Ubuntu – Ubuntu partition sizes

I will try to answer your questions in the order you asked them:

1. It depends on how Matlab and Mathematica are distributed; if they are distributed as static binaries, then you should be okay. A static binary has any of the libraries needed by the program compiled into them. Generally, this is not the default for compiled applications, as it leads to extremely large binaries.

2. There really aren't any disadvantages, per say; it depends on the application. If you're installing an application from apt-get, Synaptic or from the Ubuntu Software Centre, the application is being installed in your root partition. If you have a static binary that you have downloaded and unpackaged yourself, then your best bet would be to keep it in your home directory. For any scripts or programs I write or install, that are not provided by the Ubuntu repositories, I keep them in a bin directory in my home folder. This way, they aren't "polluting" my base system.

3. The size of your root partition really depends on how many applications and libraries you plan on installing from the Ubuntu repositories. Different Linux distributions recommend different sizes. If you allow Ubuntu to automatically partition your drive, with a separate partition for /home, the Ubuntu installer will give you a sane layout. C and C++ compilers, Lisp REPLs, Python interpreters and the various databases do not take up much room. The only large compiler is for Java; I believe it weighs in at around 80MB for the JDK (Java Development Kit). As with my answer for your second question, most of the stuff you write, you should keep to your home directory, so you do not pollute the base system. Plus, if you ever upgrade your Ubuntu install, you will not have to worry about accidentally blowing away the directory you keep your projects in. Granted, you run this risk anyways, it will just be easier to keep everything you do in your home directory; that is what it is there for.

It's difficult to know these things in advance, of course, so even with the best planning you may need to make adjustments later. However, I'd recommend the following:

You won't likely need a swap partition larger than 8 GB. You have room for it and it won't hurt, but it doesn't make much sense, either, so if I were you I'd keep /swap at 8 GB.

I've had my root partition at 30 GB for about a year, and I'm still using less than 10 GB of it. You might install larger programs than I do, so give yourself a buffer: I'd recommend 20 - 30 GB.

As for the /home partition, that's where you'll store your data and files, including pictures, videos, projects, etc., whatever sorts of things you store and keep. I don't what sorts of things you keep, but in my case my pictures take up perhaps the largest share. Even so, having given myself lots of room (about 300 GB for /home), I have used only about 50 GB. You'll have to decide for yourself, but since you'll use a large NTFS partition to share data with Windows, you can probably get away with 30 - 60 GB for /home, with the knowledge that you might make adjustments later.

As far as space for Windows and its apps, etc., if you think you need 150 GB then that sounds fine. And the rest NTFS to share? That's fine, too. (Eventually you might want to revise that, but it's certainly fine at the beginning.)

You didn't say whether or not you already have Windows installed on the drive, but I assume you do. Windows can sometimes get finicky when being resized. I would recommend resizing your Windows partition first from within Windows itself using the Windows administrative tools, and then you can create the Ubuntu partitions as you install it.