Creating a basic "hello world" kind of deformer is quite simple in Houdini. As soon as you have some geometry, you can run it through a pointwrangle node and write a few lines of VEX code to make changes.
@P.y = @P.y + 1.0;
That line of code just translated every point in a pointwrangle up by one unit. No boilerplate or compiling required.
@P = @P + @N;
That line of code is vector addition. It pushes every point in the direction of its normal.
For a whole lot more information, you can read this excellent wiki if you haven't already: http://www.tokeru.com/cgwiki/?title=HoudiniVex
You can also use vector fields (and completely control them) which might be relevant to diffeomorphisms, as far as I understand.
Houdini also has nice visualization tools. So you can create text, vectors or color to visualize your data. And you can run on millions of points if you have a decent computer.
Building a node in Maya requires a lot of boring boiler-plate. In my opinion, you'll spend most of your time learning how to read the docs in Maya and it won't be as flexible until you reach a certain level (or possibly ever).
Either tool is going to potentially come with a learning curve though. What is your goal after school? More theory and math? Employment with a production studio?