Sinossi
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."
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Contenuti
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.
Product Description
Book by Engeler Erwin
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Foundations of Mathematics: Questions of Analysis, Geometry & Algorithmics
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Foundations of Mathematics
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book appeared about ten years ago in Gennan. It started as notes for a course which I gave intermittently at the ETH over a number of years. Following repeated suggestions, this English translation was commissioned by Springer; they were most fortunate in finding translators whose mathemati cal stature, grasp of the language and unselfish dedication to the essentially thankless task of rendering the text comprehensible in a second language, both impresses and shames me. Therefore, my thanks go to Dr. Roberto Minio, now Darmstadt and Professor Charles Thomas, Cambridge. The task of preparing a La'JEX-version of the text was extremely daunting, owing to the complexity and diversity of the symbolisms inherent in the various parts of the book. Here, my warm thanks go to Barbara Aquilino of the Mathematics Department of the ETH, who spent tedious but exacting hours in front of her Olivetti. The present book is not primarily intended to teach logic and axiomat ics as such, nor is it a complete survey of what was once called 'elementary mathematics from a higher standpoint'. Rather, its goal is to awaken a certain critical attitude in the student and to help give this attitude some solid foun dation. Our mathematics students, having been drilled for years in high-school and college, and having studied the immense edifice of analysis, regrettably come away convinced that they understand the concepts of real numbers, Euclidean space, and algorithm. 112 pp. Englisch. Codice articolo 9783642780547
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book appeared about ten years ago in Gennan. It started as notes for a course which I gave intermittently at the ETH over a number of years. Following repeated suggestions, this English translation was commissioned by Springer they were most fortunate. Codice articolo 5070462
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Foundations of Mathematics : Questions of Analysis, Geometry & Algorithmics
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book appeared about ten years ago in Gennan. It started as notes for a course which I gave intermittently at the ETH over a number of years. Following repeated suggestions, this English translation was commissioned by Springer; they were most fortunate in finding translators whose mathemati cal stature, grasp of the language and unselfish dedication to the essentially thankless task of rendering the text comprehensible in a second language, both impresses and shames me. Therefore, my thanks go to Dr. Roberto Minio, now Darmstadt and Professor Charles Thomas, Cambridge. The task of preparing a La'JEX-version of the text was extremely daunting, owing to the complexity and diversity of the symbolisms inherent in the various parts of the book. Here, my warm thanks go to Barbara Aquilino of the Mathematics Department of the ETH, who spent tedious but exacting hours in front of her Olivetti. The present book is not primarily intended to teach logic and axiomat ics as such, nor is it a complete survey of what was once called 'elementary mathematics from a higher standpoint'. Rather, its goal is to awaken a certain critical attitude in the student and to help give this attitude some solid foun dation. Our mathematics students, having been drilled for years in high-school and college, and having studied the immense edifice of analysis, regrettably come away convinced that they understand the concepts of real numbers, Euclidean space, and algorithm. Codice articolo 9783642780547
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