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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Analysis 0. Ein logischer Einstieg in die Analysis
Analysis 0. Ein logischer Einstieg in die Analysis

Analysis 0. Ein logischer Einstieg in die Analysis


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About the Book

Was bedeutet eigentlich das Gleichheitszeichen? Was ist ein Beweis? Warum ist ungerade mal ungerade ungerade, aber minus mal minus plus? Auf solche Grundlagen gehen die Lehrveranstaltungen zur Analysis an unseren Hochschulen selten ein. In Wolfgang Helbigs Einf�hrung finden sich Antworten auf Fragen wie diese.Anders als in vielen Einf�hrungen geht Helbig nicht nur auf die reellen und komplexen, sondern auch auf die nat�rlichen, ganzen und rationalen Zahlen ein. Sie werden durch Axiome so definiert, da� sie l�ckenlose Beweise nicht nur in der Analysis, sondern auch in der Zahlentheorie oder der Kombinatorik erm�glichen. Die Widerspruchsfreiheit dieser Axiome wird durch vollst�ndig ausgef�hrte mengentheoretische Konstruktionen nachgewiesen, wobei einzig die Existenz einer Peano-Struktur vorausgesetzt wird.Die Eigenschaften stetiger Funktionen, konvergenter Folgen und Reihen, zusammenh�ngender und kompakter Mengen werden aus den Axiomen des metrischen Raums abgeleitet und als weiteres Beispiel der axiomatischen Methode auf Zahlenbereiche und Funktionenr�ume �bertragen, um Potenzen mit reellen und komplexen Exponenten zu studieren.Alle S�tze, vom Prinzip der rekursiven Definition bis zum Satz von Heine-Borel, und alle Formeln, von der geometrischen Reihe bis zum Cauchyprodukt, werden allein aus den Axiomen abgeleitet. In Helbigs Analysis 0 gibt es nichts "Triviales", jeder Schlu� wird begr�ndet. Dabei legt Helbig besonderen Wert auf die Leserfreundlichkeit der Beweise.So kann der Leser die Chance wahrnehmen, die Schl�ssigkeit der Argumentation selbst zu beurteilen. Auch der mathematisch Fortgeschrittene zieht aus der Lekt�re Gewinn - findet doch auch er die Herleitung zahlreicher vertrauter S�tze, die er bislang beweislos und unkritisch benutzt hat, etwa zu Eigenschaften endlicher Mengen oder den Rechengesetzen endlicher Summen.

About the Author :
Wolfgang Helbig, Studium der Mathematik, Physik und Biologie in T�bingen (1976-1980) und der Informatik an der Fernuniversit�t Hagen (1990-1995). Lehrt�tigkeit an der Dualen Hochschule Baden-W�rttemberg in Stuttgart. Der Autor arbeitet als Programmierer.


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Product Details
  • ISBN-13: 9783838203010
  • Publisher: Ibidem Press
  • Publisher Imprint: Ibidem Press
  • Height: 210 mm
  • No of Pages: 206
  • Returnable: N
  • Returnable: N
  • Weight: 299 gr
  • ISBN-10: 3838203011
  • Publisher Date: 01 Sep 2011
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Returnable: N
  • Spine Width: 11 mm
  • Width: 148 mm


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