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I think learning mathematica may be useful for certain things. Another motivation comes from Matt Henderson's blog. He uses mathematica to render really interesting graphics.

Mathematica is a functional language, a type I have no experience with, and it will be both challenging and educational to try learning the language. The documents to introduce the language is not as numerous as ones for MATLAB, but I've located (supposedly) two very good introductions:

1.Fundamentals of Mathematica Programming by Gaylord Mathematica Programming: an Advanced Introduction by Shifrin

But perhaps the best place to start Mathematic may be at wolframalpha.com itself.

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett