Contemporary Abstract Algebra
Contemporary Abstract Algebra, written by Joseph Gallian, is a comprehensive and accessible introduction to the principles of modern algebra. This book is an ideal resource for undergraduate students pursuing a degree in mathematics, as well as anyone interested in expanding their knowledge of abstract algebra.
Joseph Gallian is a distinguished professor of mathematics at the University of Minnesota Duluth. He has authored several publications in the field of algebra, and has received numerous awards for his work, including the prestigious Haimo Award for Distinguished Teaching from the Mathematical Association of America.
In the preface of the book, Gallian emphasizes the importance of abstract algebra in modern mathematics and its applications to various fields, including computer science, physics, and engineering. The book is designed to introduce students to the fundamental concepts of algebraic structures, including groups, rings, fields, and modules.
The first chapter provides an overview of the basic properties of sets and relations, which serves as a foundation for the subsequent chapters. The subsequent chapters delve into group theory, with topics including permutation groups, subgroups, homomorphisms, and quotient groups. Ring theory is covered in depth in the following chapters, with discussions on polynomial rings, ideals, factorization, and integral domains.
The final chapters of the book introduce more advanced topics, including field extensions, Galois theory, and module theory. Throughout the text, Gallian provides numerous examples and exercises to reinforce key concepts and encourage independent exploration.
Overall, Contemporary Abstract Algebra is a comprehensive and engaging introduction to abstract algebra, written by an expert in the field. It is an essential resource for students and professionals alike, seeking to expand their knowledge of modern algebraic structures.
Author: Joseph Gallian
Link to buy: https://www.amazon.com/Contemporary-Abstract-Algebra-Joseph-Gallian/dp/1133599702
Ratings: 4.5 out of 5 stars (from 356 reviews)
Best Sellers Rank: #1,067,388 in Books
#108 in Abstract Algebra (Books)
#408 in Elementary Algebra (Books)
#653 in Algebra & Trigonometry
