Linear Algebra (with CD-ROM)

Author: Wang Liqin, Li Naihua
Publisher:
Publish Date: 2005-03-01
Features: In today's rapidly developing science and economy, with the increasing popularity of computer and network technologies, human society is accelerating its transition to 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 the information age. Since future high-tech industries can be, to some extent, attributed to mathematical technology, the universality of mathematical applications and the quality of mathematical education reflect a nation's comprehensive strength to a certain degree and directly impact the improvement of citizens' literacy. Given that many mathematical models involve complex and extensive scenarios, linear algebra has gradually become one of the most widely applied mathematical disciplines. As a foundational course in mathematics, 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 and methods into teaching while ensuring students acquire the computational skills in linear algebra 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 reforms in 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, explain 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 cultivating and enhancing students' mathematical abilities (including foundational knowledge, theoretical understanding, and computational skills). The textbook "Linear Algebra" presented here aims 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.
The textbook features the following characteristics:
1. Logical structure, smooth flow, and a progressive approach from simple to complex, making the content clear and easy to understand, with appropriate examples to aid comprehension.
2. Reduced emphasis on lengthy theorem proofs and formula derivations, replaced by more examples.
3. Added practical teaching sections in each chapter, 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 accessible and practical reference for self-study. The authors of 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 also referenced multiple textbooks and monographs and adapted some examples and exercises, for which we express heartfelt gratitude. Due to the authors' limited expertise, any inaccuracies in the book are sincerely appreciated by the readers for correction.