Experience the culmination of mathematical exploration with Relations: From Sets to Structures, a textbook that reimagines foundational mathematics through the lens of relational thinking. Serving as the bridge between traditional ZFC set theory and modern relational algebra, this book offers a fresh perspective on how relations underpin mathematical structures. Key Features: Begins with elementary set theory, introducing the reader to the ZFC framework while emphasizing the role of relations in defining sets. Explores functions, equivalence relations, partial orders, and Galois connections, showcasing the profound interplay between relations and algebraic structures. Delves into advanced topics such as residuated mappings, well-founded relations, and confluent relations, blending traditional mathematical approaches with innovative insights. Provides a unique focus on the relational background behind calculus, linear algebra, and number theory, synthesizing concepts from the previous books in The Connection Prelude Series. Designed for readers familiar with foundational mathematics, offering rigorous explanations, examples, and exercises that illuminate the foundational role of relations. Relations: From Sets to Structures is a landmark text that challenges conventional perspectives and provides the tools to view mathematics through the powerful lens of relational theory.

Ideal for students and mathematicians seeking a deeper understanding of foundational mathematics, this book is the perfect preparation for the revolutionary field of Connection Theory.