For a detailed example of length contraction, and references to many other paradoxes, see Is length contraction really paradoxical? in the October 1987 issue of The American Journal of Physics.
The May 2002 issue of Physics Today contains an article on Relativity and the Global Positioning System. (After you click, the link to the full text will be on the left of the screen.)
To obtain a student copy of Mathematica, visit the following ITS web site: https://help.lafayette.edu/mathematica/students.
There are a variety of on-line tutorials available for Mathematica. I recommend going to Wolfram.com and exploring their on-line resources. Some students have reported the following to be useful:
The National Institute of Technology and Standards maintains a useful page with the current best values for many fundamental constants, at http://physics.nist.gov/cuu/Constants/.
The July 2014 issue of Physics Today included an interesting article about a proposed revamping of the standards used for many fundamental constants. You can read about it in the article A more fundamental International System of Units.