Group Theory: A Journey from Intuition to Abstraction: SUNIL KUMAWAT

Book Title: Group Theory: A Journey from Intuition to Abstraction Author: Sunil Kumawat Description: Group Theory: A Journey from Intuition to Abstraction is a thoughtfully crafted book designed to bridge the gap between concrete understanding and formal mathematical rigor in the study of group theory. It guides readers on a progressive journey, starting from everyday intuitive examples like symmetries, modular arithmetic, and geometric transformations, and gradually leading them into the deeper abstract structures and theorems that form the foundation of modern algebra. Written with clarity and purpose, this book is ideal for undergraduate students, aspiring mathematicians, and curious learners who seek to build a strong conceptual and practical grasp of group theory. Each chapter is carefully structured, featuring detailed explanations, visual illustrations, motivating examples, and well-developed proofs. The book also includes carefully selected exercises to reinforce learning and promote deeper exploration of topics. Key topics covered include: The definition and classification of groups Subgroups, cosets, and Lagrange’s theorem Group homomorphisms and isomorphisms Cyclic groups and permutation groups Group actions and their applications Sylow theorems and the structure of finite groups Simple groups and composition series An introduction to representation theory and character tables What sets this book apart is its commitment to accessibility without compromising mathematical rigor. By emphasizing the "why" behind definitions and theorems, it builds a strong narrative that invites readers to see the beauty and logic of abstract algebra View Less