Discrete Mathematics

This book provides a concise and accessible introduction to counting and existence problems in discrete mathematics. It is aimed at students of mathematics, computer science, and related fields and demonstrates the power of simple principles. Only basic knowledge of linear algebra and analysis, as well as elementary probability theory, is required.

The topics range from classical results in combinatorics to generating functions (with a focus on partitions), extending to probabilistic methods in graph theory and the construction of block designs and codes. In this way, this book leads up to some of the gems of the twenty-first century and offers both theory and tools for solving problems in discrete mathematics.

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

Is written in a very clear and comprehensible manner Presents both classical and modern results Demonstrates the power of simple principles, readable without extensive prior knowledge

Autorentext

Eberhard Triesch has worked in various areas of discrete mathematics. He taught as a professor at the University of Bonn and RWTH Aachen University. He has been retired since 2022.

Inhalt

Fundamentals of Combinatorics.- Existence Problems.- Generating Functions.- The Incidence Algebra.- Counting Isomorphism Classes.- Hypergraphs.- The Probabilistic Method.- Block Designs.- Codes.