Abstract: Advanced mathematics is a public basic course with a wide range of courses and the most class hours in the university teaching. It is not only an important carrier to cultivate students' logical thinking ability and application ability, but also the theoretical basis of other related professional follow-up courses. However, in the context of application transformation, it is faced with some disadvantages, such as the disconnection between teaching content and major, the emphasis on traditional theoretical knowledge teaching, the neglect of students' application ability training, and the single teaching mode centered on teachers' teaching. In order to stimulate students' enthusiasm for learning and cultivate students' ability to apply theoretical knowledge to solve practical problems, this paper carries out teaching reform and exploration from the aspects of teaching content specialization, teaching process case and teaching mode diversification.

Key words: Advanced mathematics, Teaching reform, Teaching content specialization, Mixed teaching mode