"In reality, Wolfram Alpha queries are more often for the sake of fun than for the sake of discovery"
In advanced math classes (upper undergraduate or graduate) it is almost impossible to check results or do a complex operation on a simple calculator.
In many cases I have to turn to a tool like Mathematica/Wolfram Alpha. I have a W|A Pro account and it has worked wonders for me. For example, entering "integral from 0 to infinity of (ye^(-y)((-1/y)(e^(-t))+1/y)) with respect to y" into Wolfram Alpha is so much easier than doing the same with a TI-89. I can copy/paste and adjust very easily and the software produces multiple interpretations/representations which is very useful.
Your comment reminded me of a very interesting observation I had when I was looking at Wolfram Alpha analytics - for some reason, the number of queries drops dramatically around mid-December, and only returns to the original volume around mid-January. I was puzzled by how this phenomenon repeated itself every year.
It took me a minute to realize that during that time, every college student is on vacation.
I use IPython/SymPy for the same purpose. It is nice to be able to do these calculations on my local machine, in stead of relying on an internet conection. Plus I get the powers of Python to back me up if I want to do anything more compilcated.
It's not nothing, however, that Wolfram Alpha works spectacularly well on a phone. The mobile app even has a very useful keyboard that has common math symbols. With mobile data, at any given time, I'm much more likely to have a computing device with an internet connection than I am to have one with a useable programming keyboard.
Not that I'm against the progression of these tools, far from it, I just think that wolfram alpha does a better job at math homework type problems for most people most of the time. If you have more complicated modeling/statistical/etc. work, then bring out the bigger guns.
I used the Wolfram Alpha iPad app in real-time during mathematics / statistics lectures to check the notes on the blackboard and to try out alternatives. Very useful in the classroom.
I see that some professors (not in my school though) publish they’re lecture notes as IPython notebooks. That is super clever and allows interactivity with the lecture material. I don’t know the mobile/tablet support of IPython notebook however.
In advanced math classes (upper undergraduate or graduate) it is almost impossible to check results or do a complex operation on a simple calculator.
In many cases I have to turn to a tool like Mathematica/Wolfram Alpha. I have a W|A Pro account and it has worked wonders for me. For example, entering "integral from 0 to infinity of (ye^(-y)((-1/y)(e^(-t))+1/y)) with respect to y" into Wolfram Alpha is so much easier than doing the same with a TI-89. I can copy/paste and adjust very easily and the software produces multiple interpretations/representations which is very useful.