Mathematical methods in research involve the application of mathematical techniques and tools to analyze, model, and solve complex problems in various fields such as physics, engineering, economics, and biology. These methods include calculus, linear algebra, differential equations, numerical analysis, optimization, probability theory, and statistics. Mathematical modeling is often used to represent real-world phenomena and make predictions or solve specific problems. These methods are essential for researchers to understand and interpret data, formulate hypotheses, test theories, and make informed decisions.