Hower W. Discrete Mathematics. Combinatorics, Counting, Proofs,...Solutions 2025

Textbook in PDF format

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