Journal of Higher Education Research

Limit theory is a fundamental and crucial theory within the discipline of mathematical analysis. Its rigorous logical framework and wide-ranging applications make it irreplaceable in higher mathematics education. Based on the teaching practice of mathematical analysis courses in higher education institutions, this article systematically explores the basic concepts of limit theory, the core methods for determining convergence, and its practical applications in fields such as calculus and series theory. Through scientific and rational teaching design, this article guides students to deeply understand the essential meaning of limit theory, effectively improving their abstract thinking skills and mathematical analysis literacy, and laying a theoretical foundation for their subsequent study of advanced courses such as real analysis and functional analysis.