Linear Algebra, 21st Century Higher Education Series Textbooks

Author: Niu Fengwen
Publisher:
Publish Date: 2005-09-01
Features: Modern Algebra is a fundamental course for undergraduate mathematics majors, covering the structure of basic algebraic systems. This book introduces the structural theories of groups, rings, and modules. The theory of groups emerged early in history, with rich research content and typical research methods, making it the most widely applied branch of algebra. The book provides a relatively in-depth discussion of several important topics in group theory. The ideas and methods of abstract algebra are permeating various scientific fields and continuously giving rise to new branches. This book does not pursue completeness of knowledge but strives to thoroughly explain the connotations of important ideas and methods such as quotient, homomorphism, and extension. The selection of theorems and propositions not only focuses on their importance in the theoretical system but also considers the demonstrative nature of their proofs. This book was gradually revised and completed based on various lecture notes used by the author in teaching Modern Algebra at Jilin University for many years, incorporating the achievements of teaching reform by the author's teachers and colleagues.