Peter J. Cameron Boeken

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.

This book serves as an introduction to enumerative combinatorics, a crucial field in mathematics with applications across various disciplines. It is designed to be used as a textbook for courses or for self-study, making it accessible for both students and independent learners seeking to deepen their understanding of combinatorial techniques and principles.

Focusing on permutation groups, this text highlights recent advancements influenced by the Classification of Finite Simple Groups and its connections to logic and combinatorics. It introduces relevant computer algebra systems capable of handling large groups and includes sketch proofs of key theorems alongside practical examples. Designed for beginning graduate students and experts from various fields, the content is based on a short course held at the EIDMA institute in Eindhoven, making complex topics accessible to a broader audience.