The study and application of advanced mathematics is compiled according to the requirements of advanced mathematics teaching in higher vocational colleges in China, the present situation of students in higher vocational colleges and the problems encountered by front-line teachers in their work, which embodies three characteristics: ① according to the content of the textbook, it is divided into several parts, and modular learning is adopted to guide students to form a network from point to surface, so as to draw inferences when solving problems; (2) equipped with exercise answers and tips to provide students with "grasping hands"; ③ Meet the needs of "upgrading from college to undergraduate" and participating in the national model contest.

The book is divided into three parts: problem-solving and prompting of teaching materials, guidance and development, teaching modeling and application.