Study Guide for Advanced Mathematics: A Must-Read for Postgraduate Entrance Examinations

Author: Chen Dingxing
Publisher:
Publish Date: 2006-04-01
Features: This book is a teaching reference for advanced mathematics, suitable for middle-aged and young teachers and students teaching and learning advanced mathematics in engineering colleges. It is particularly suitable for students who aim to solidify their mathematical foundation and achieve further advancement, such as those preparing for postgraduate entrance exams or those who wish to excel in mathematical competitions. The book has the following features:
It selects 554 examples and 407 exercises, covering a wide range and representing strong significance. It emphasizes the integration and application of knowledge, offering "multiple solutions" for many problems. Nearly half of the examples include annotations, which analyze the problems, point out their origins, reveal their essence, suggest directions for further extension and research, clarify their significance, or provide advice on common mistakes. These annotations are the author's decades of teaching experience and insights, offered to the readers.
The solutions are striving to be novel and concise. Modern analytical methods, such as the contraction mapping principle and integral factors, are introduced into the book in an accessible way, simplifying problem-solving while broadening perspectives. While solving examples, the book aims to cultivate scientific thinking methods, such as the general-to-specific thinking model, divergent thinking like association, analogy, analysis, induction, and reverse thinking, multi-angle problem-solving approaches, and the development of intuitive judgment and scientific aesthetics.
It advocates the integration of mathematics with practical applications, showcasing the entire process of researching and solving real-world problems in multiple places, hoping to provide inspiration for beginners. The book strives to present calculus from a high starting point and introduces relevant knowledge of modern analysis through appendices and other means, for the reference of teachers.
The author sincerely hopes to explore teaching methods that integrate knowledge, qualities, and abilities with many wise people, and dedicates this book to them.