Linear Algebra with Mathematica
This website provides two things: One is comprised of equations and proofs which together constitute the bedrock of mathematics. The other is Wolfram software code which automates processing and reduces the tedium of solving many mathematical problems. The second, and the use of computers in general, must be viewed as a "black box" which may be specifically and completely understood only in terms of the equations and proofs contained therein.
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Mathematica is a great computer algebra system to use, especially if you are in applied areas where it is necessary to solve differential equations and other complicated problems. It was created by a brilliant entrepreneur, who inspired by Maxima, the first computer algebra system in the world, produced an elegant, coherent, and extremely general approach to computing. Mathematica provides friendly tools to solve and plot solutions to differential equations, but it is certainly not a panacea of all problems. This computer algebra system has tremendous plotting capabilities. There is a free version of Mathematica featuring its syntax and functions---Mathics that was developed by a team led by Jan Pöschko. It is backed by highly extensible Python code, relying on SymPy for most mathematical tasks. Mathics is released under the GNU General Public License (GPL).
A solution of a realistic problem is often hampered because the algebra is too complex for anyone but the dedicated researcher. Just as the calculator eliminated laborious numerical computations, symbolic software programs eliminate arduous algebraic computations. While computer power is no substitute for thinking, it spares the scientist from performing mundane mathematical steps, and thereby frees time for creative thinking. This tutorial can be used to introduce students who are taking the first course in Linear Algebra to a symbolic mathematical computation program Mathematica that was conceived by a theoretical physicist Stephen Wolfram (born in 1959 in London, England) in late 1980's.
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