An Introduction to Abstract Algebra” by CK Taylor is a comprehensive textbook that provides students with an in-depth understanding of the fundamental concepts of abstract algebra. This book is ideal for students who are taking a course in abstract algebra for the first time, as well as for those who want to refresh their knowledge of the subject.
The book covers all the core topics of abstract algebra, including groups, rings, and fields. The author uses clear explanations and a wealth of examples to help students understand the concepts and apply them to real-world problems. Throughout the book, Taylor emphasizes the importance of using abstract concepts to solve concrete problems, helping students to see the connection between theory and practice.
One of the strengths of “An Introduction to Abstract Algebra” is its focus on developing the abstract reasoning skills that are so important in mathematics. The book encourages students to think critically and systematically and provides plenty of opportunities for them to apply the concepts they have learned. The author also includes a large number of exercises, so students can practice what they have learned and develop their problem-solving skills.
TABLE OF CONTENTS
Preliminaries
- Introduction to Abstract Algebra
- Logic and Proof
- Set Theory
- Mappings and Equivalence Relations
Group Theory
- Binary Operations
- Introduction to Groups
- Cyclic Groups
- Dihedral Groups
- Groups of Permutations
- Alternating Groups
- Subgroups
- Homomorphisms and Isomorphisms
- Cosets and Normal Subgroups
- Quotient Groups
- Direct Products
- Catalogue of Finite Groups
Field Theory
- Introduction to Fields
- Polynomials
- Irreducibility
- Vector Spaces
- Extension Fields
- Algebraic Extensions
- Geometric Extensions
- Geometric Constructions
Ring Theory
- Introduction to Rings
- Integral Domains
- Ideals
In addition to its pedagogical approach, “An Introduction to Abstract Algebra” is also notable for its comprehensive coverage of the subject. The author has taken care to ensure that all the key concepts are covered in sufficient detail and has included a wide range of examples to help students understand how the concepts can be applied in different contexts.
In conclusion, “An Introduction to Abstract Algebra” by CK Taylor is an excellent textbook for students who are studying abstract algebra for the first time, or for those who want to deepen their understanding of the subject. The book is well-written, clear, and comprehensive, and provides students with the knowledge and skills they need to succeed in abstract algebra.
For the convenience of students, this book is available in PDF format for download, making it easier for students to access the information they need and study on the go.
