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Abstract Algebra A Proof-Based Approach with Complete Solutions
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ISBN13: 9798248522705
Publisher: Independently Published
Published: Feb 15 2026
Pages: 212
Weight: 0.64
Height: 0.45 Width: 6.00 Depth: 9.00
Language: English
Publisher: Independently Published
Published: Feb 15 2026
Pages: 212
Weight: 0.64
Height: 0.45 Width: 6.00 Depth: 9.00
Language: English
Abstract Algebra can feel intimidating-until you see the patterns clearly and practice the proofs step by step.
This book is a student-friendly, proof-focused guide designed to help you understand the core structures of algebra and confidently solve problems the way instructors grade them. Inside, you'll build mastery through clear explanations, worked examples, and fully written solutions that model the logic and structure of strong mathematical writing. What you'll learn (with complete solutions) Groups, subgroups, cyclic groups, permutations, and group actions Homomorphisms, kernels, images, isomorphism theorems, and quotient groups Rings, ideals, ring homomorphisms, and quotient rings Integral domains, fields, polynomial rings, and factorization Modular arithmetic, congruences, and applications to number theory Proof techniques used in abstract algebra: induction, contradiction, contrapositive, and construction proofs Why this book works Proof-based approach: every major idea comes with a proof blueprint you can reuse Complete solutions: no skipped steps-solutions are written in a way you can learn from Practice-first design: definitions → examples → exercises → solutions (ideal for self-study) Exam-ready coverage: matches the standard undergraduate abstract algebra sequence Whether you're taking your first course in abstract algebra or reviewing for an exam, this book helps you move from I recognize the topic to I can prove it and solve it.
This book is a student-friendly, proof-focused guide designed to help you understand the core structures of algebra and confidently solve problems the way instructors grade them. Inside, you'll build mastery through clear explanations, worked examples, and fully written solutions that model the logic and structure of strong mathematical writing. What you'll learn (with complete solutions) Groups, subgroups, cyclic groups, permutations, and group actions Homomorphisms, kernels, images, isomorphism theorems, and quotient groups Rings, ideals, ring homomorphisms, and quotient rings Integral domains, fields, polynomial rings, and factorization Modular arithmetic, congruences, and applications to number theory Proof techniques used in abstract algebra: induction, contradiction, contrapositive, and construction proofs Why this book works Proof-based approach: every major idea comes with a proof blueprint you can reuse Complete solutions: no skipped steps-solutions are written in a way you can learn from Practice-first design: definitions → examples → exercises → solutions (ideal for self-study) Exam-ready coverage: matches the standard undergraduate abstract algebra sequence Whether you're taking your first course in abstract algebra or reviewing for an exam, this book helps you move from I recognize the topic to I can prove it and solve it.
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