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Results tagged with soft-question
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user 9652
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
5
votes
Sparse representation for continuous function?
Sure, there is a lot about this, but maybe not under that name. You can find related ideas under the name of "best $k$-term approximation", for example in Ron DeVores Acta Numerica paper "Nonlinear Ap …
- 12.7k
53
votes
What do you do when you're stuck?
Here is an answer which may be math-specific: If you are stuck in some proof of some claim that you believe is true:
Add the missing piece as assumption and continue as planned.
- 12.7k
4
votes
Fiction books about mathematicians?
The book "De wilde getallen" by Philibert Schogt ("The wild numbers") is a great story about a young mathematician and his struggle with an (imaginary) theorem in number theory. It illustrates the emo …
- 4,713
6
votes
Archiving mathematical correspondence
The book "Der Briefwechsel Richard Dedekind – Heinrich Weber" transcribes the full correspondence between the two. From the description:
This volume provides the very first transcription of correspon …
- 12.7k
13
votes
Math videos containing real time rough thinking
When I taught a beginners course in analysis a few years ago I wanted to give the students an impression of how one can work on exam problems. I asked somebody to prepare a test exam (I had my exam pr …
- 12.7k
50
votes
Changes forced by the pandemic
Online seminars
Research (and other) seminars have gone virtual. The obvious advantage is, that anyone can attend from basically all over the world. The page https://researchseminars.org/ compiles a h …
- 12.7k
16
votes
What's a great christmas present for someone with a PhD in Mathematics?
You may adopt a polyhedron in their name!
- 12.7k
9
votes
Books that teach other subjects, written for a mathematician
Well, it's not exactly science, but
The Mathematics of Juggling by Burkhard Polster is written by mathematician and is for mathematicians. I may add that you can enjoy the book, even you can't juggle. …
- 12.7k
3
votes
Examples of "irregularities" in mathematics, other than prime numbers
Finite simple groups.$\mbox{}\mbox{}$
(Not totally unrelated to prime numbers but more general...)
- 12.7k
35
votes
Modeling in pure math
This one is pretty basic: linearization, e.g. replacing a nonlinear dynamic with a linear one allows to study stability and such.
Also, linearization is behind Newton's method and Taylor polynomials …
- 12.7k
4
votes
Unconventional examples of mathematical modelling
I suggest models in the social sciences like the Krause-Hegselmann model of consensus dynamics. Also the Kuramoto model for synchronizing oscillators is nice and can be used to model other things e.g. …
- 12.7k
6
votes
What definitions were crucial to further understanding?
Well, this is basically the same answer as the one by Alexandre Eremenko, but here goes: The particular form of the definition of derivative is crucial for partial differential equations. Using weaker …
- 12.7k
4
votes
Why should one still teach Riemann integration?
When I was introduced to measure theory, the professor chose to use the Choquet integral to obtain the Lebesgue integral. An this uses the "good old" Riemann integral to integrate the pseudo-inverse o …
- 4,713
5
votes
Mathematical difference between entropy and energy
It is probably worth mentioning that the the heat equation is inherently linked to energy and entropy in two ways:
The heat equation is the gradient flow of the energy in the Hilbert space $L^2$ (cl …
- 12.7k
99
votes
Mathematical games interesting to both you and a 5+-year-old child
The game "Set" seems to fit the bill. It's a card came where there are cards that show images which have four different features, each of which comes in three possibilities:
number (1, 2, or 3 objec …
- 12.7k