Hill J. Elementary Abstract Algebra. Examples and Applications 2017 torrent

Textbook in PDF format

This textbook introduces the basic notions of group theory by a thorough treatment of important examples, including complex numbers, modular arithmetic, symmetries, and permutations. Also included are applications to communications, cryptography, and coding theory.
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, most if not all published abstract algebra texts are totally 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 two-way interaction rather than rehashing the same material in lecture format. The book is highly modular, and chapters may be readily omitted if students are already familiar with the material. Some chapters (“In the Beginning” and “Sigma Notation”) are remedial. Other chapters cover topics that are often covered in courses in discrete mathematics, such as sets, functions, and equivalence classes. We have found from experience that students need this re-exposure in order to gain the necessary facility with these concepts, on which so much of the rest of the book is based. Whenever possible we have introduced applications, which may be omitted at the instructor’s discretion. However, we feel that it is critically important for preparing secondary teachers to be familiar with these applications. They will remember these long after they have forgotten proofs they have learned, and they may even be able to convey some of these ideas to their own students.
Preliminaries.
Complex Numbers.
Modular Arithmetic.
Set Theory.
Functions: Basic Concepts.
Equivalence Relations and Equivalence Classes.
Symmetries of Plane Figures.
Permutations.
Abstract Groups: Definitions and Basic Properties.
Cosets and Factor Groups.
Isomorphisms of Groups.
Homomorphisms of Groups.
Groups Actions and Regular Polyhedra.
Applications of Group Theory I: Introduction to Cryptography.
Group Theory Applications (II): Error-Detecting and Correcting Codes.
Sigma Notation.
Polynomials.
Appendix: Induction proofs–patterns and examples.
Hints