How to learn discrete mathematics well \x0d\ discrete mathematics is an important branch of modern mathematics and the core course of basic theory in computer science. The main goal of discrete mathematics is to study the structure and relationship of discrete quantities, and its research object is generally finite or countable elements, so he fully describes the characteristics of discreteness in computer science. Because of the importance of discrete mathematics in computer science, many universities regard it as one of the specialized courses for postgraduate entrance examination, or as a part of it. \x0d\ Discrete Mathematics, as a course of computer department, has some similarities with other courses, but it also has its own characteristics. Now we will simply analyze its characteristics as an examination content. \x0d\ 1, many definitions and theorems. \x0d\ 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. On the basis of these concepts, we should pay special attention to the relations between concepts, and the entities that describe these relations are a lot of theorems and properties. The \x0d\ part of the exam is to examine your memory, understanding and application of definitions and theorems. For example, in the examination questions of Shanghai Jiaotong University in 2002, what was the compatibility relationship? If you know, it is easy to score; If you don't know, you won't get points anyway. This kind of topic is often ignored in review because of its low difficulty. In fact, this is a rather wrong understanding. In the examination questions of postgraduate courses, there are often questions that directly examine the memory of a certain knowledge point. For this kind of topic, candidates should be able to reproduce this knowledge point accurately, comprehensively and completely. Any ambiguity and omission will result in extremely regrettable loss of points. We suggest that readers, when reviewing, must take the above-mentioned "accuracy, comprehensiveness and completeness" as the standard to demand themselves. If they can't reach it, it means they still have to work hard. On this point, we will emphasize it in the later chapters, and let it run through the whole review process of discrete mathematics. The definition of \x0d\ discrete mathematics is mainly distributed in the relations and functions of set theory, and in groups, rings, fields, lattices and Boolean algebras of algebraic systems. Be sure to learn by heart and understand well. \x0d\2, strong methodology. \x0d\ In the proof of discrete mathematics, the method is very strong. If you know how to prove a problem, you can prove it easily, otherwise you will get twice the result with half the effort. Therefore, in the usual review, we should be good at summing up, so that we can be comfortable with unfamiliar questions. In this book, we have summarized many problem-solving methods for readers. Readers should first be familiar with and know how to use these methods. At the same time, we also encourage readers to think hard and explore as many solutions to a problem as possible. \x0d\3。 There is poverty. \x0d\ Because discrete mathematics is "inflexible", it is more difficult to create new questions. No matter what exam, many questions are old or slightly changed. "I am familiar with 300 Tang poems, and I can sing even if I can't write poems." 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. \x0d\ This book is specially written for postgraduate entrance examination and is suitable for readers to review postgraduate entrance examination. If you still have time, you can recommend two sets of problem sets. One is "Theory, Analysis and Solution of Discrete Mathematics" written by Zuo Xiaoling and others, and the other has three books, which is a set of discrete mathematics exercises written by Geng Suyun and others. Most of the questions in these two books are the same, but because of some differences in symbols and definitions, the setting and solution of questions are somewhat different. \x0d\ Now let's analyze what types of questions there are in the postgraduate entrance examination and how we should deal with them. \x0d\ 1, basic questions \x0d\ Basic questions are the recitation of inspection definitions, as well as simple proof and reasoning. The topic mainly revolves around mathematical logic and set theory. These topics don't need thinking, they are easy to get started. \x0d\ The main problem of this sub-topic is to prevent carelessness and specious scores from being lost in the defined memory. People who don't pay attention to this will suffer big losses in the exam. For example, in the main conjunctive normal form, the assignment corresponding to the maximum term code is contrary to the assignment corresponding to the truth table, which will also make mistakes in many reference books; It is also necessary to prevent errors caused by not following certain methods. For example, when we do equivalent deduction in mathematical logic or set theory, we can omit some unimportant steps, as long as teachers and candidates are clear, but we can't omit any step in reasoning theory, otherwise it will be considered as a logical error. \x0d\ In our study, we should also pay attention to mastery. For example, mathematical logic and set theory are interlinked, and we can combine them when memorizing or summarizing methods to facilitate comparison and understanding. \x0d\2。 Theorem application problem \x0d\ This part is the most "dead" part, which mainly embodies the strong methodological characteristics of discrete mathematics. Moreover, this part accounts for most of the exam content, so we must work hard on this part and remember various methods, and most of the scores of discrete mathematics will be obtained. \x0d\ Here we list several common applications: \x0d\● Prove equivalence relation: that is, prove that relation is reflexive, symmetric and transitive. \x0d\● Prove the partial order relation: that is, prove that the relation is reflexive, antisymmetric and transitive. There are two kinds of proofs of special relationship, and the rest only need to be combined with definitions. \x0d\● Prove injectivity: function f: xy, that is, prove that there is xX for any yY, so that F(x)= y \ x0d \● Prove correlation: function f: xy, that is, prove that for any x 1, x2X, x 1≠x2, then f Or for any f(x 1)=f(x2), then x 1=x2. \x0d\● Prove set equipotential: that is, prove that there is bijection in two sets. There are three situations: first, it is proved that two specific sets are equipotential, and either a bijection is directly constructed or the correlation between the two sets is constructed by the construction method; Second, the cardinality of the set is known. If it is, we assume that there is a bijection F between it and R, and then we derive another bijection from the properties of F, so it is equipotential; If it is 0, let there be bijection between and n; Third, the equipotential of two groups is known, and then the equipotential of the other two groups is proved. At this point, let the two known sets be bijective, and then prove that the two sets to be proved are bijective according to the residual conditions. \x0d\● Prove the group: that is, prove that the algebraic system is closed, combinable, unitary and inverse. Similarly, there are many concepts that can be used as proof questions in this part, so we should thoroughly understand them with definitions. \x0d\● Prove subgroups: Although subgroups have two proving theorems, if we prove subgroups, it is usually the second theorem, that is, let it be a group and S be a nonempty subset of G. If any element A and B in S has a *b- 1S, it is a subgroup. For finite subgroups, we can consider the first theorem. \x0d\● Prove the normal subgroup: if it is a subgroup, H is a subset of G, that is, it needs to be proved that there is aH=Ha for any aG or-1 *h*aH for any hH. This is the method used in the most common problems. \x0d\● Proof Lattice and Sublattice: Sublattice has no conditions, so like proof lattice, it is proved that the largest and smallest elements of any two elements in the set are in the set. \x0d\ Graph theory is not as methodological as the previous parts, but there are some methods, such as the longest path method, construction method and so on. \x0d\3, the problem \x0d\ The problem is that the exam is very difficult to start, and most candidates can't do the questions to open the grade. So, how do we analyze the problem? \x0d\ There are four kinds of questions, which we will analyze one by one: \x0d\① Comprehensive questions \x0d\ Comprehensive questions are questions whose contents cover several chapters. Most of these problems are in coset, Lagrange theorem, normal subgroups and quotient groups in group theory. This part combines a lot of contents, which is both complicated and difficult to understand, and it is a difficult point in the whole discrete mathematics.