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Circular games constitute a fascinating area of discrete mathematics that receives far too little attention. We cover fundamental areas of discrete mathematics, thereby providing all the tools needed to study circular games. Using the duality-generating function-the z-transformation-we bridge the gap to engineering mathematics methods for dealing with differences. Contents: Calculus of differences, difference equations, solution methods, and approaches to recursive formulas; asymptotic comparisons, permutations, cycles, and counting coefficients; graphs and their decomposition; round-robin tournaments as combinatorial problems; construction and properties of game schedules; linear optimization.
There are many articles on the topic of round-robin tournaments, but a systematic presentation has been lacking until now. There is still much to discover in this field.
Walter Strampp was a Senior Academic Advisor and Adjunct Professor at the University of Kassel's Institute of Mathematics. He has many years of teaching experience in STEM fields and has gained extensive experience in the transition from high school to university. He has published several textbooks on engineering mathematics and approximately 60 research articles on integrable systems.
