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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 my book "Luck, logic and white lies: The mathematics of games", a translation of my German book "Glück, Logik und Bluff". Publisher is AK Peters.

504 pages ISBN: 1-56881-210-8 Price: 49 $ preface and contents Online versions: Amazon, order at amazon.com Reviews

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 "Spiele aus mathematischer Sicht" and "Games in the view of mathematics" on the Mathematikertag at the FH Stuttgart/Hochschule für Technik on 17.11.2000 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).

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) .

180 pages ISBN: 0-8218-3817-2 Price: 35 $ Preface and Contents Online versions: Amazon, AMS order at amazon.com Reviews Errata

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).

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.

Now, since 1998, I am Managing Director 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). I am also Managing Director of GeWeTe which is producing change machines and automated pay machines.

Last but not least: My favourite Web-links and a short overview how to generate, read and print postscript- and Acrobat-Files (ps resp. pdf).

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