Contemporary Abstract Algebra by Joseph A Gallian is a comprehensive textbook for students studying abstract algebra at the undergraduate level. Now in its seventh edition, this book has remained a popular choice for students and instructors alike, thanks to its clear and engaging writing style and its thorough coverage of the subject.
The book is divided into three parts, with the first part covering the basics of groups, rings, and fields. The second part delves deeper into group theory, including topics such as homomorphisms, isomorphisms, and subgroups. The third and final part covers field theory, with a particular focus on Galois theory and its applications.
One of the strengths of this textbook is the way it balances rigor with accessibility. Gallian presents the material in a clear and straightforward manner, without sacrificing the necessary mathematical rigor. The book is well-organized, with each chapter building upon the previous one, and it includes many helpful examples and exercises to aid in the understanding of the material.
Another strength of this book is its numerous applications of abstract algebra to other areas of mathematics and science. For example, in Chapter 10, the author applies group theory to the study of symmetry in geometry, while in Chapter 14, he uses Galois theory to solve a classic problem in geometry known as the impossibility of trisecting an angle.
In addition to its clear writing style and numerous applications, Contemporary Abstract Algebra also features many helpful resources for students and instructors. The book includes a detailed table of contents and index, as well as a comprehensive list of symbols and notation. Instructors can also access a solutions manual, test bank, and PowerPoint slides to aid in course preparation and teaching.
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In conclusion, Contemporary Abstract Algebra by Joseph A Gallian is an excellent textbook for students studying abstract algebra at the undergraduate level. Its clear writing style, comprehensive coverage of the subject, and numerous applications make it an ideal choice for both students and instructors alike. Whether you are studying abstract algebra for the first time or looking to deepen your understanding of the subject, this book is an excellent resource.
