Learning Abstract Algebra with ISETL

2015

The tone and level of mathematical sophistication of these two chapters is considerably different in these two chapters from those in the others. Much more background is expected from the reader interested in these sections.

This text is intended for a one-or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

ii This is a supplement to Abstract Algebra, Second Edition

iii v This text is written with the conviction that it is more effective to teach abstract and linear algebra as one coherent discipline rather than as two separate ones. Teaching abstract algebra and linear algebra as distinct courses results in a loss of synergy and a loss of momentum. Also with this text the professor does not extract the course from the text, but rather builds the course upon it.

Preface 1 The present book is an English translation from my book with the same title in Arabic language which are based on my lectures given to students of various colleges studying mathematics. In designing this course, the author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches. Therefore, in most cases we did not give rigorous formal proofs of the theorem. The rigorousness of a proof often fails to be fruitful and therefore it is usually ignored in practical applications. The book can be of use to readers of various professions dealing with applications of mathematics in their current work. The subject matter is presented in a very systematic and logical manner. It contains material which you will find of great use, not only in the technical courses you have yet to take, but also in your profession after graduation, as long as you deal with the analytical aspects of your field. In designing this book the author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches. This book consists of seven chapters. Chapter 1, "Sets -Relations -Functions" in abstract algebra, Chapter 2 contains the "Groups" as one of the main subjects. In Chapter 3 , we will discuss "Permutation Group" as a practical part and very useful in Linear Algebra. Chapter 4 presents "Isomorphism" which a fundamental part, and has many applications. Chapter 5, contains "The Natural Numbers" and how to extend the natural numbers up to real filed. Chapter 6 contains " Rings -Fields" as the second main subjects to abstract algebra. Chapter 7, which deal with "Continuation on Groups".

2023

Lecture Notes

Discrete Mathematics and Its Applications, 1999

Stitzinger. p. cm.-(Discrete mathematics and its applications) Includes bibliographical references and index. ISBN 0-8493-8170-3 (alk. paper) 1. Algebra, Abstract-Data processing. 2. Maple (Computer file)

2018

Introduction to school algebra can happen through varied approaches. Some prefer to start with an unknown in an equation, while some prefer to start with a formula and some others may prefer to use a pattern based approach. Does it make a difference which approach one uses? Is one approach better than the others? These questions can be debated. However, each of these approaches relates to different conceptions of algebra