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Linear Algebra in Every Day Life Read chapter Read first chapter

2015 | OriginalPaper | Chapter

2. Basic Mathematical Concepts

Authors : Jörg Liesen, Volker Mehrmann

Published in: Linear Algebra

Publisher: Springer International Publishing

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Abstract

In this chapter we introduce the mathematical concepts that form the basis for the developments in the following chapters. We begin with sets and basic mathematical logic. Then we consider maps between sets and their most important properties. Finally we discuss relations and in particular equivalence relations on a set.

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previous chapter Linear Algebra in Every Day Life
next chapter Algebraic Structures
Footnotes
1
Georg Cantor (1845–1918), one of the founders of set theory. Cantor published this definition in the journal “Mathematische Annalen” in 1895.
 
2
The notations \(M\cup N\) and \(M\cap N\) for union and intersection of sets M and N were introduced in 1888 by Giuseppe Peano (1858–1932), one of the founders of formal logic. The notation of the “smallest common multiple \(\mathfrak {M}(M,N)\)” and “largest common divisor \(\mathfrak {D}(M,N)\)” of the sets M and N suggested by Georg Cantor (1845–1918) did not catch on.
 
3
Named after René Descartes (1596–1650), the founder of Analytic Geometry. Georg Cantor (1845–1918) used in 1895 the name “connection set of M and N” and the notation \((M.N)=\{(m,n)\}\).
 
Metadata
Title
Basic Mathematical Concepts
Authors
Jörg Liesen
Volker Mehrmann
Copyright Year
2015
Book
Linear Algebra

Print ISBN: 978-3-319-24344-3

Electronic ISBN: 978-3-319-24346-7

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-24346-7_2

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