Those 3 softwares are quite different: - matlab is at first dedicated to statistics and signal processing from real dataset; you can easily get data from oracle database, real-world sensors, etc. Matlab is efficient to process this kind of data. - maple is at first usefull to work on formal equations and formula. You cannot do that with Matlab (unless you have the Maple package for Matlab see this). - mathematica is between the two others: not as formaly efficient as Maple for formal calculus, but more fast than Maple to work with real datasets. I use intensively Maple and Matlab for about 15 years, but I only use Mathematica occasionnaly, so may be that my point of view abot the former is not the best you can have,