Abstract: The innovative teaching ideas of the course of Probability Theory and Mathematical Statistics are investigated by combining with the teaching of the course of Probability Theory and Mathematical Statistics and starting from the five problems existing in the course according to The Opinions of the Ministry of Education on the Implementation of the Construction of First-class Undergraduate Courses. The innovative teaching covers the following ideas: teaching with the idea of induction and extension, introducing teaching cases with the times, quasi bilingual teaching, statistical simulation with R, strengthening the teaching of ideological and political education and mathematical history, and making full use of network platforms and resources. Finally, the teaching results achieved are presented, and the results of the course goal achievement questionnaire survey are given.

Key words: first-class undergraduate course construction, Probability Theory and Mathematical Statistics, innovative teaching