Discrete and Algebraic Structures

This textbook presents the topics typically covered in a standard course on discrete structures. It is aimed at students of computer science and mathematics (teaching degree and Bachelor's/Master's) and is designed to accompany lectures, for self-study, and for exam preparation.

Through explanatory introductions to definitions, numerous examples, counterexamples, diagrams, cross-references, and outlooks, the authors manage to present the wide range of topics concisely and comprehensibly.

Numerous exercises facilitate the deepening of the material. Due to its compact presentation of all important discrete and algebraic structures and its extensive index, the book also serves as a reference for mathematicians, computer scientists, and natural scientists.

Contents: From propositional and predicate logic to sets and combinatorics, numbers, relations and mappings, graphs, to the rich spectrum of algebraic structures, and a brief introduction to category theory. Additional chapters include rings and modules as well as matroids.

This book is a translation of the second German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so the book may read stylistically differently from a conventional translation.

To learn the basics as well as revision for exam preparation Offers a compact, yet precise introduction in all relevant and discrete algebraic structures Offers a comparing overview over structures, not available in this form otherwise

Autorentext

Prof. Dr. Dr. h.c. Ulrich Knauer is a retired professor of mathematics at Carl von Ossietzky University of Oldenburg (Oldenburg).

Dr. habil. Kolja Knauer is an associate professor in discrete mathematics and computer science at Aix-Marseille University (France) and at the University of Barcelona (Spain).

Inhalt

1. Fundamentals .- 2. Sets and Counting .- 3. Numbers and their Representations .- 4. Relations.- 5. Mappings.- 6. Graphs.- 7. Groupoid, Semigroup, Group.- 8. From Semirings to Fields.- 9. Act, Vector Space, Extension.- 10 Rings and Modules. 11 Matroids.- 12 Categories.- Literature.- Symbols.- Index.