Algebraic Structures Volume 01: Groups: Foundations of Binary Operations, Groups, Subgroups, Permutations, Isomorphisms and Homomorphisms (Bachelor's Degree in Mathematics)
English | 25 Jan. 2026 | ASIN: B0GJN8JGF6 | 340 pages | PDF | 6.84 MB
Ready to master the foundations of abstract algebra? Algebraic Structures: Volume I - Groups is a comprehensive guide for students, instructors, and self-learners who wish to understand algebraic structures from their very foundations: binary operations and groups. This first volume provides a progressive and rigorous study of groups, subgroups, permutations, isomorphisms, and homomorphisms-core concepts of modern algebraic theory. What will you find in this volume? Binary operations and their importance Discover how basic operations structure algebraic systems. Explore classical examples, construct operation tables, and learn to identify properties such as closure, associativity, and commutativity. Formal definition and properties of groups Delve into the axioms of group theory through detailed examples, including numerical groups, permutation groups, and matrix groups. Understand the role of identity and inverse elements, and their connection to symmetry in mathematics and science. Subgroups, cyclic subgroups, and their classification Study the formal criteria for identifying subgroups and learn how to determine generators and orders. This practical approach enables you to apply the concepts to real problems and visualize structures through Cayley tables. Permutation theory and alternating groups Expand your knowledge by exploring cycle decompositions, alternating groups, and their applications to symmetry and combinatorics, which are essential in algebra and equation theory. Isomorphisms, Cayley's Theorem, and equivalent structures Understand how algebraic structures can be represented equivalently through isomorphisms, and explore the universality of permutation groups via Cayley's Theorem. Normal subgroups, quotient groups, and homomorphisms Learn how to simplify structures using normal subgroups and quotient groups. Study homomorphisms and their Fundamental Theorem, which is key to relating and connecting different groups. Why choose this book? * Rigor and clarity: Definitions, theorems, and proofs are presented in a detailed and well-structured manner. * Examples and exercises: Includes step-by-step solved problems and a wide range of proposed exercises. * Accessible and progressive: Ideal for those beginning abstract algebra or seeking to consolidate their knowledge. * Academic and practical focus: Perfect as a core university textbook or for self-study. This book is ideal for: * Undergraduate students in mathematics, physics, engineering, and computer science. * Instructors and educators in algebra and pure mathematics. * Self-learners interested in exploring group theory in a formal and comprehensive way. With a balanced combination of theory and practice, Algebraic Structures: Volume I - Groups provides the essential tools to understand, analyze, and apply algebraic structures, paving the way for advanced studies in algebra, topology, Galois theory, and beyond. Series: Bachelor's Degree in Mathematics Legal Information: Legal Deposit No.: 2026-00833 Country of origin: Peru Independent Publisher: Helbert Justo Luque Zevallos Legal address: Coop. Vista Alegre E-2, Alto Selva Alegre, Arequipa, Peru Available on Amazon Click "Buy Now" and begin your journey toward mastering abstract algebra.
Buy Premium From My Links To Get Resumable Support,Max Speed & Support Me
Rapidgator
6jxgv.7z.html
DDownload
6jxgv.7z
FreeDL
6jxgv.7z.html
AlfaFile
6jxgv.7z
Links are Interchangeable - Single Extraction
