Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects. Provides a wealth of exercises and problems to support self-study. Additional online resources on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.
Focusing on the foundational concepts of linearity, this book delves into the principles of linear algebra, emphasizing operations that maintain addition and scalar multiplication. It contrasts traditional approaches with modern mathematical styles, advocating for a pure mathematician's perspective in the study of linear algebra. The text aims to highlight the elegance and theoretical aspects of the subject, distinguishing itself from application-focused works. It presents essential theories and results, catering to those interested in the pure mathematical framework of linear algebra.
This book offers a comprehensive introduction to linear algebra, focusing on its fundamental properties and theorems through a pure mathematical lens. Topics include vector spaces, matrices, determinants, and applications in various fields. It features numerous examples, exercises, and solutions, making it suitable for both beginner and advanced students.