On mathematical reasoning and proof the complex review the main points-毕业论文翻译.doc

1On mathematical reasoning and proof the complex review the main pointsOne, focusing on main points of review (1) inductive reasoning In recent years, the college entrance examination in particular focus on examining the induction conjecture, the main form the basis of known conditions to formulate a conclusion, if the answers to the questions, then deductive reasoning to prove the conclusions of inductive reasoning pay attention: ① inductive reasoning is based on a particular phenomenon infer a general phenomenon, beyond the scope of the premise inclusive conclusions obtained by inductive reasoning, and thus must be based on observation, on the basis of test, experiment, (2) using inductive reasoning to draw conclusions, remember not to generalize, not according to several The special circumstances of general conclusions, the need to re-use the knowledge to prove that the conclusion is correct, so be careful. (2) analogical reasoning Analogical reasoning frequently appear in the entrance examination in the past few years, and ever-changing, not only to examine the 2candidates’ grasp of the association, analogy, and other methods, but also examine the candidate’s interpretation of the (logical reasoning ability. Attention point of analogical reasoning: 1 analogical reasoning from the properties of the things people have mastered, suggesting that the properties of the things being studied based on the old cognitive-based, analog to the new results, ② The analogical reasoning is speculated that the special attributes of a thing to another the special properties of things, by special reasoning ③ in geometric reasoning, is usually the case, points in the plane figure, line, surface comparable space graphics, line, surface, body, flat graphics the surface area can be compared to the size of the graphics for the space of geometry. 3 deductive reasoning The general steps of deductive reasoning: the flexibility to choose according to the specific questions the reasoning steps, but several inference rules basically follow this three-step “condition - reasoning - Conclusions. Attention point for deductive reasoning: ① in mathematics to prove that the correctness of the proposition is to use deductive 3reasoning, and sensible reasoning can not be used as proof of; ② interpretation of the reasoning in the syllogism, the premise of the reasoning process of the specific issues can sometimes be omitted, but it must be clear what the premise is. (4) direct proof Synthesis method and analysis method is the two ideas are diametrically opposed to the method of proof synthesis method is characterized by: “known” from the “known” to see, and gradually push the “unknown” is actually a step to find the necessary conditions, while the characteristics of the analysis: “unknown” “Notes,” and gradually move closer to the “known”, in fact, is to find the establishment of a sufficient condition to make the step. Analysis and synthesis method has advantages and disadvantages: From the point of view to seek problem-solving ideas, the analysis of thinking, and clear sense of direction, the idea of natural synthesis method often minor phenomena, not easy to reach the conclusion to prove. ② from the expression process in terms of analysis describes the complicated, diction lengthy simple form of the 4synthesis method, the clarity of analysis that is, conducive to thinking, comprehensive method is appropriate to write, therefore, in practical problem solving, often the two ways to combine the use of the first analysis to explore the way of the card title, then write the proof of the synthesis method, which is an important method used to solve mathematical problems. (5) indirect evidence The general steps required to prove that a mathematical proposition as follows: (1 to distinguish between the proposition of the conditions and conclusions, (2) to make assumptions and propositions contradict; (3 hypotheses, and apply the correct reasoning method, the introduction of contradictions, (4 concluded that generate contradictory results because of the beginning assumptions made are not true, so the original conclusion, and thus indirectly prove that the establishment of the original proposition. Links in the free paper mathematical induction Use mathematical induction to prove the key lies in two steps to do recursive basis and no less, use the induction hypothesis to conclusion write 5Mingmo forget the “. It is necessary to note the following: (1 verify the basic mathematical induction The principle: The first step is to find a number, this number is the smallest natural number to prove the proposition objects, the natural numbers is not always “1”, “Looking for a starting point and foundation stability” is the right use mathematical induction to pay attention to the first question. (2 Recursion is the key to the essence of mathematical induction is recursive, “k” to “k +1” to assume that n = k “n = k +1” propo。