The Symmetry of Equations: Galois Theory and Tschirnhausen Transformations
The previous chapter uses group theory to study spatial and permutational symmetry. This chapter extends the application of group theory to the symmetry inherent in algebraic equations, which is closely linked to the methods required for their solution. The group-theoretical aspects of algebraic equations were first introduced by Evariste Galois (1811-1832) so that this area of mathematics is frequently called Galois theory. An excellent discussion of Galois theory is given in a book by Stewart.
KeywordsIntegral Domain Galois Group Field Extension Minimum Polynomial Galois Theory
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