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.
