Discrete Stochastics

This electronic textbook is based on courses on probability theory developed by O.Moeschlin. The aim is to describe the typical ways of thinking and the working methods of stochastics on an intermediate level. One problem in this context is that probability theory dealing with continuous basic 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. The way out taken here is to use a discrete basic 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. This textbook comes on a fully linked CD-ROM together with fifteen so-called experiments, i.e. screen visualizations of complex notions and facts. To make reading easier the textbook is accompanied by a printed text.

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 EinfA1/4hrung in die Wahrscheinlichkeitsrechnung suchten: Das Buch desgebA1/4rtigen Schaffhausers Otto Moeschlin und seiner Mitarbeiter bietet sie ihnen.

Wie schreibt man eine "korrekte" Wahrscheinlichkeitsrechnung ohne Masstheorie vorauszusetzen? Moeschlins souverAne LAsung dieses Problems: Er beschrAnkt sich auf diskrete WahrscheinlichkeitsrAume (was fA1/4r die wenigsten Leser eine EinschrAnkung bedeutet). Einerseits kann er so alle Beweise vollstAndig fA1/4hren (er braucht nur etwas Reihentheorie), andererseits sind die Konzepte so angelegt, dass sie sich auf allgemeine WahrscheinlichkeitsrAume 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 einfA1/4hrt - entwickelt werden.

NatA1/4rlich weiss auch Otto Moeschlin, dass der Formalismus allein die Studierenden nicht zu "A1/4berzeugen" vermag. Deshalb wird mit dem Buch eine CD-ROM geliefert. Neben dem kompletten Text des Buches enthAlt die CD verschiedene "Experimente": hervorragende Visualsierungen der schwierigen wahrscheinlichkeitstheoretischen Begriffe (z.B. der UnabhAngigkeit zweier Zufallsvariablen).

Ich kann das Buch all jenen empfehlen, die eine "ausbaufAhige" EinfA1/4hrung in die Wahrscheinlichkeitstheorie brauchen (etwa bei der Planung eines Leistungskurses) und vor allem auch jenen, die die dem Mittelschulstoff quasi von einer "hAheren" Warte wiederbegegnen mAchten. 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 probabilitytheory in the discrete case a ] . It is suitable for everyone who wants to understand probability a ] . It can also be useful for a beginner in probability or statistics a ] . The textbook offers examples accompanied frequently by illuminating pictures a ] . 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 a ~Discrete stochasticsa (TM) 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. a ] The interactive experiments support gaining intuition into the concepts of probability theory considered in the book." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1041 (16), 2004)