Generalizing Calculous Conclusion Using The Method Of Plausible Reasoning

G. Polya, contemporary famous mathematician, educator, is the expert of plausible reasoning. He suggested that one of the main purposes of mathe-matics education is to develop the students ability to solve problems, teach students to how to think.plausible reasoning is a kind of possibility reasoning. It is possible conclusion reasoning according to people's experience, knowledge, intuitive and feeling etc. The result of plausible reasoning is conjecture, which is called mathematic hypothesis. We know we can make sure our mathematical knowledge by demonstration reason-ing, but the plausible reasoning can provide us with guess basis. Mathematician creative work namely is arguably the reasoning results prove, But the proof is found by the plausible reasoning and guess. G. Polya points out that a student who seri-ously thinks mathematics as his lifelong career must learn argument reasoning that is his profession and his mark subject. However, he must learn plausible reasoning in order to get the real achievement in which his creative work depends on the kind of reasoning. That is to say plausible reasoning is almost everywhere in math study, and its role cannot be underestimated.At present many people learn mathematics in our country. They learn and store a lot of math knowledge and skill, which is good to improve population average quality. However, how to make these store things produce more (even more) use value? This is a real problem which is worth thinking for math research workers. For example, the student can make further improvement or thinking (even research) which is a more effective learning. It usually will produce the effect of practice makes perfect. The teacher's guidance (including provision of analogy, imitating some guide material) is extremely important in the process. This paper will provide people with introductory material.This paper introduces the methods for plausible reasoning and uses them to discover a new topological theorem according to calculus step by step. It shows plausible reasoning plays a very important role in higher mathematics learning.The paper concludes three parts.The first chapter introduces the plausible reasoning university math learning applications. Firstly, you can see the common plausible reasoning ways such as the induction, general method, specialization, analogy, RMI principle, etc. Secondly, we put it to topological space through a familiar proposition in real space.Chapter 2 is the key part in the paper. We expound the concrete application of the plausible reasoning through a calculus topic. Therefore we get some wonder-ful conclusion and theorem. The chapter can be divided into three parts to show clearly the application of the plausible reasoning method. We introduce preliminary knowledge related to theorem 1 in the first part. In the second part we expound the theorem of the formation of the process and get results through a familiar with the theorem. By means of the mathematical analysis using analogy, induction gen-eralization and so on, we get some known results in general topology and several equivalent descriptions of Hausdorff L-closure space. In the third part is a note of this chapter. This part illustrates methods in plausible reasoning is quite important in mathematics learning by examples.Chapter 3 is the thinking of plausible reasoning. We demonstrate the rela-tionship between argumentation and plausible reasoning reasoning. We advocate students should be given guess of space in teaching. Finally, we hope everyone can pay more attention to plausible reasoning in the higher mathematics learning and use it much more.