I was told that coding is a very good skill to have in order to conduct math research (and a good skill to have in general, of course). (I also know that many people in the MathOverflow community hold this viewpoint, for instance Steve Huntsman.)
Nowadays, there are many good online resources for learning the coding skills. However, there seems to be very few resources with emphasis on using coding for answering mathematical questions.
My Question: are there resources (books, courses, etc.) with emphasis on using coding for answering mathematical questions?
Here, I am thinking of something in a similar vein as Project Euler but with harder mathematics.
I prefer to use one of the following languages since they seem to be the best general-purpose tools:
Python/Sage
Mathematica
Maple is also acceptable.
Just to make my question more specific: my goal is to be able to work computationally for all undergraduate (group/ring/Galois theory, single/multivarib calculus, linear algebra, ODEs, complex analysis, combinatorics, elem number theory, etc.) and standard graduate topics (functional analysis, representation theory, algebraic geometry, algebraic/differential topology, Riemannian geometry, etc) whenever possible.
