An Introduction to Essential Algebraic Structures.

Intro -- An Introduction to Essential Algebraic Structures -- Copyright -- Contents -- Preface -- Chapter 1 Sets -- 1.1 Operations on Sets -- Exercise Set 1.1 -- 1.2 Set Mappings -- Exercise Set 1.2 -- 1.3 Products of Mappings and Permutations -- Exercise Set 1.3 -- 1.4 Operations on Matrices -- Exercise Set 1.4 -- 1.5 Binary Algebraic Operations and Equivalence Relations -- Exercise Set 1.5 -- Chapter 2 Numbers -- 2.1 Some Properties of Integers: Mathematical Induction -- Exercise Set 2.1 -- 2.2 Divisibility -- Exercise Set 2.2 -- 2.3 Prime Factorization: The Fundamental Theorem of Arithmetic -- Exercise Set 2.3 -- 2.4 Rational Numbers, Irrational Numbers, and Real Numbers -- Exercise Set 2.4 -- Chapter 3 Groups -- 3.1 Groups and Subgroups -- Exercise Set 3.1 -- 3.2 Cosets and Normal Subgroups -- Exercise Set 3.2 -- 3.3 Factor Groups and Homomorphisms -- Exercise Set 3.3 -- Chapter 4 Rings -- 4.1 Rings, Subrings, Associative Rings -- Exercise Set 4.1 -- 4.2 Rings of Polynomials -- Exercise Set 4.2 -- 4.3 Ideals and Quotient Rings -- Exercise Set 4.3 -- 4.4 Homomorphisms of Rings -- Exercise Set 4.4 -- Chapter 5 Fields -- 5.1 Fields: Basic Properties and Examples -- Exercise Set 5.1 -- 5.2 Some Field Extensions -- Exercise Set 5.2 -- 5.3 Fields of Algebraic Numbers -- Exercise Set 5.3 -- Hints and Answers to Selected Exercises -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Index -- End User License Agreement.

A reader-friendly introduction to modern algebra with important examples from various areas of mathematics Featuring a clear and concise approach, An Introduction to Essential Algebraic Structures presents an integrated approach to basic concepts of modern algebra and highlights topics that play a central role in various branches of mathematics. The authors discuss key topics of abstract and modern algebra including sets, number systems, groups, rings, and fields. The book begins with an exposition of the elements of set theory and moves on to cover the main ideas and branches of abstract algebra. In addition, the book includes: Numerous examples throughout to deepen readers' knowledge of the presented material An exercise set after each chapter section in an effort to build a deeper understanding of the subject and improve knowledge retention Hints and answers to select exercises at the end of the book A supplementary website with an Instructors Solutions manual An Introduction to Essential Algebraic Structures is an excellent textbook for introductory courses in abstract algebra as well as an ideal reference for anyone who would like to be more familiar with the basic topics of abstract algebra.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.