I am currently studying mathematics on my own. In my imagination, software tools like Mathematica, R, etc. seem like they have great potential for mathematical education.
Some (imagined) advantages of such software:
- As an intuition pump for mathematical concepts
- For visualization
- For getting through the tedious "calculator" parts of exercises not related to the concept being learned
However, despite my fantasies, I have struggled in practice to use such tools to supplement learning.
How can one, if at all, use software to better learn mathematics? Or is one better off staying away?
In my experience it's best to learn by doing. Pick a project that naturally lends itself to a particular tool and they'll supplement each other nicely. There are some textbooks arranged around using particular tools, like Rob Beazer's Intro to Linear Algebra text and its SageMath integration.