Mathematica: Probably the best choice for symbolic work. A little slower at numerical work. Fairly steep learning curve, but once you learn it well, you can write very powerful programs very quickly. Worth learning if you intend to do high level math or theoretical physics.
Maple: Not as powerful as Mathematica, easier to learn, good for occasional users solving (relatively) simple symbolic and/or numeric problems. Worth using if you want something to help you with your homework, but not do too much beyond that.
Matlab: Easier to use than Mathematica, not as easy as Maple. Many toolboxes available for many different tasks, interfaces well with lots of other software. More commonly used than Mathematica or Maple in industry and many research disciplines. It is popular because you can quickly write programs to process large amounts of data. While the programs won't be as efficient as ones written in lower level languages (C++ for example), the time saved in writing them often makes up for this. There is a symbolic package for doing simple symbolic work, but it's nowhere near as powerful as Mathematica or even Maple. Worth learning if you intend to do a lot of numerical data processing work, or work in industry.
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