Foundations of Mathematics: Questions of Analysis, Geometry & Algorithmics - Softcover

Engeler, Erwin

Softcover

ISBN 10: 3642780547 ISBN 13: 9783642780547

Verlag: Springer, 2011

Inhaltsangabe

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."

Über diesen Titel

Reseña del editor

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.

Reseña del editor

This book is concerned with those foundational questions in elementary algebra, calculus and geometry, that are almost always left unanswered in undergraduate courses in these subjects. Among the topics considered are non-standard analysis, the relationship between classical geometric theorems (such as those of Pascal and Desargues) and field axioms, questions of decidability, and combinatorial logic. An attractive feature is the case given to the historical context in which foundational questions have arisen, and to the early attempts made to resolve them. From the ZENTRALBLATT review of the German edition: "It isone of those rare books which give you freedom and fantasy to reconsider themost common concepts of mathematics...The book explains carefully, using motivating examples and sometimes quite original proofs, the developmentof crucial ideas in important branches of mathematics. It is a pleasure to read it."

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 3642780547
• ISBN 13: 9783642780547
• Einband: Tapa blanda
• Anzahl der Seiten: 112
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland