Guide: Guide 1 Look at the thinking behind the solution. How should Fu Chengde teach mathematics? How to learn? Looking back on our math lessons from childhood, most of them are an established model: the teacher teaches you some math tools, and then tells you what tools to use for one math problem and what tools to use for another math problem. For example, the teacher teaches you to arrange and combine, and then tells you how to calculate three men and five women sitting around a round table; When I teach you trigonometric functions, I will tell you how to find the area of a triangle by sine theorem. During the exam, students will follow suit. "The teacher said that this problem should be calculated by permutation and combination", so he applied the formula of permutation and combination. "This question is not written in the reference book, so we should use the sine theorem", so we take out the sine theorem and use it. When encountering a topic that has not been read, the students spread their hands: "I haven't learned it, I won't." As a result, students have a lot of magic weapons in their hands, but they are helpless about problems they have never seen before. He doesn't know how to do it unless the teacher has taught him. But most of the problems in the world are not taught by teachers, and there is no way to teach them. In this ever-changing era, no matter in academic circles, in practice, in mathematical olympiad competitions, or even in real life, we are constantly facing new questions, which no one in the world has ever seen and no one knows how to answer. Under such circumstances, we can no longer rely on the school teacher to give us the answer, because the answer simply does not exist in this world! Therefore, we urgently need to cultivate the ability of "finding solutions by ourselves". We need to know how an answer "pops up": Why is the problem of three men and five women calculated like this? Why use sine theorem for this region? When faced with these problems, how do mathematicians who come up with these solutions make gradual analysis, find out the appropriate mathematical tools and then solve them? We need to see the "thinking behind the solution" in order to understand how to create new solutions when facing new problems. This is the essence of this book. Professor Tao Zhexuan, a "prodigy", became a national athlete in Olympia at the age of 65,438+00, and is still active in the field of mathematics. In this book, his problem-solving ideas are completely spread out in front of you. He not only tells you how to solve problems, but more importantly, how he "thinks" about these solutions. With this book, I believe readers can clearly understand that these solutions did not fall out of thin air; That is, through step-by-step analysis, the feasible scheme is summarized step by step and laid out slowly. You can imagine. You can do it too! This book is of great help to the study and understanding of mathematics, and can help readers learn how to transform the mathematical knowledge learned in class into personal mathematical ability, so it is recommended to students, teachers, parents and the public. I believe that after reading this book, you will have a brand-new understanding of mathematics, a subject that most people find "mysterious and difficult to understand", and it will have very positive significance for you to think about problems (no matter what kind of problems) in your future life. (The writer is the chair professor and director of the Institute of Statistics of Central University, and the host of the Mathematical Olympiad of the Republic of China. ) The book in the hands of young enthusiastic readers of top mathematicians is a problem-solving manual written by Tao Zhexuan, a brilliant top mathematician, at the age of 15. The book tells the ideas and methods of solving mathematical problems through some test questions. Most of the topics in the book are not difficult, but they are all math competitions that need to be considered. But to be honest, there are too many books on solving "mathematical problems" or "solving mathematical competition problems" on the market. Choose one, the depth of content and the breadth of search are probably more than that. Like reference books for further studies, such books have developed into series of questions, simulation questions and intimate points. By this standard, this book can't get in. But if you really love math and care about education, I strongly recommend this book by Tao Zhexuan. All students who love math and math teachers and parents who have the opportunity to teach gifted students can watch it. Why? First of all, this is the first-hand data of problem-solving ideas. How did you come up with this question? This may be all those who are struggling in mathematics ... suggesting to experience the beauty of mathematics with simplicity and complexity. Reading this book, I have experienced the characteristics of thinking, keen intuition, rigorous logic and artistic problem-solving strategies and processes, which are amazing! You can also write and think together and do it! Or find two or three friends to discuss PK together, and then compare the solutions in the book to see what is ingenious; You can also take Tao Zhexuan as a tutor, watch him explain how to solve problems, follow him in the process of solving problems, feel the spirit and beauty of mathematics with simplicity and complexity, and enjoy the fun of solving problems together! People often ask: Are those "mathematical geniuses" really abstruse in solving problems? Did their extraordinary insight come from the Oracle? Or do you have excellent problem-solving tools and skills? I think Tao Zhexuan, who has an IQ of over 220 and is considered as the smartest scientist, has given his answer! (The writer is a tutor and math teacher in the gifted class of Mathematics and Science in Taipei Jianguo Middle School. )