A Gentle Introduction to Group Theory

ISBN-13: 9789819901463 / Angielski

Bana Al Subaiei; Muneerah Al Nuwairan

Opis

The book is intended to serve as an introductory course in group theory geared towards second-year university students. It aims to provide them with the background needed to pursue more advanced courses in algebra and to provide a rich source of examples and exercises. Studying group theory began in the late eighteenth century and is still gaining importance due to its applications in physics, chemistry, geometry, and many fields in mathematics.

 

The text is broadly divided into three parts. The first part establishes the prerequisite knowledge required to study group theory. This includes topics in set theory, geometry, and number theory. Each of the chapters ends with solved and unsolved exercises relating to the topic. By doing this, the authors hope to fill the gaps between all the branches in mathematics that are linked to group theory. The second part is the core of the book which discusses topics on semigroups, groups, symmetric groups, subgroups, homomorphisms, isomorphism, and Abelian groups. The last part of the book introduces SAGE, a mathematical software that is used to solve group theory problems. Here, most of the important commands in SAGE are explained, and many examples and exercises are provided.

Spis treści

Background Results in Set Theory.- Algebraic Operations on Integers.- The Integers Modulo.- Semigroups.- Groups.- The Symmetric Group.- Subgroups.- Groups Homomorphisms and Isomorphic Groups.- Classification of Finite Abelian Groups.- Group Theory and SageMath.

O autorze

Bana Al Subaiei is Associate Professor at the Department of Mathematics and Statistics, King Faisal University, Saudi Arabia. She earned her Master and Ph.D. degrees from the University of Southampton, United Kingdom. Al Subaiei has more than 10 years of experience in higher education during which she served in many committees at department, college and university levels. Her research interest includes group theory, semigroup theory, ring theory and graph theory. She has published research appears in several academic journals, including Mediterranean Journal of Mathematics and Communication in Algebra.

Muneerah Al Nuwairan is Associate Professor at the Department of Mathematics and Statistics, King Faisal University, Saudi Arabia. She obtained her Master’s degree from King Faisal University, and then a Ph.D. degree in mathematics from the University of Ottawa, Canada. An active researcher in applied mathematics, she has been teaching mathematics since 1994. One of her main research interests is group theory.