Elementary Abstract Algebra (original) (raw)
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".
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