iPad 3rd vs Nexus 7 for an engineering student

I've read most of the posts here asking almost the same thing (i.e. iPad vs N7) but I still couldn't come to any conclusion. So I've decided to ask here, alongside what I already have and my predicted use case.

I already have a laptop (MSI GE620DX (15.6" FullHD, 2nd gen. i7, NIVIDIA GT 635M (2GB), 8GB RAM)). This is as you would've guessed, is a desktop replacement, but for whatever it's worth, it's still pretty light (2.4 kg) considering I don't cart it around everyday, only once in a blue moon. My current phone is a Nokia N8, and am planning to go for the PureView 808 (yes yes, I know. :P )

My class usually consists of me trying to understand and catch up with what my lecturer is talking about in Russian (and I'm not a Russian) while trying to copy what he said and write in front. In addition to that, I also cart around printed pdf notes and textbooks. Software wise, I've mostly used MATLAB, MathCad, a few older programming language (can't remember what it is as time of writing) and possibly a few other things in the future.

Predicted use case:

Primary (in no particular order):

  1. record lectures,
  2. view/read textbooks/notes pdf files,
  3. probably using WolframAlpha,
  4. search/Google for anything on-the-go

Secondary (ditto):

  1. watching anime (not streaming)
  2. reading manga (both from my own collection and from the internet)
  3. "personal"
  4. probably music, but this is lower priority
For primary-4, I can probably use my smartphone to tether it to the internet, so 3G-enabled tablets is no worries. Looking from my predicted use case, this would also mean that I will cart it around along with my notebooks (the dead tree kind) in my bag. Email, social sites, etc. are a given with these kinds of devices, so I felt I don't need to state it here. I'm also may be looking for some tablet-optimised boardgames, but that's even lower priority for me than secondary-4.
So fire away with well-explained recommendations and suggestions.