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Elementary Abstract Algebra Examples and Applications Justin Hill

Contributor(s): Material type: TextTextSeries: Open textbook libraryDistributor: Minneapolis, MN Open Textbook LibraryPublisher: Killeen, Texas Justin Hill and Chris Thron 2019Copyright date: ©2019Description: 1 online resourceContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780359042111
Subject(s): LOC classification:
  • QA37.3
  • QA150-272.5
Online resources:
Contents:
1 Preliminaries -- 2 Complex Numbers -- 3 Modular Arithmetic -- 4 Modular Arithmetic, Decimals, and Divisibility -- 5 Set Theory -- 6 Functions: Basic Concepts -- 7 Introduction to Cryptography -- 8 Sigma Notation -- 9 Polynomials -- 10 Symmetries of Plane Figures -- 11 Permutations -- 12 Introduction to Groups -- 13 Further Topics in Cryptography -- 14 Equivalence Relations and Equivalence Classes -- 15 Cosets and Quotient Groups (a.k.a. Factor Groups) -- 16 Error-Detecting and Correcting Codes -- 17 Isomorphisms of Groups -- 18 Homomorphisms of Groups -- 19 Group Actions -- 20 Introduction to Rings and Fields
Subject: This book is not intended for budding mathematicians. It was created for a math program in which most of the students in upper-level math classes are planning to become secondary school teachers. For such students, conventional abstract algebra texts are practically incomprehensible, both in style and in content. Faced with this situation, we decided to create a book that our students could actually read for themselves. In this way we have been able to dedicate class time to problem-solving and personal interaction rather than rehashing the same material in lecture format.
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1 Preliminaries -- 2 Complex Numbers -- 3 Modular Arithmetic -- 4 Modular Arithmetic, Decimals, and Divisibility -- 5 Set Theory -- 6 Functions: Basic Concepts -- 7 Introduction to Cryptography -- 8 Sigma Notation -- 9 Polynomials -- 10 Symmetries of Plane Figures -- 11 Permutations -- 12 Introduction to Groups -- 13 Further Topics in Cryptography -- 14 Equivalence Relations and Equivalence Classes -- 15 Cosets and Quotient Groups (a.k.a. Factor Groups) -- 16 Error-Detecting and Correcting Codes -- 17 Isomorphisms of Groups -- 18 Homomorphisms of Groups -- 19 Group Actions -- 20 Introduction to Rings and Fields

This book is not intended for budding mathematicians. It was created for a math program in which most of the students in upper-level math classes are planning to become secondary school teachers. For such students, conventional abstract algebra texts are practically incomprehensible, both in style and in content. Faced with this situation, we decided to create a book that our students could actually read for themselves. In this way we have been able to dedicate class time to problem-solving and personal interaction rather than rehashing the same material in lecture format.

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In English.

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