A brief analysis of mathematical thinking and problem-solving ideas in advanced mathematics

Abstract

In this paper, some points were summarized to help students improve their advanced mathematical thinking after analyzing various problem-solving ideas and many advanced mathematical thinking points. The sources for the review are almost papers that were published from 1994 to 2022. This time period was chosen because advanced mathematics has developed greatly during this period, and many excellent papers have emerged, which can be better to refer to and draw conclusions. The review of this paper is guided by major mathematical journals. The review summarizes the research themes, research objectives, research methods, and conclusions reached in different papers. The paper also finds many kinds of methods to solve advanced mathematic problems. At the end of the paper, probabilistic thinking, infinite thinking, functional thinking and calculus thinking five kinds of thinking were proposed to help people to learn about the mathematical thinking in advanced mathematics.