Study Guide for Advanced Mathematics Learning and Improvement - 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 instructors and students teaching and learning advanced mathematics in engineering colleges. It is particularly beneficial for students who aim to solidify their mathematical foundation and pursue further studies, such as those preparing for postgraduate entrance exams or those seeking to excel in mathematical competitions. The book has the following characteristics:
It includes 554 selected examples and 407 practice problems, covering a broad range and representing strong significance. It emphasizes the integration and comprehensive understanding of knowledge, offering "multiple solutions to a single problem" for many issues. Nearly half of the examples come with annotations, which may analyze the problem, point out its origin, reveal its essence, suggest further generalization and research directions, clarify its significance, or provide advice on common mistakes. These annotations reflect the author's decades of teaching experience and insights, offered to the readers.
The book strives for novel and concise solutions to problems. It introduces modern analytical methods, such as the contraction mapping principle and integral factors, in an accessible manner, simplifying problem-solving while broadening perspectives. While solving examples, it integrates the cultivation of scientific thinking methods, such as the general-to-specific mindset, divergent thinking (e.g., association, analogy, analysis, induction, reverse thinking), multi-angle problem-solving approaches, and the development of intuition and scientific aesthetics.
The book advocates for the integration of mathematics with real-world applications, showcasing the entire process of researching and solving practical problems in multiple places, hoping to provide inspiration for beginners. It aims to present calculus from a high starting point and introduces relevant knowledge of modern analysis through appendices and other means, serving as a reference for instructors.
The author sincerely hopes to explore teaching methods that combine knowledge, qualities, and abilities with a wide range of knowledgeable individuals and dedicates this book to such discussions.