(1) methods in logic, such as analysis (including reduction to absurdity), synthesis, induction, and exhaustive method (requiring classified discussion). These methods should not only conform to the basic laws and rules in logic, but also have mathematical characteristics because they are used in mathematics.
(2) General methods in mathematics, such as modeling method, elimination method, reduction method, substitution method, image method (also called coordinate method, which is often called image method in algebra, and we will learn coordinate method later in analytic geometry), comparison method (which mainly refers to comparison size in mathematics, which is different from many aspects in logic), scaling method, and vector method and mathematical induction to be learned later.
(3) Special methods in mathematics, such as collocation method, undetermined coefficient method, addition and subtraction (elimination) method, formula method, substitution method (also called intermediate variable method), decomposition method (including the mathematical idea of adding auxiliary elements to realize transformation), factorization method, parallel movement method, and folding method. These methods also play an important role in solving some mathematical problems, and we can't afford to wait.