Abstract algebra is a general term for the study of mathematics concerning axiomatically defined algebraic structures such as groups, rings, fields, modules, vector spaces and linear rings. Without a deep understanding of the significance of the formation of classical mathematics, it is difficult to fully understand the significance of abstract mathematics. In the first place, the significance of using symbols instead of figures in mathematics proofs, the problem of the existence of mathematical objects such as imaginary numbers, and other historical philosophical problems have nothing to do with the significance of the formation of abstract mathematics. The Évariste Galois theory was proposed by a Frenchman in the early 19th century. And "prove the impossibility'' is the joy of Galois theory. It is said that it was discovered by mathematicians such as the It seems that algebraic solutions are obtained by using the four arithmetic operations and n-th roots. This means that for equations of degree 5 and above, there is no formula for their solution. To prove this conclusion, he considered the equations themselves. He used the fundamental theorem of algebra proposed by Gauss that "an algebraic equation of degree n has exactly n complex solutions, including duplication''. The proof is reached without any effort (learned in junior high school mathematics, elimination method is common). In today's terms, this method seems to be the forerunner of the technique of exploring the underlying properties of the subject mathematics. It seems that Galois theory was something he came up with when he was a teenager. To his friend Auguste Chevalier, he wrote a letter summarizing his mathematical work on Galois theory and elliptic function theory. Later, in 1846, Joseph Liouville, who learned of Galois' achievements, published a collection of articles in his journal. Diophantine approximation: Reminds me of Arithmetica.
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