1, observation method and enumeration method: observation method refers to finding the answer to the question by observing the changing law of numbers and graphs. Observation method is usually suitable for some simple problems of finding laws, such as digital sequence and graphic mosaic. Enumeration refers to listing all possible situations and verifying them one by one, so as to find the law.
2. Induction and hypothesis: induction refers to the induction of general laws through the observation and analysis of a series of specific cases. Induction is usually suitable for some abstract problems, such as the general term formula of series and the combination number formula. The hypothesis is that a certain law exists first, and then it is verified with known conditions.
3. Reduction to absurdity and algebra: Reduction to absurdity is to assume that a certain law is not established, and then draw a contradiction through reasoning, thus proving that the law is established. The reduction to absurdity is usually applied to some problems of reverse thinking, such as some reverse formulas. Algebraic method refers to transforming the problem into algebraic form through algebraic operation and equation solving, so as to find the law.
Mathematics related content
1, the origin of mathematics: Mathematics originated from human abstraction and induction of the real world, and is an important part of human culture. It is a science that explores patterns, structures, relationships, spaces, quantities and changes, involving logic, symbols, images, abstract thinking and many other aspects.
2. The core of mathematics: The core of mathematics lies in its axiomatic system and strict logical reasoning. From Euclid in ancient Greece to Bourbaki School in modern times, mathematicians have constantly constructed and refined this system, making it gradually perfect. In this system, every concept and theorem needs to be strictly proved before it can be accepted, which makes mathematics an extremely rigorous science.
3. Application of mathematics: Mathematics is widely used and permeates all aspects of our lives. From arithmetic and measurement in daily life, to complex calculation and simulation in scientific research and engineering design, to model building and data analysis in economics and sociology, mathematics has played a vital role. It can be said that mathematics is the basic tool for human beings to understand and solve practical problems.