실해석학, or real analysis, is a branch of mathematics that focuses on the study of real numbers and real-valued functions. It involves understanding concepts such as limits, continuity, differentiation, and integration. Real analysis provides the foundational framework for calculus and helps in exploring the properties of sequences and series. In 실해석학, mathematicians analyze the behavior of functions and their convergence. This field is essential for various applications in science and engineering, as it lays the groundwork for more advanced topics like 복소해석학 (complex analysis) and 위상수학 (topology).