Wanxue Education Wen Hai Kao Yan Kao Yan Teaching Research Center Deng Zhixiang
20 14 Postgraduate Mathematics has just come to an end, and the teachers of our Wanxue Education Wenhai Postgraduate Teaching and Research Center also gave you a real problem analysis at the first time. The linearity of the first, second and third calculation papers accounts for 34 points. Judging from this year's exam questions, linear algebra is not very difficult, and it is the part with high score rate in our exam. Therefore, it is suggested that candidates must grasp the scores of linear algebra questions. Next, I will give you a brief analysis of the characteristics of this year's online exam questions.
We found that the test questions have four main characteristics:
First, the amount of calculation is large. Generally, the big problem of generating a line has two problems, solving equations, finding eigenvalues and eigenvectors. These calculations are very large, and one mistake after another is wrong. There are big problems in these two points every year.
The second feature is high flexibility. Line generation often changes the conditions slightly, which will lead to the change of the whole problem-solving method, so the problem is very flexible.
The third feature is comprehensiveness. In fact, the knowledge points of the line generation are very closely related, and it is easy to produce comprehensive problems. It is often said that online generations can test a book together; For example, the first solution of line generation this year is the combination of several chapters;
The last feature is the small difference. As we all know, our mathematics has three volumes, one, two and three. In recent years, the topics about linear algebra in the three volumes are almost the same.
According to the characteristics of this year's linear algebra exam, students preparing for 20 15 should pay attention to three points when reviewing:
Bearing main line
The knowledge point of linear algebra is "scattered in form but not scattered in spirit". If you want to learn linear algebra well, you must find this "god", that is, find a main line to string together the knowledge points in each chapter. How to grasp the "God" of linear algebra? 1. From the origin of linear algebra, taking linear equations as the main line, linear algebra-* * includes determinant, matrix, vector, linear equations, eigenvalue, eigenvector and quadratic form.
Grasp three foundations
70% of the mathematics for postgraduate entrance examination examines the contents of the "three basics", that is, basic concepts, basic theories and basic methods, so we should pay attention to grasping the three basics when reading. With regard to "basic concepts", to learn to distinguish which concepts only need to be understood, such as the definition of matrix, block matrix and vector, which are not directly propositional; However, some concepts, such as maximal independent group, linear correlation, linear independence and so on. , will directly examine, some problems are solved by these concepts, so we must firmly grasp these concepts when reviewing; "Basic theory" is also the key part to be tested every year, such as the properties of rank, the judgment theorem of solutions of linear equations, the properties of eigenvalues and eigenvectors, etc. Postgraduate entrance examination should not only remember the content of theorem, but also master how to examine it. The examination of the "basic method" of linear algebra for postgraduate entrance examination is relatively fixed. For example, you can get this part of the score by teaching you the steps to solve homogeneous and inhomogeneous linear equations, plus some calculation training.
Practice hard and pay attention to calculation.
When you do a problem, you should first pay attention to the details, which determine success or failure. Pay attention to the details of the known conditions in the problem when doing the problem.
For example, if two matrices can get or? We know that the product of two numbers in the number field is equal to 0, and at least one of them must be 0. However, in the multiplication of matrices, generally speaking, it is still impossible to be determined by. This is different from the multiplication of numbers. Students should pay attention to this detail.
The review of linear algebra should not only pay attention to details, but also summarize knowledge points, common questions and problem-solving methods. We will introduce this to the students in detail in future classes;
Then the students study hard according to our method. I believe it is not a problem to get all 34 points on the line generation. Finally, on behalf of the teachers of the Wenhai Graduate Teaching and Research Center of Wanxue Education, I wish me to become the No.1 graduate student of 20 15.