First of all, discrete mathematics provides a theoretical basis for computer science. Many problems in computer science, such as data structure, algorithm design, computational complexity theory and so on, require knowledge of discrete mathematics. For example, graph theory is an important branch of discrete mathematics, which is widely used in computer science, such as network design and routing algorithm.
Secondly, discrete mathematics also plays an important role in information science. Coding theory, cryptography and information retrieval in information science all need knowledge of discrete mathematics. For example, linear algebra is an important part of discrete mathematics, and it is widely used in information science, such as image processing and speech recognition.
In addition, discrete mathematics also has important applications in operational research and cybernetics. Optimization and decision-making in operational research need knowledge of discrete mathematics. Problems such as system analysis and stability analysis in cybernetics also need knowledge of discrete mathematics.
Generally speaking, the importance of discrete mathematics in mathematics mainly lies in that it provides theoretical basis and tools for other disciplines. The theory and method of discrete mathematics have important guiding significance for solving practical problems.