Integrating the Thoughts and Methods of Mathematical Modelling into the Teaching of Advanced Mathematics

At present, there are many problems in the teaching and learning methods of Advanced Mathematics in China's higher education: the teaching methods is single and the course is boring, lacks fun, and students do not take the initiative to learn but are being passively indoctrinated. Aiming at these problems, This paper introduces the theory of mathematical modelling, introduces the thought of mathematical modelling and methods and then apply them into the reform of advanced mathematics of higher education. Finally, this paper provides some bold hypotheses and researches. With the progress of science and technology as well as the society, mathematics is playing an ever enhanced role in scientific research. Some colleges and universities not only provide the course Advanced Mathematics to science majors, but also to some liberal arts majors. Learning the thoughts and methods of advanced mathematics can not only cultivate students' computing capacity, but also their logical thinking, spatial imagination ability and the ability to analyze and solve problems, so that their comprehensive quality will be improved. Therefore, advanced mathematics has become one of the most important public compulsory courses at colleges and universities. With the development of advanced mathematics, more and more problems have emerged during the teaching process. For example, in the traditional teaching mode, teachers "impart" knowledge at the class and students "listen to the teachers and take notes". In this teaching mode, the main body of teaching activities is teachers and students are always passively following the teachers, so the teaching mode is tedious and boring without fun and the "teaching" and "learning" are separated from each other. Meanwhile, mathematical modelling is vigorously developing in the United States and its thoughts and methods were introduced into the teaching in China in 1985 and become one of the main courses among college students' extracurricular activities. This paper conducts in-depth analysis of the thoughts and methods of mathematical modelling, and explores applying the thought of mathematical modelling into the reform of teaching advanced mathematics at colleges and universities.