Study Guide for Advanced Algebra (Volume 1)

Author: Qiu Weisheng
Publisher:
Publish Date: 2005-07-01
Features: This book serves as a supplementary learning guide for the national-level planning textbook "Advanced Algebra (Second Edition, Volume 1)" under the "Tenth Five-Year Plan." It embodies the author's 34 years of teaching experience, particularly the 26 years dedicated to advanced algebra and linear algebra, as well as the culmination of many years of teaching advanced algebra at Peking University. Key Features:
· This book focuses on cultivating students' mathematical thinking and enhancing their quality and abilities.
· It provides numerous proof strategies and problem-solving methods, summarizing important techniques and skills in advanced algebra to enable readers to generalize and apply knowledge.
· Unlike other similar books, the essence of this book differs in its content. The author does not merely list concepts and theorems but explains the problems to be studied and the approaches to solving them, revealing the underlying principles of the subject.
· The problem-solving strategies and detailed solutions for typical examples in this book differ from those in similar books. The author emphasizes inspiring readers' problem-solving approaches, strengthening their analytical skills, and providing insights into the significance of problems, solution methods, and common pitfalls.
· The exercises in this book are diverse, including those aligned with teaching requirements as well as those designed to enhance analytical skills and broaden readers' perspectives. This book is a companion to the national-level planning textbook "Advanced Algebra" (Second Edition, Volume 1), edited by Qiu Weisheng and published by Higher Education Press. It reflects the author's many years of teaching advanced algebra at Peking University. The book consists of 6 chapters, with each chapter structured into three main parts: essence of content, typical examples, and exercises. Additional supplementary problems are provided at the end of each chapter. The book elaborates on the theory of advanced algebra, summarizes important typical and postgraduate examination problems, and distills the principles, methods, and techniques for solving problems. Through the explanation of theory and the analysis of problem-solving methods, it aims to help readers master the theory, generalize knowledge, and apply it effectively. This book can serve as supplementary material for college students and self-learners studying advanced algebra, as a reference for teachers teaching advanced algebra or linear algebra, and as a review guide for postgraduate entrance examinations in mathematics for students of engineering, science, economics, management, and other disciplines.