Miscellany

Harold M. Edwards

Chapter Chapter 5 in Essays in Constructive Mathematics, 2022, pp 173-194 from Springer

Abstract: Abstract The miscellany of this chapter begins with a proof of what is called the Fundamental Theorem of Algebra in fact two proofs of it. The main point is that this theorem is not truly a theorem of algebra at all because it relates in an essential way to the nonalgebraic notion of complex numbers. The next essay discusses proofs by contradiction and proves the Sylow theorems in the theory of finite groups. The following two essays summarize a constructive and algorithmic approach to linear algebra, including the spectral theorem. This gives yet another example of the clarifying power of algorithmic methods. The final essay is a further correction to the Kronecker legend.

Date: 2022
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DOI: 10.1007/978-3-030-98558-5_5

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