Titlebook: A History of Abstract Algebra; From Algebraic Equat Jeremy Gray Textbook 2018 Springer Nature Switzerland AG 2018 MSC (2010): 01A55, 01A60,

PAGAN

Lecture Notes in Networks and Systemsn much more simply in terms of modules and ideals in a quadratic number field, which in turn explained the connection between forms and algebraic numbers. In this chapter, we look at how this was done.

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Human Decision Making and Ordered SetsFollowing an overview of Carl Friedrich Gauss’s . in the previous chapter, in this chapter we turn to another major topic in Gauss’s book: cyclotomy. We will see how Gauss came to a special case of Galois theory and, in particular, to the discovery that the regular 17-sided polygon can be constructed by straight edge and circle alone.

磨坊

Graphical Data Structures for Ordered SetsIn this chapter, we discuss two of Gauss’s proofs of quadratic reciprocity: one (his second) uses composition of forms, and the other (his sixth) uses cyclotomy. The sixth was the last proof of this theorem he published, although he went on to leave two more unpublished.

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Generation of combinatorial objects,Galois’s theory was considered very difficult in its day, and was also poorly published. This chapter looks at what had to happen before it could become mainstream mathematics, and how as it did so it changed ideas about what constitutes algebra and started a move to create a theory of groups.

羞辱

填满

Sets, trees, and balanced trees,The book that established group theory as a subject in its own right in mathematics was the French mathematician Jordan’s . of 1870. In this chapter, we look at what that book contains, and how it defined the subject later known as group theory.

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Host142

https://doi.org/10.1007/978-3-031-01516-8This chapter picks up from the previous one and looks at how Dedekind analysed the concept of primality in an algebraic number field. This was to mark the start of a sharp difference of opinion with Kronecker.

Endearing

https://doi.org/10.1007/978-3-031-01516-8In this chapter, we look at how Dedekind refined his own theory of ideals in the later 1870s, and then at the contrast with Kronecker