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Results tagged with mathematics-education
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For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/
23
votes
Psychological test for Euclidean geometry
The FCI is a "concept inventory" test for classical mechanics. There exist several such tests for mathematics. Some may be implemented as "peer instruction" (as Eric Mazur advocates), but they can als …
- 188k
1
vote
One-step problems in geometry
Von Neumann's law for two-dimensional cell growth
A soap froth or polycrystalline slab is modeled by a two-dimensional network of piecewise smooth curves, joined at vertices at internal angles of $2\p …
13
votes
Accepted
How does a Masters student of math learn physics by self?
I can recommend Leonard Susskind's Theoretical Minimum:
A number of years ago I became aware of the large number of physics
enthusiasts out there who have no venue to learn modern physics and
cosmolo …
- 188k
7
votes
PhD dissertations that solve an established open problem
Since the OP mentions Gauss, this entry could be an appropriate addition to the list:
Manjul Bhargava's PhD thesis, Higher composition laws (2001), concerns a problem going back to Gauss. In the ninet …
41
votes
Are hypergeometric series not taught often at universities nowadays, and if so, why?
[Q1] Gert Heckman from Nijmegen University teaches a course on hypergeometric functions (here are the lecture notes, first taught at Tsinghua Univ.).
[Q2]
In the foreword, Heckman hints at why this to …
21
votes
Books on the relationship between the Socratic method and mathematics?
An influential book on the teaching of mathematics via the Socratic method is Imre Lakatos, Proofs and Refutations. The full book can be browsed on Google, and individual chapters can be donwloaded fr …
- 188k
0
votes
Accepted
Generalized Fourier integral and steepest descent path, saddle point near the endpoints
Series expansion of the integrand around $\varphi=\pi$ and integration gives
$$H = 2ika\int_{-\pi/2}^{\pi/2}\cos{(\varphi-\phi)}e^{ika[\cos{\varphi}+\cos{(\varphi-\phi)}]}\ d\varphi$$
$$\qquad\qquad=2 …
- 188k
5
votes
Accepted
Books on the History of math research at European universities
The classic reference is The History of Mathematics in Europe from the Fall of Greek Science to the Rise of the Conception of Mathematical Rigour by Sullivan (1925).
Do note that Ph.D.'s in mathemat …
- 188k
14
votes
Accepted
What kind of computer tools topologists/geometers use to visualize the objects they deal with?
Here is one case study:
An impressive animation of the Hopf fibration created by Niles Johnson using only open-source tools, available for all platforms: The Python-based mathematics program Sage was …
- 188k
20
votes
Teaching prime number theorem in a complex analysis class for physicists
"Newman's short proof of the prime number theorem" by Don Zagier might work, in particular since there is an extensive discussion of the steps in that proof in this MSE posting. "The proof has a beaut …
- 188k
114
votes
PhD dissertations that solve an established open problem
I find George Dantzig's story particularly impressive and inspiring.
While he was a graduate student at UC Berkeley, near the beginning of
a class for which Dantzig was late, professor Jerzy Ney …
6
votes
Source for analysis of identification of structures in learner's mind and mathematical struc...
A much-cited attempt to analyze Piaget's ideas and carry them further has been given by Ed Dubinsky in Reflective abstraction in advanced mathematical thinking (1991).
Reflective abstraction is a con …
- 188k
8
votes
Accepted
How to be a Great mathematician in prison/without a master?
The answer to the title question might well be "yes":
At the start of WWII, the French mathematician André Weil, a pacifist, was charged with failure to report for military duty, and was imprisoned i …
5
votes
Accepted
Cambridge Mathematical Tripos papers from late 19th century
Here is a collection, with solutions, from the period 1864-1878 (published by Joseph Wolstenholme). An earlier period, 1800-1820, was collected by I.M.F. Wright.
These are transcriptions of the probl …
- 188k
28
votes
When exactly and why did matrix multiplication become a part of the undergraduate curriculum?
The article by J.-L. Dorier in On the Teaching of Linear Algebra suggests the answer to your question will be different for the UK and for continental Europe:
In an attempt to answer your questio …
- 188k