I am a math student. I’d like to find out if tablets (iPads, Galaxy Note 10.1) are worth the cost.
How good are tablets for the purposes of reading textbooks as PDF and writing mathematics with a stylus?
For writing math in TeX, it looked like the Android app store was in need of a TeX editor, so I had all the fun writing one which renders the TeX as on math.stackexchange, and can also export to PDF.
I can only speak from personal experience here, so don’t take anything I say as a universal statement about doing math with iPads.
Reading math on an iPad is great. I’ve been using my iPad to read during meals, at cafes, and in other places where it’s more convenient because of its size than taking out my laptop, and it also has substantially better battery life (not too big an issue now but it will be very useful the next time I take a long flight / train ride / bus ride). My current setup is that I only transfer reading material that I actually plan on reading soon (rather than my entire library), so the somewhat limited selection forces me to actually read what I was planning to read. Earlier I had a long backlog of things I was planning on reading, but it was so large that it was intimidating to start. As far as specific apps, GoodReader is good for .pdfs but doesn’t read .djvus; for the latter you can use Stanza.
Writing math on an iPad is not great. I don’t have a stylus myself, but a friend of mine who tried taking notes with a stylus found it both too slow and too imprecise, and based on my experiences I’m not surprised. This may change depending on the stylus but not, I think, substantially. If you want to TeX on an iPad, the best option I’m aware of is TeX Touch, which I haven’t tried because I find typing on an iPad annoying compared to typing on a laptop.
Non-obvious advantage: it is very easy to draw mathematical graphics in some iPad app (I use Paper) and not terribly difficult to include them in LaTeX’ed notes (such as these). As a general rule, iPad apps heavily prioritize ease of use, so I didn’t have to learn how to use a sophisticated tool: I just downloaded an app and started drawing. I think in general most mathematics could benefit from an increased use of graphics and I’m happy to have a tool that allows me to use graphics more easily.
My standard answer to your last question, which is not specific to iPads, is that mathematics which is typed up rather than handwritten is 1) more legible and 2) much, much easier to copy and distribute. But this is an argument for doing mathematics electronically, not an argument for doing mathematics with an iPad.