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Thursday, April 17, 2008

Abstract Algebra and Mathematica

I found a promising e-book on ( Explatory ) Galois Theory. The book is written at the undergraduate level and it has 'Explatory' in the title because the text uses and refers to the Mathematica ( and Maple ) packages.

What is Galois Theory anyway? Galois only wrote one ( unfinished ) paper before he died at the age of 19 in a duel, but the contribution he made to mathematics is very significant. Before Galois mathematicians were searching for a formula to find the roots of a fifth degree polynomial equation.

a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5=0

Galois proved that it is impossible to find such a formula. It does not exist. In his proof he introduced the concept of a Group.

Abstract Algebra and computers. I learned a lot of concepts in Abstract Algebra by using the package of Hibbard and Levasseur: Exploring Abstract Algebra with Mathematica. It is a book and a software package combined as one. The package though, can be downloaded freely. Mathematica (6.0) is a requirement as the package is written in the Mathematica language.
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