Mathematical Experiment: Textbook for 21st Century Universities

Author: Han Xianxi
Publisher:
Publish Date: 2003-09-01
Features: This book takes the teaching content of advanced mathematics, linear algebra, complex function, probability theory, and mathematical statistics as the main line, guided by the idea of deepening students' understanding of basic concepts and stimulating their interest in hands-on exploration, with the aim of cultivating students' mathematical modeling and numerical computing abilities. It meticulously designs and organizes 33 mathematical experiments. The book consists of two parts and an appendix. Part I is the Basic Experiments. The Basic Mathematical Experiments section uses the method of mathematical experiments to deepen students' understanding of more abstract concepts in advanced mathematics, linear algebra, complex functions, and probability statistics, presenting fundamental concepts and conclusions in an intuitive and visual manner. This enables students to thoroughly grasp basic mathematical concepts and conclusions. Thus, it truly achieves the goal of "cultivating students' mathematical literacy, providing them with necessary mathematical thinking methods and tools for future learning, work, and research," while also fostering their ability to self-update knowledge. This part includes 22 experiments primarily designed in conjunction with the learning of fundamental courses.
Part II is the Research Experiments. These experiments involve observing and analyzing mathematical phenomena in engineering mathematics courses, allowing students to experience how to discover and summarize mathematical patterns. Centered around advanced mathematics, linear algebra, probability theory, and mathematical statistics, they radiate outward to related disciplines such as differential geometry, numerical analysis, mathematical statistics, and the numerical solution of differential equations, primarily reflecting the philosophy of "theory + computation + experiment." They also encompass emerging modern disciplines and directions, such as fractals and chaos. Students are encouraged to discover and summarize patterns through hands-on experimentation and observation, further learning new mathematical knowledge and integrating modern mathematical thinking. The key focus of the entire book is to treat Mathematical Experiments as a series of courses that span the entire mathematics learning process from the first to the third year of university. It aims to cultivate students' ability to observe, abstract, and research problems from a quantitative perspective; to develop their logical and rigorous thinking; to foster their awareness, interest, and ability to solve practical problems using mathematical principles and methods; and to encourage innovative thinking.
This book is suitable for students in science and engineering majors at universities, undergraduate students in normal universities, as well as readers with preliminary knowledge of advanced mathematics and computer science, particularly those studying complex functions, differential equations, numerical analysis, and related courses in mathematics.