Preparation skills of self-study discrete mathematics Discrete mathematics is an important branch of modern mathematics and the core course of basic theory in computer science. Many colleges and universities have listed it as an elective course in the entrance examination for computer master students. This paper aims to summarize some of our review experiences and provide reference for friends who choose discrete mathematics. The writing of this paper is mainly aimed at friends who are not very good at discrete mathematics foundation across majors and undergraduates, hoping to be helpful. The first question is: What kind of candidates are suitable for discrete mathematics? Discrete mathematics is characterized by concentrated knowledge points and high requirements for abstract thinking ability. No matter which discrete mathematics textbook, each chapter will list several definitions and theorems, followed by the direct application of these definitions and theorems. It is difficult for people with poor abstract thinking ability to learn further. At the same time, the topic of discrete mathematics is relatively dull, so it is difficult to produce new topics. No matter what exam, many questions are old or slightly changed. Among the discrete mathematics test questions we collected from various institutions, only those of Peking University, Fudan University and Institute of Automation of Chinese Academy of Sciences are "heterogeneous". Among them, Peking University is more difficult, while Fudan University and Institute of Automation have different emphases. Other institutions are similar. Therefore, friends who are rigorous, standardized and logical (but not necessarily too active) can consider taking discrete mathematics, and from the perspective of examination, friends with good memory can also get good grades by memorizing various questions (even a large number of typical questions). The second question is: What books should I choose for review? First of all, you should contact the R&D department of the college you want to apply for, find out the designated teaching materials for professional courses, and buy books according to the information you get. Many colleges and universities choose Zuo Xiaoling's Discrete Mathematics as a reference textbook. Friends who apply for these colleges and universities should try their best to find a supporting tutorial book "Theory, Analysis and Solution of Discrete Mathematics". The overall quality of this tutorial book is very good, even if it is used as a problem set for general study. In addition, introduce other books. 1, three discrete textbooks of Peking University. This is the most difficult and extensive discrete mathematics textbook we know at present. A friend admitted to Peking University is a must. The rest can be bought for later use. You don't need to watch it at ordinary times. These books come in handy once you encounter strange knowledge points in other books. 2. Discrete Mathematics Problem Set written by Teacher Geng Suyun. Most of the questions in Mr. Zuo's book are the same, but because of some different symbols and definitions, the setting and answers of the questions are somewhat different. 3. Complete True Question Solution (Discrete Mathematics Volume). Our own problem set has collected a large number of postgraduate entrance examination questions from various institutions in recent years, summed up a variety of questions and put forward targeted solutions, as well as in-depth and detailed analysis and expansion. It is a good choice for preparing for the exam. 4. "Discrete Mathematics" and "Detailed Solution of Discrete Mathematics Exercise 2000" in the "National Classic Learning Counseling Series". This is a new book just published this year (2002), foreign book (translation), published by Science Press. It's a good book, but it doesn't conform to the discrete teaching system of China people. Not bad as an improvement book. 5. DISCRETEMATHEMATICALSTRUCTURES, an English photocopying textbook published by Higher Education Press, is absolutely good in simple terms, but it is not targeted when used for preparing for the exam. The advantage of using it is to kill two birds with one stone, and at the same time you can exercise your English ability. But friends who need to spend more time on math and other courses should use it with caution. In addition, some non-computer major friends who are still in their freshman and sophomore years want to take an examination of interdisciplinary computer graduate students and plan to study discrete mathematics. These friends, if they haven't chosen the colleges to apply for, then teacher Zuo Xiaoling's book is a very good introductory textbook, so you can buy it first and lay a good foundation. Then it's time to start reviewing. The whole process can be roughly divided into three stages. The first stage, the stage of a large number of knowledge reserves. Discrete mathematics is a logical reasoning subject based on a large number of definitions. Therefore, understanding concepts is the core of our study of this subject. Because these definitions are very abstract, beginners often can't establish a connection with objective things in the real world in their minds. This is especially true for friends who study independently across disciplines. This is the first difficulty in discrete mathematics learning. Therefore, for the first review, we put forward one of the most important requirements, that is, to memorize all definitions and theorems accurately, comprehensively and completely. The specific way can be: after learning a chapter, use special time to memorize the definitions and theorems contained in the chapter until you can write them down correctly. There is no need to insist on understanding. Remembering and accurately repeating the definition theorem is the highest requirement at this stage. You don't need to do too many questions (you don't even need to do after-school exercises, just understand the examples), and the focus is on the memory of definitions and theorems. Please remember that this is a necessary preparation for the future expansion to breadth and depth. This process takes about one to two months according to everyone's situation. The second stage is the stage of in-depth study and doing a lot of after-school exercises. This is the longest stage and it is estimated that it will take a long time. Generally speaking, if you can skillfully solve more than 75% of the after-school exercises in a chapter, you can consider ending this chapter. This method is very important for solving discrete mathematical problems. If you encounter a problem, you can immediately see its type and related knowledge points, and it is not difficult to choose the right method to solve it, otherwise you will get twice the result with half the effort. For example, the part of propositional logic is nothing more than the following topics: symbolization of propositions expressed in natural language, mutual transformation of equivalent propositions (including transformation into principal conjunctive normal form and principal disjunctive paradigm), reasoning and proof under the premise of given propositions. You can also put forward corresponding countermeasures immediately. Taking the reasoning problem as an example, we mainly use P and T rules, plus implication and equivalent formula table, and deduce from the given premise, or adopt truth table method, CP rule and reduction to absurdity according to the characteristics of the problem. It can be seen that in the usual review, we should be good at summing up and carefully understand the types of topics and the problem-solving routines of such topics. With so many exercises, even if you encounter unfamiliar problems, you can quickly understand their essence and solve them easily. "I am familiar with 300 Tang poems, and I can recite them if I can't write." If you get a problem set, do it from beginning to end, or even recite it. Then in the examination room, you will find that most of the questions are familiar or familiar. At this time, it is not too difficult to get better grades. This kind of situation is universal and suitable for many college exams. The third stage is to carry out real problem simulation training to improve the overall level and comprehensive ability. This stage lasts from the end of the second stage to the exam. In addition to the textbooks mentioned above, we should also try our best to obtain professional courses in colleges and universities. Because each unit has different emphasis on this subject after all, we can get a lot of useful information from the test questions over the years. These years of doubts have played a huge role at this time. Generally speaking, mathematical logic will be a relatively simple part of the whole test paper. But that doesn't mean you can get all or most of the scores easily. Where are its traps? Not in the examination questions themselves, but in the wrong guiding ideology in review. The title of this part is often ignored because it is simple and "clear at a glance". As a result, there is not enough practice. It seems that you can't make a big mistake when you start to do the problem, but the minor problems are always constant, and it is difficult to make 100% correct. In fact, we must establish the understanding that we must get more than 85% marks in the test questions of mathematical logic. Otherwise, the score of the whole discrete mathematics subject will be very low, which will put you at an extremely unfavorable position. Always remember that this is not preparing for the final exam, and everything will be fine after 60 points. This is preparing for the postgraduate entrance examination! Every point is a matter of life and death! Therefore, it is necessary to pursue high accuracy and efficiency in doing problems. Set theory is not difficult, and equivalence relation (often combined with equivalence class division) is the most important in this part, so we should pay special attention to it. Algebraic structure usually has the problem of distinguishing between upper-middle level candidates and high-level candidates. But you don't have to worry. It should be noted that the difficulty of these problems is not caused by too flexible thinking and too complicated skills. On the contrary, the solutions to these problems are often standardized and always based on certain "routines". It's just that there are many knowledge points involved and they are unfamiliar, which will be more difficult. To deal with this kind of problem, we only need to do two things: 1, and be familiar with the knowledge related to the problem; 2. Master the "routine" of solving problems. Graph theory is the key and difficult point in discrete mathematics examination. Compared with other parts of discrete mathematics, the topic of graph theory is slightly flexible and requires higher spatial thinking and imagination. But its solution still has rules to follow. Commonly used methods include: reduction to absurdity, mathematical induction, longest (shortest) path method, etc. In addition to paying attention to these routine things, we should also pay attention to the habit of writing questions in colleges and universities, so as to determine the focus of strengthening training. This is a major event directly related to the quality of review, which should not be underestimated. One or two weeks before the exam, we should also consolidate our memory of various knowledge points. Remember what you forgot again to ensure that you won't lose your easy marks in the exam. All kinds of problem-solving methods should be familiar with, and one or two typical examples can be combined. Www.zxks.org/zikaobeikao/fuxifangfa/20170417/136.html # ZK The number of discrete mathematics problems is infinite, but the types of problems are limited. Taking the discrete math exam is like taking part in a competition. Opponents only have dozens of tricks. As long as you disassemble these moves one by one at ordinary times, there is no doubt that you will win the contest. What's more, the method of disassembling moves has already been given by predecessors, and all you have to do is to understand it with your heart. Understand this, you will understand the review and preparation of the whole discrete mathematics.