Linear algebra

Author: Wang Liqin / Li Naihua (Editor-in-Chief)
Publisher:
Publish Date: 2005-03-01
Features: In today's rapidly advancing science and economy, with the increasing popularity of computer and network technologies, human society is accelerating towards an information-based society. The application of mathematics is permeating various fields more broadly and deeply, and the demand for mathematical skills among professionals in different fields is continuously rising. This undoubtedly presents new challenges for mathematics education in an information-based society. As future high-tech industries can be, to some extent, reduced to mathematical technologies, the universality of mathematical applications and the quality of mathematical education reflect a nation's comprehensive strength to some extent and directly impact the improvement of citizens' literacy. Since many mathematical models involve extensive and complex scenarios, linear algebra has gradually become one of the most widely applied mathematical disciplines. As a foundational mathematics course, linear algebra is inherently theoretical, computationally intensive, and often perceived as dry and abstract. How can we improve the content and teaching methods of mathematics to enhance students' interest and motivation to learn? How can we integrate mathematical thinking into the curriculum while equipping students with the computational skills they need now and in the future? With this objective in mind, we have carefully summarized years of teaching experience and conducted thorough research on the reform trends of mathematics education both domestically and internationally. We believe that any reform of the "Linear Algebra" course, whether in content or teaching methods, should consider the unique characteristics of the subject. It should transform dry and complex material into engaging and accessible content, introduce theoretical concepts and principles through practical problems, illustrate computational methods and theoretical derivations with relatively simple examples, and use computers to perform complex large-scale calculations in practical teaching. This approach ensures the integration of theory with practice and the effective application of computer technology, truly fostering and enhancing students' mathematical abilities (including foundational knowledge, theoretical understanding, and computational skills). The "Linear Algebra" textbook presented to you now strives to integrate fundamental knowledge, computational skills, and computer applications into a cohesive whole. Complex calculations are facilitated using Mathematica, helping students transform knowledge into practical skills. We hope this textbook is applicable, practical, and user-friendly.
This textbook is characterized by the following:
1. A well-structured and logical flow, progressing from simple to complex, making the content clear and easy to understand, with appropriate examples to aid comprehension.
2. A reduction in some tedious theorem proofs and formula derivations, replaced by more examples.
3. Each chapter includes a practical teaching section, introducing the mathematical software Mathematica, enabling students to master the skill of using software for complex calculations after learning the basic concepts, theories, and operational methods of linear algebra.
This textbook is suitable for undergraduate students of all disciplines and serves as an easy-to-understand and learn reference for self-study.
Contributors to this book include: Wang Liqin, Li Naihua, Zhao Junying, An Jianye, Li Meifeng, Luo Zhiming, Hu Jizhou, and Xie Xiaoliang.
During the writing process, this book received guidance from the Higher Education Department of the Tianjin Municipal Education Commission and the Academic Affairs Office of Tianjin University of Commerce. Special thanks are extended to the Textbook Center of Tianjin University of Commerce and the China Renmin University of Political Science and Law for their strong support. The teachers of Hunan University of Commerce provided many valuable suggestions. To enhance the depth and breadth of the content, we referred to multiple textbooks and monographs and incorporated some examples and exercises, for which we express our heartfelt gratitude. Due to the authors' limited expertise, any inaccuracies in this book are sincerely appreciated by the readers.