Elementary Abstract Algebra: Examples and Applications

Format:

Book

Contributor:

Hill, Justin, editor.

Thron, Chris, editor.

Language:

English

Subjects (All):

Mathematics--Textbooks.

Mathematics.

Physical Description:

1 online resource

Place of Publication:

Killeen, Texas Justin Hill and Chris Thron 2019.

Language Note:

In English.

Summary:

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.

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

Notes:

Description based on print resource