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[Diese Seite in deutsch]

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My main interests are mathematics and (real played) games. For details please have a look to the second US edition of my book "Luck, logic and white lies: The mathematics of games", a translation of the 7th edition of my German book "Glück, Logik und Bluff". Publisher is Routledge (Taylor & Francis Group).

568 pages ISBN: 978-0-367-54841-4 Price: 49 $ Online versions: Google order at amazon.com Reviews Errata

Luck, logic and white lies: three ways to win a game depending on its character. There is a close relation with three mathematical theories: probability theory makes it possible to compute winning rates of games of luck. Algorithms used by chess programs are part of the combinatorial game theory. Quite different methods belonging to the game theory are needed for instance in card games, because the knowledge of the current situation during such a game isn't the same for each player. Based on examples methods of the three theories are explained. Some of the examined games are Roulette, Numbers Lottery, Monopoly, Risk, Black Jack, Snakes and Ladders, Chess, Go, Nine Men's Morris, Go-Moku, Nim, Backgammon, Mastermind, Memory (Concentration), Poker and Baccarat. The book is written in a quite popular manner. Specialists will find a lot of references to original papers.

An overview can be found on the sheets of my talks "Games in the View of Mathematics (2017)" and "Games in the view of mathematics (2000)" at the University of Strathclyde, Glasgow on 23/11/2017 resp. on a symposium of AIMe (Association of Industrial Mathematics Eindhoven) on 3.11.2000.

During the preparation of my book I wrote also a little overview concerning "Go and Mathematics" (in German).

In the years 2017 to 2019 I published some papers concerning the topic of measuring skill in games, which are the base of the new forth part of the book.

Also you can find: Test your skill of bluffing in the simple betting-and-bluffing game QUAAK! (The computer is playing a mixed minimax strategy). And you can look at two animations of Monopoly: How to find the probabilities using a Monte Carlo simulation resp. a computation of the Markov chain. Finally there is a JavaScript based calculator for the odds in the game blackjack (description as pdf file) .

217 pages ISBN: 978-1-4704-6500-1 Price: 59 $ Preface and Contents Online versions: Amazon, AMS order at amazon.com Reviews

Another overview is dealing with the "Ideas of galois theory" (in German) - of course there isn't any relation to games. But there is a relation to my second book "Galois theory for beginners: A historical perspective. " (a translation of my German book "Algebra für Einsteiger: Von der Gleichungsauflösung zur Galois-Theorie"). The book contains the classical formulas for solving equations up to the fourth degree, methods to solve cyclotomic equations and special equations of fifth degree. Last but not least I give an introduction to Galois theory including a lot of concrete examples. The translated book was published by the AMS (American Mathematical Society). In the 2nd edition were added twenty facsimiles of milestones of classical algebra and a detailed description of Artin's approach of Galois theory.

About my person:

In 1985 I made my Ph.D. in Bonn. In my thesis, which was supervised by Günter Harder (later one of the directors of the "Max-Planck-Institut für Mathematik" in Bonn) , I used topological methods to prove a Lefschetz fixed point formula for twisted Hecke operators (on the level of the cohomology of arithmetic groups). In the case of rank one I characterised the boundary contributions of the Lefschetz number as a Lefschetz number of a truncated Hecke correspondence defined on the contracting parts of the boundary. As a conclusion I got arithmetic results like class number relations. In the general case the terms of the adelic version are based on orbital integrals. For newer and more general results look to Goresky/MacPherson, Arthur and Mahnkopf.

From 1998 until 2019 I was Managing Director of subsidiaries of the Gauselmann AG: First of Mega-Spielgeräte in Limburg, which is designing AWPs (amusement with prices, that means "slot machines" to be operated in German pubs and arcades; see also DMV-Mitteilungen 3/98) and internet terminals (Mega Web) and later of GeWeTe, which is producing change machines and automated pay machines.

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