Discrete Mathematics

Combinatorics, Counting, Proofs, Recurrences, Solutions

By: Walter Hower

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Paperback | 7 July 2025

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136 Pages

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24.0 x 17.0 x 1.27

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Discrete Mathematics presents the material in an easily accessible manner. Beside the usual content (expanded a little bit), a special writing style is used. We start with the natural numbers, function and relations, as well as the powerset lattice. The second chapter illustrates set theory with its laws and the Generalized Continuum Hypothesis. Chapter 3 delivers Boolean Algebra, with the double exponential formula for the # different boolean functions. The next chapter covers the induction, direct, and indirect proof. Chapter 5 presents combinatorics: Rules of sum, product, quotient, the pigeonhole principle, in/exclusion, permutation and binomial coefficient, plus Stirling numbers of 1st and 2nd kind as well as the Bell number; additionally, the recurrence relation with back- and forward reasoning is offered. We conclude with general and conditional probability, incl. the Monty Hall problem. Discrete Mathematics presents the material in a lively fashion, including topics which are usually not presented. Providing an annex with questions and solutions it offers the chance to the readers worldwide to grasp the subject in this handy and clearly arranged treatise.

Industry Reviews

Review of the German edition: "The whole book bears the clear signature of the author, at least for those who know him. This includes precision and a sense of the whole as well as the detail. The author's enthusiasm for the material to be conveyed cannot be overlooked. Accompanied with the appropriate pace and high conciseness, it is an excellent source for teaching the fundamentals of mathematics to computer scientists." Prof. Dr Juraj Hromkovic, ETH Zurich

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