(untitled) (Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2020)
Complex analysis is a fundamental branch of mathematics with wide-ranging applications in various fields. This paper provides an overview of recent progress in complex analysis, focusing on two key areas: Riemann surfaces and holomorphic dynamics. We begin by discussing the historical development of complex analysis, highlighting the contributions of Cauchy, Riemann, and Weierstrass. We then delve into the theory of Riemann surfaces, including their definition, basic properties, and classification theorems. Next, we explore holomorphic dynamics, examining its definition, fundamental concepts, and recent advances. We also explore the interactions between Riemann surfaces and holomorphic dynamics, showcasing the unifying principles in complex analysis. Finally, we discuss the applications of complex analysis in quantum mechanics, number theory, and other areas of mathematics and physics. This paper aims to provide a comprehensive overview of recent developments in complex analysis and its implications for mathematics and beyond.