Abstract:  In the context of the integration of science and education, integrating the concepts, methods, and processes of scientific research into undergraduate teaching is an effective way to cultivate top-notch innovative talents with open thinking, innovative spirit, and innovative ability. Accurately finding the connection point between textbook knowledge and scientific research content is the key to its implementation. This article takes Amperes circuital law in electromagnetics as an example and finds that its proof process is naturally appropriate for the topological concept of the number of loops. Explore the topological origin of Amperes circuital law and clarify the topological essence of magnetic field integral loop fine-tuning invariance.Enable students to have a profound understanding of Amperes circuital law and vector field properties, while also gaining a preliminary understanding of topology knot theory.At the same time, in tracing the formation of scientific knowledge, understanding the spirit of scientific inquiry, mastering scientific inquiry methods, and subtly cultivating students innovative spirit and ability. This provides effective methods and examples for integrating the concepts, methods, and processes of scientific research into classroom teaching in universities.

Key words:  knot topology, linking number, Amperes circuital law