How to understand abstract problems in mathematics
If you feel abstract, you can try to find examples of images. For example, arrangements. Three people in a row can be called abc. There are three possibilities for the first place and two possibilities for the second place. Ab ac ba bc ca cb (it can't be the first, so it is 3- 1=2 possibilities), and the second place is only 1 possibilities. (3-1= 2) The total probability of ABC, ACB, BAC, BCA, Cab and CBA is 3*2* 1=3! =P33=6 Learn induction and deduction again. From the three-line example above, it can be concluded that each line is an arrangement. They are P3 1=3, P32=3*2 and P33=3*2* 1. Starting from 3, multiply by 1, 2, 3 respectively. It can also be written as 3*2* 1/(2* 1)=3! /2! =3! /(3- 1)! Furthermore, we can deduce the general form Pnm=n! /(n-m)! . Another example is combination. Take two out of three. The second line in the above example is all the methods. But 1 and 3,2 and 5,4 and 6 are the same. So it is 6/2=3 combinations. How is 6/2 calculated? 6=P32, which is pushed from above. (Remember the conclusion of the push! ) and 2 is actually 2! =P2 1, which is the arrangement of any two. So C32 = P32/P22 = 3 * 2/(2 *1) = [3! /(3-2)! ] / [2! /(2-2)! ] and then deduce Cnm=Pnm/Pmm=n! /(n-m)! /m! *0! =n! /(n-m)! /m! So remember three points: 1, find specific examples, just talk in general, not too complicated. 2, learn to induction and deduction, through simple examples to sum up the general law, and then deduction to a more complex general situation. 3. Practice the derivation process and remember the derivation results. Explain the third point again. How to remember the derivation results and understand the derivation process will naturally remember the results; If you want to memorize the results without independent derivation, you can't remember them and it won't work. Therefore, there is no shortcut to science, and success will come naturally.