2 of 2 Syntax, Semantics, Overall meaning.

Only if taken with a grain of salt.

First of all, no man cries stinking fish (according to the first Google hit this is the translation of a saying that literally goes "do not ask the innkeeper if his wine is good"). In here you will find mostly - if not only - Mathematica enthusiasts, so the answer to your question will most certainly be "Hell yeah!!!".

Mathematica is a wonderful environment to do science - not only math - and you will find it useful in many ways in the years to come. Consider it as an investment. Wolfram did a very good thing (marketing-wise it's more a pusher's move... :-) ) with the Home edition, so that it is now affordable to almost everyone.

Here's one possible downside of using Mathematica: you might find yourself relying on it a little bit more than you should. Mark my words, young apprentice: the most delightful moment when studying is not when you understand something that appeared difficult at first; it's when you finally understand it after having figuratively banged your head against the wall for days. That satori moment is something that will be with you for the rest of your life. Mathematica can save you from that apparently useless bashing, but it's that banging against the wall that brings new order in your mental architecture.

You will find yourself tempted to use Mathematica as a shortcut too often. Try to resist the urge to cheat figure out answers before said banging has taken place and you will find in Mathematica a powerful ally. Indulge in getting the right answer in the shortest possible time, and Mathematica will be an unnecessary crutch, an impairment along your learning path.

Of course, once you have reached the enlightenment for a given subject, Mathematica will be invaluable in letting you efficiently explore different scenarios, to cement your understanding. But do not underestimate the therapeutic value of a good head-banging.

I might be the only one in here to think that the best way to use Mathematica is to use it the least possible amount, so take my advice, too, with a grain of salt.

EDITed to avoid lawsuits :-), fixin some of my lousy grammar and to remove the impression that studying is a gory activity.