning on organizing it as a math history course, hitting on major threads through about 1900, and ...