Erwin Engeler

Foundations of Mathematics (eBook, PDF)

Questions of Analysis, Geometry & Algorithmics
Übersetzer: Thomas, C. B.

• Format: PDF

Produktbeschreibung

From MATH REVIEWS (for the German edition): "The book is addressed to students of mathematics at the undergraduate or first year graduate level, with the objective of critically examining and clarifying the assumptions underlying basic concepts and axioms. For this purpose, the examples for the continuum, geometry and the theory of computability are used. The goal of getting the nonspecialist interested in foundational problems, and awakening a critical level of appreciation, is achieved to perfection by this text via a well thought out, successful selection both of the topics and of the level of analysis devoted to the individual themes."

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 100
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642780523
• Artikelnr.: 53097943

Inhaltsangabe

I. The Continuum.-
1 What Are the Real Numbers?.-
2 Language as Part of Mathematics.-
3 Elementary Theory of Real Numbers.-
4 Non-Standard Analysis.-
5 Axiom of Choice and Continuum Hypothesis.- II. Geometry.-
1 Space and Mathematics.-
2 Axiomatization by Means of Coordinates.-
3 Metatheoretical Questions and Methods in Elementary Geometry.-
4 Geometric Constructions.- III. Algorithmics.-
1 What is an Algorithm?.-
2 The Existence of Combinatory Algebras: Combinatory Logic.-
3 Concrete Combinatory Algebras.-
4 Lambda Calculus.-
5 Computability and Combinatorss.