Discrete Stochastics describe the typical ways of thinking and the working methods of stochastics on an intermediate level. In producing this textbook the author was faced with the challenging fact that probability theory dealing with continuous occurrence spaces uses measure and integration theory to a high degree. This implies a considerable complication, which is hardly consistent, with the objective of an introduction. To get around this problem the author uses discrete occurrence space. The formulations and notations are kept in such a way that they can be extended in a straightforward way to the general theory. The text is accompanied by several exercises as well as solutions.
Rezensionen / Stimmen
From the reviews:
"The (electronic) textbook ``Discrete stochastics'' introduces fundamental notions of probability theory for discrete probability spaces at an intermediate level. Installing the textbook on the computer and experimenting with it works without problems. Obviously considerable effort has been put into the development of the user-friendly program. The electronic version is accompanied by a printed edition. ... Each chapter includes exercises, the solutions are given, either upon pressing the button ``Solutions'' or at the end of the printed book. The interactive experiments support gaining intuition into the concepts of probability theory considered in the book."
E.Buckwar, Zbl. 1041.60003
" This textbook presents a rigorous treatment of probability theory in the discrete case that culminates by the weak law of large numbers. It is suitable for everyone who wants to understand probability and avoid corresponding measure theoretic complications. It can also be useful for a beginner in probability or statistics who has not yet mastered measure and integral theory. The authors assume a reader with passable skills in calculus. The textbook offers examples accompanied frequently by illuminating pictures, some of the exercises are solved separately at the end of the book. The enclosed CD, containing an electronic version of the text, is ready to install the corresponding program automatically in case you have MS Windows installed on your Computer."
(pd) EMS - European Mathematical Society Newsletter, March 2004, p. 43
" ... Wenn Sie schon lange nach einer kompakten, formal korrekten Einführung in die Wahrscheinlichkeitsrechnung suchten: Das Buch des gebürtigen Schaffhausers Otto Moeschlin und seiner Mitarbeiter bietet sie ihnen.
Wie schreibt man eine "korrekte" Wahrscheinlichkeitsrechnung ohne Masstheorie vorauszusetzen? Moeschlins souveräne Lösung dieses Problems: Er beschränkt sich auf diskrete Wahrscheinlichkeitsräume (was für die wenigsten Leser eine Einschränkung bedeutet). Einerseits kann er so alle Beweise vollständig führen (er braucht nur etwas Reihentheorie), andererseits sind die Konzepte so angelegt, dass sie sich auf allgemeine Wahrscheinlichkeitsräume verallgemeinern lassen. Im Zentrum steht dabei der Begriff des (diskreten) Wahrscheinlichkeitsmasses, aus dem die Grundbegriffe der Wahrscheinlichkeitsrechnung - etwa in dem Umfang wie man sie auf dem Gymnasium einführt - entwickelt werden.
Natürlich weiss auch Otto Moeschlin, dass der Formalismus allein die Studierenden nicht zu "überzeugen" vermag. Deshalb wird mit dem Buch eine CD-ROM geliefert. Neben dem kompletten Text des Buches enthält die CD verschiedene "Experimente": hervorragende Visualsierungen der schwierigen wahrscheinlichkeitstheoretischen Begriffe (z.B. der Unabhängigkeit zweier Zufallsvariablen).
Ich kann das Buch all jenen empfehlen, die eine "ausbaufähige" Einführung in die Wahrscheinlichkeitstheorie brauchen (etwa bei der Planung eines Leistungskurses) und vor allem auch jenen, die die dem Mittelschulstoff quasi von einer "höheren" Warte wiederbegegnen möchten. Allein die mitgelieferte CD mit den Experimenten rechtfertigt schon die Anschaffung des Werkes."
Urs Oswald, Bulletin des Vereins Schweizer Mathematik- und Physiklehrer, Issue 96, p. 26-27, 2004
"This textbook presents a rigorous treatment of probability theory in the discrete case . . It is suitable for everyone who wants to understand probability . . It can also be useful for a beginner in probability or statistics . . The textbook offers examples accompanied frequently by illuminating pictures . . The enclosed CD, containing an electronic version of the text, is ready to install the corresponding program automatically in case you have MS Windows installed on your computer." (EMS - European Mathematical Society Newsletter, March, 2004)
"The (electronic) textbook 'Discrete stochastics' introduces fundamental notions of probability theory for discrete probability spaces at an intermediate level. Installing the textbook on the computer and experimenting with it works without problems. Obviously, considerable effort has been put into the development of the user-friendly program. The electronic version is accompanied by a printed version. . The interactive experiments support gaining intuition into the concepts of probability theory considered in the book." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1041 (16), 2004)
