2006 New Edition Reference Book for Graduate Entrance Examination Mathematics

Author: Li Hengpei, Editor-in-Chief
Publisher:
Publish Date: 2005-04-01
Features: This book is compiled for candidates taking the national mathematics unified examination for postgraduate entrance, and can also serve as supplementary reading for university students and teaching reference material for teachers. Following the content specified in the examination syllabus, the book is divided into three parts (Higher Mathematics: Chapters 1-8, Linear Algebra: Chapter 9, Probability Theory and Mathematical Statistics: Chapter 10), totaling ten chapters. Each chapter is further divided into sections, with each section consisting of two parts: "Content Summary and Key Focus" and "Example Analysis." The first part concisely introduces the content of the section and highlights the key focus; the second part provides typical examples to analyze problem-solving approaches and demonstrates the types of examination questions. These examples emphasize conceptual understanding, theoretical mastery, and methodological application, enabling candidates to generalize and apply knowledge effectively. At the end of the book, there are three appendices: Appendix 1 is an introduction to difference equations (for candidates taking "Mathematics 3" as a supplementary reference), while Appendices 2 and 3 are the 2004 and 2005 postgraduate entrance examination mathematics questions and reference answers, respectively, to facilitate review for candidates. This book can also be used by undergraduate students for deepening their learning, reviewing for examinations, and by teachers as a teaching reference. Based on, the questions exhibit the following characteristics:
(1) Strong conceptual focus. They emphasize the mastery of fundamental concepts and the ability to apply basic theorems to prove propositions, assessing candidates' proficiency from various perspectives and formulations (i.e., transformations and variations).
(2) Strong comprehensiveness. A single question may focus on one aspect of content, which contains numerous knowledge points. It is impossible to cover everything, so only a few key points are integrated to assess candidates' abilities and mathematical proficiency. Such questions appear almost every year in the exam, aiming to evaluate candidates' skills and mathematical qualities.
(3) Strong computational emphasis. Correct calculations depend on accurate concepts and methods. Although the mathematics questions involve a certain amount of computation, as long as candidates have a clear grasp of fundamental concepts, a thorough understanding of basic theories, and the ability to apply basic methods flexibly, they can solve problems efficiently and accurately. The questions are designed to be flexible, assessing candidates' abilities from different angles (or perspectives or related knowledge points), encouraging multiple solutions to allow candidates to perform well under pressure. Additionally, the questions emphasize argumentation and application, testing candidates' logical reasoning and comprehensive application skills, which are indispensable for all candidates, regardless of whether they are pursuing engineering, economics, or management. This book is tailored to the above characteristics by carefully selecting examples and exercises. The content is closely aligned with the syllabus, comprehensive yet concise, well-organized, and highlights key points. It reproduces examination questions, features diverse and typical examples with thorough analysis, provides regular summaries with logical connections for easier mastery, and includes exercises at the end of each chapter for self-assessment. The examples and exercises in this book complement each other, deepening the understanding of the content. Candidates are required not only to comprehend the examples but also to practice the exercises, as both are equally important.