Discrete mathematics is an important branch of modern mathematics and the theoretical basis of computer science and technology. Discrete mathematics is the foundation of computer professional courses, and it is also an essential course for courses such as data structure, compilation principle, programming language, database principle, operating system, artificial intelligence, algorithm analysis and design. Through the study of discrete mathematics, students can not only master the mathematical knowledge of the structure and relationship of discrete quantities necessary for further study of other courses, but also cultivate their abstract thinking ability and strict logical reasoning ability, and also enhance their ability to analyze and solve problems by using the learned discrete mathematics knowledge.
Discrete mathematics includes mathematical logic, set theory, algebraic structure, graph theory, formal language, automata and computational geometry. This course mainly introduces mathematical logic and set theory.
Mathematical logic is a branch of mathematics that studies the rules of reasoning logic. It adopts mathematical symbolization method, gives reasoning rules and establishes reasoning system. Then the consistency, reliability and completeness of the reasoning system are discussed. The research content of mathematical logic is two calculus plus four theories, specifically, propositional calculus, predicate calculus, set theory, model theory, recursion theory and proof theory. Mathematical logic is the product of the combination of formal logic and mathematics. But mathematical logic studies the general logical laws that all disciplines (including mathematics) follow, while all disciplines only study their own specific laws.
Set theory can be regarded as a branch of mathematical logic and an independent branch of modern mathematics. It is the common language and foundation of all branches of mathematics. Set theory is a mathematical theory about infinite sets and ultra-finite sets. Ancient mathematicians were exposed to the concept of infinity, but they lacked understanding of the essence of infinity. Finding the strict foundation of calculus promotes the study of the structure of real number sets. The early work was related to number sets or function sets. Set theory plays an important role in computer science, artificial intelligence, logic, economics, linguistics and psychology.