Am I missing out on anything if I use a tool like picrel to learn math for self study?

>>15389931 (OP)

why would using a program to augment your understanding be cheating?

Yes, all true math wizards begin with abaci and clay tablets

Well I am inclined to agree but the education system still includes long division and various tricks for solving integrals in the curriculum. Even Spivak’s calculus book insists the reader ought to be able to compute integrals ‘with aplomb’ so I wonder if I’ll really be missing out on something by letting my symbol pushing skills atrophy any further

>>15389931 (OP)

cheating in what?

>>15389931 (OP)

maybe its even cheating if you use your fingers to learn counting, it really depends on the perspective of the of who lost his finger with 3.

I saw some picture of John Ellis' office one time. Among dozens of stacks of papers and books stacked three feet high or more, the only book that looked like it had been touched was the Mathematica book, which had its own space next to his computer with nothing stacked on top of it. That should answer your question. That's how the "professionals" churn out the calculations that I don't bother with.

>>15389931 (OP)

just learn with the computer (if that's your thing) and then revise on paper? then you will catch any gaps.

>>15389931 (OP)

Learn at all costs. It doesn't matter how you learn, it matters what you learn. Some books &amp; sites will help you more than others, but there is no "wrong way"

Does going through the whole process of substitution, observing symmetries, picking the best trig identity etc. hone a skill or fluency necessary for something like real analysis?

If you are using SymPy at all you probably aren't even learning real math so who cares

>>15389931 (OP)

this brute forces to solve. it might not give you the result you expect. 

>self study

your calculus ta will see that the answer you got to is unusual

I don’t have a ta or any tests to worry about since I am self studying. So the real question is what is the value in learning to efficiently carry out tedious hand calculations if there is no test to be concerned with. I am genuinely asking whether there is any real value in the skill or whether I’d be better served moving onto more complex things more quickly. For instance, will bring rusty on trig substitutions prevent me from writing certain proofs, this kind of thing.

>>15389931 (OP)

It's not cheating if you're having fun and learning

>>15389931 (OP)

Honestly, learning how to effectively use a software package such as this is far better of a learning exercise than any level of math this would be helpful with.



I would expect software such as this to be completely unable to cope with some types of problems you'd encounter in a calculus class but I am a math teacher and completely incapable of thinking outside the school and assessment structure and honestly can't think of any good reason you'd have to be even competent at solving integrals if you're not using the math for any engineering or related applications.
