Advanced Algebra Tutorial and Problem Solutions (Volume 1). New Edition

Author:, Luo Jian, Wu Hong, Chen Li
Publisher:
Publish Date: 2006-04-01
Features: Advanced Algebra is an important foundational course in the field of mathematics and a mandatory subject for the postgraduate entrance examination of mathematics majors. Advanced Algebra is characterized by its theoretical abstraction, rigorous logical reasoning, and broad applicability. Most students find Advanced Algebra abstract and difficult to understand during the learning process, struggling to grasp fundamental concepts and the conclusions of theorems. When it comes to solving problems, they often lack ideas and find it hard to get started. To help readers master the basic theories and methods of Advanced Algebra, as well as to improve their ability to comprehensively apply various problem-solving techniques and methods, analyze, and solve problems, we have compiled this supplementary textbook (Volume 1 and Volume 2) based on the "Advanced Algebra" written by Professor Qiu Weisheng. This supplementary textbook consists of the following parts:
1. Key Concepts and Formulas: Lists the basic concepts, important theorems, and important formulas of each chapter, highlighting the core content that must be mastered and understood.
2. Solving Key and Difficult Points: Lists the key and difficult points of each chapter and provides corresponding explanations to help readers gain a deeper understanding of the relevant content.
3. Complete Solutions to After-Class Exercises: The textbook contains a large number of after-class exercises with varying difficulty levels. Many fundamental problems help readers understand basic concepts and theories from multiple perspectives, refine their basic methods, and many advanced problems further improve and apply their knowledge. Some problems have unique problem-solving approaches and methods. In response to these two points, we have provided detailed solutions to all after-class exercises in the textbook. Due to the diverse methods of solving problems in Advanced Algebra, most exercises only provide one reference solution, leaving other methods for readers to explore on their own.
4. Solutions to Entrance Examination Questions: We have selected and provided detailed solutions to representative questions from past entrance examination papers of various institutions for postgraduate studies. These examples cover a wide range of content, include multiple question types, and are highly skillful, enabling students to learn by example and generalize their knowledge. They can also broaden their problem-solving perspectives and better master the basic content and methods of Advanced Algebra.