Pierce the postgraduate entrance exam mathematics (economics) 2007

Author: Mou Junlin et al.
Publisher:
Publish Date: 2004-02-01
Features: The systematicity and uniqueness of this book in mathematics demonstrate that ingenuity triumphs over brute force. The authors meticulously studied and summarized the wisdom of numerous mathematical elites of this era to overcome the limitations of individual thinking. Their sole purpose is to help students easily grasp the shortcut for passing the postgraduate entrance exam and change the fate of candidates. The distinctive feature of this book lies in establishing a living problem framework based on the intrinsic connections of each point in the syllabus. To enable candidates to master this new problem framework, we have enhanced its internal connections from the following four aspects:
1. A Fresh and Rational Chapter Arrangement: We have abandoned the traditional method of arranging content according to textbook chapters and instead integrated related chapters, allowing readers to achieve a comprehensive understanding through comparative analysis. For example, following the textbook order, there is an intermediate chapter on indefinite integrals between the derivatives of single-variable and multi-variable functions. Students often struggle to see the intrinsic connection between single-variable and multi-variable function differentiation, as both share similarities in problem-solving methods and thinking approaches. Therefore, we have combined these two chapters. Similarly, in linear algebra, proof problems are scattered across chapters on determinants, matrices, vectors, and linear equations, making it difficult for students to grasp the overall picture. We have consolidated them into a single chapter titled "Proof Problems in Linear Algebra." For the specific chapter arrangement and its rationale, please refer to "Chapter Arrangement of This Book."
2. Grouping Similar Examples into Problem Types: Within each chapter and section, we categorize examples with similar problem-solving methods into types, summarizing each section into several or a dozen types. The advantages of this approach are:
- Fewer problem types per section, with strong internal connections among them, making them easier to master compared to a scattered set of dozens of examples.
- Each problem type includes several similar sub-problems, allowing students to analyze and master them from different angles, thereby grasping the essence of each type. Through our summarization, all problem types can be fully presented in a single table, giving candidates confidence in mastering them. See "Table of Contents."
3. Explanation of Problem-Solving Methods: We generally introduce basic methods first, followed by special methods, while summarizing a series of basic steps to provide readers with a clear problem-solving approach. These steps help you quickly find a solution and improve efficiency. For example, when calculating limits, non-standard problems should first be converted into standard ones, which may involve logarithmic identities, substitution, or common denominators. Then, methods like L'H?pital's Rule should be applied, with attention to solving factors that can be determined first.
4. Two Important Appendices: At the beginning of the book, we have compiled two key appendices: "Fundamental and Important Theorems" and "Fundamental Problem Types and Solving Methods." These are the essence of this book. Many candidates struggle to memorize trigonometric formulas and complex equations before exams, yet finding a specific formula often requires flipping through multiple books, which is inconvenient. Additionally, without a clear and comprehensive understanding of various problem types, students may not have time to review but worry about not doing so. To address these challenges, we have carefully prepared these two appendices. This transforms the learning process into a more memorization-based task, requiring only ten minutes of review daily. This helps stabilize candidates' minds, avoid unnecessary anxiety, and is crucial!