Application of Mathematical Principles and Methods in Scientific Research: A Comprehensive Review

Abstract

Mathematics serves as the backbone of scientific inquiry, providing a universal language for modeling, analysis, and prediction across various disciplines. This paper presents a comprehensive review of the mathematical principles and methods commonly employed in scientific and engineering research. Key areas discussed include calculus, linear algebra, differential equations, probability theory, and statistical inference. Emphasis is placed on how these tools aid in problem formulation, hypothesis testing, data interpretation, and model validation. The study also explores the integration of computational methods and software in mathematical modeling to enhance the precision and reproducibility of results. By systematically evaluating case studies from physical sciences, engineering, and social sciences, the paper highlights the indispensable role of mathematical thinking in advancing modern research methodologies. This review aims to serve as a foundational reference for interdisciplinary researchers, educators, and students seeking to strengthen their quantitative research frameworks.

Cite as:

R. Panchal, & Awasare Anant. (2025). Application of Mathematical Principles and Methods in Scientific Research: A Comprehensive Review. Journal of Applied Mathematics and Statistical Analysis, 6(2), 27–31.

https://doi.org/10.5281/zenodo.16411525