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Discrete Mathematics: count before you promise every combination

Richard Johnsonbaugh · Pearson, sixth edition, 2005
10 de mayo de 2026 por
Discrete Mathematics: count before you promise every combination
Andrés Briñez

It covers logic and proof, sets and functions, relations, number theory, counting and combinatorics, recurrences, graphs, trees, networks, boolean algebra and automata. The standard syllabus of a first course, with many worked examples and pseudocode.

What I took from it

The chapter on relations, which is literally where the relational model comes from. The properties of a relation — whether an element relates to itself, whether it holds in both directions, whether chaining two implies a third — stop being abstractions the moment you model customer hierarchies, product structures or approval routes. That is where it gets decided whether a query can be written plainly or has to walk a tree by hand.

The counting chapter left me a reflex that has saved me work: when somebody asks for every combination of something, count them first. Four attributes with ten values each is already ten thousand variants, and the conversation changes completely — it stops being a programming problem and becomes a business decision about which combinations actually sell. That arithmetic takes a minute and prevents configurations nobody can maintain.

Recurrences, finally, are what let you reason about processes that call themselves, which show up in an ERP more than people expect: bill of materials explosions, accounting hierarchies, consolidations.

What I left out

Automata, boolean circuits and most of the proofs. And a warning about the book as an object: it is a course text, and the real content is in the exercises. Anyone reading it like an essay will turn the pages with a feeling of understanding and take away almost nothing. That is not the author's fault, it is the genre.

Mastering ArchiMate: I kept the discipline and dropped the notation
Gerben Wierda · Edition III, 2017
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