Discrete Mathematics is a mathematical discipline that studies the structure of discrete quantities and their interrelationships. It is an important branch of modern mathematics and a basic core discipline of computer science. It is an indispensable prerequisite course for courses such as data structure, operating system, compilation technology, artificial intelligence, database, algorithm design and analysis，mainly cultivating students' meticulous thinking and improving their comprehensive quality. Under the background of the vigorous development of artificial intelligence and big data, the study of discrete mathematics is particularly important.

The contents of this course mainly include mathematical logic, set theory, algebraic structure, graph theory, comprehensive experiment and so on. The learning of the whole course mainly relies on the textbook Discrete Mathematics ( National 12th five-year plan textbooks in China, Beijing high-quality textbooks) edited by our teaching team.

The teaching of the whole course presents several distinct characteristics:

(1) In view of the characteristics of discrete mathematics learning content, on the basis of the traditional teaching methods, we introduce the cognitive structure teaching theory which is proposed by our teaching team and integrates "knowledge logic structure" and "mind map"(KM teaching theory for short). The basic connotation of KM teaching theory (that is, the teaching idea of "core theory of knowledge logic structure"; the teaching mechanism of "double picture fusion"; the teaching mode of "teaching loop"; the teaching content of "three-dimensional structure"; the teaching method of "syllogism") throughout the course organization and teaching process.

(2)The teaching materials under the guidance of the research-oriented teaching concept compiled by the teaching team fully embody the "Generative" logic of knowledge. In the exploration and practice of research-oriented teaching of Discrete Mathematics, the teaching team combined the basic connotation of research-oriented teaching with KM teaching theory and compiled the textbook of Discrete Mathematics. It breaks through the traditional idea of treating discrete mathematics as "Patchwork Structure", absorbs the theory of Structuralism, and forms a new idea of "Structural Correlation"; It is the path of teaching material deductive spread: the summary of the book - the passage introduction (Tree Class Diagram) – Chapter Rough Sketch - Chapter Application Sketch – Expanded with Sections (the core knowledge, Embedded Thinking Form Note Figure, the brief summary of each section) - Chapter Exercises Generalization (common typical exercises analysis) - Chapter Knowledge Logic Structure Diagram - Extended Reading – Exercises – Passage Knowledge Logic Structure Diagram. In terms of mode and style, this textbook is completely consistent with the cognitive law of students and has a strong enlightening effect. It has been awarded the title of Excellent Textbook of Beijing, and has been selected as the national planning textbook for undergraduates of general higher education during the “12th Five Year Plan” period.

(3)Introduce the "problem-driven" concept into the course teaching. On the one hand, at the beginning of each chapter, by introducing the application overview of the relevant fields in the knowledge subject of the chapter, students can have a general understanding of the application of the course content in the subject field before learning each chapter of knowledge, and stimulate their initiative and interest in learning; On the other hand, the experimental teaching link is designed to train students to use computer technology to achieve solutions to typical problems in discrete mathematics, thereby deepening their understanding and mastering of theoretical knowledge.

I believe that through this course of study, you will have an in-depth understanding, proficiency and the flexibility to apply discrete mathematics learning content.

Through the study of this course, students can master the discretization and formalization of computing problems and the methods of solving scientific computing problems with computers, master the mathematical description methods of discrete systems, and be able to formally describe and prove computational problems. At the same time, cultivate students' abstract thinking ability, and lay the foundation for students to further study the follow-up courses. Specifically, the main teaching objectives include:

(1) Master the discrete and formal knowledge and methods of computing problems, and use the basic knowledge and professional theory related to mathematical logic, set theory, algebraic structure and graph theory to formally describe the computing problems;

(2) Master the mathematical description method of discrete systems, and apply it reasonably to the formal representation of calculation problems, logical calculus, logical reasoning, and construction of calculation models;

(3) Master the comprehensive and system knowledge related to discrete mathematics, analyze and design information technology-related systems and models, and be able to formally prove calculation problems.

Basic knowledge of:

• Calculus
• Linear Algebra
• Programing

[1] Yang B R, Xie Y H, Liu H L, Hong Y, Luo X. Discrete Mathematics. Beijing, China: Higher Education Press, 2012. (in Chinese)

[2] Zuo X L, Li W J, Liu Y C. Discrete Mathematics. Shanghai, China: Shanghai Scientific and Technological Literature Press, 2000. (in Chinese)

[3] Zuo X L, Li W J, Liu Y C. Key to Exercises in Discrete Mathematics. Shanghai, China: Shanghai Scientific and Technological Literature Press, 2004. (in Chinese)

[4] Qu W L, Geng S Y, Zhang L A. Discrete Mathematics. Beijing, China: Higher Education Press, 2008. (in Chinese)

[5] Qu W L, Geng S Y, Zhang L A. Key to Exercises in Discrete Mathematics. Beijing, China: Higher Education Press, 2009. (in Chinese)

[6] Yang B R. Discrete Mathematics. Beijing, China: Posts & Telecom Press, 2006. (in Chinese)

[7] Yang B R. A Summary of Graph Theory. Tianjing, China: Tianjing Scientific and Technological Literature Press, 1985. (in Chinese)

[8] Zhou L Q. Encyclopedia of Logic. Chengdu, China: Sichuan Education Press, 1994. (in Chinese)

[9] Fu Y, Gu X F, Wang Q X, Liu Q H. Discrete Mathematics and Its Application. Beijing, China: Higher Education Press, 2007. (in Chinese)

[10] Zhang M Y. Discrete Mathematics. Beijing, China: China Machine Press, 2008. (in Chinese)

[11] Mei J B, Liu H L, Luo J, et al. Key to Exercises in Discrete Mathematics (3rd Version). Wuhan, China: Huazhong University of Science & Technology Press, 2008. (in Chinese)

Note: The above reference [1] (authored by us) is used as the textbook in this course.

Q: Why is the course called "discrete" mathematics?

A: According to the explanation of the English version of Wikipedia, there is no universally accepted precise definition of discrete mathematics. Discrete mathematics is a young course. It began in the 1980s as a computer support course. At the beginning, the content of the course was relatively arbitrary, and computer-related mathematics could be placed in it. With the continuous efforts of mathematics and computer-related organizations, the curriculum is gradually standardized and becomes the core curriculum of the computer major.

Q: What are the specific uses of discrete mathematics?

A: Some examples will be given in the comprehensive experimental part of this course. In addition, set theory is the foundation of mathematics, so as long as you want to use mathematics to model problems, you can’t do without set theory, as long as anyone who writes science and engineering papers later will use it. It should be said that the more abstract the content of work in the future, the more mathematics is needed, and the more specific the less mathematics. For example, if the content of future work is to study computational theory, then the discrete mathematics content of this course is far from enough, and even further study of other branches of discrete mathematics is needed.

We suggest that college students do not have to be too entangled in mathematics. As long as they are science and engineering, mathematics is definitely useful, but it may only be that some mathematics is useful in certain fields, so it is likely that students will feel a certain Mathematics courses are really useless, but this is also a manifestation of the broad foundation of the university. The goal of the university is not just skills training, and the goal of talent training is not just to make students find a better job. Learners outside the school can choose what they need to learn according to their actual work needs.

Q: Why are some test questions garbled?

A: Some mathematical symbols cannot be displayed on the mobile phone. At present, we are turning all symbols into pictures. If you still encounter this kind of situation, please check it on your computer. At the same time, you can remind us in the discussion area that we will replace it with pictures as soon as possible.

Q: Why is the progress of the MOOC and the learning progress at school different?

A: The discrete mathematics courses in our school are divided into 2 categories, one is the computer major and the duration is longer; the other is the other related majors and the duration is shorter. Therefore, all students cannot be taken care of.