INTERNATIONAL JOURNAL FOR INNOVATIVE RESEARCH IN MULTIDISCIPLINARY FIELD

Abstract:    The theoretical underpinnings of mathematics is crucial for modern data science, enabling the creation of data science algorithms, comprehension of data, and extraction of actionable insights from data. This paper gives a thorough overview of the mathematical underpinnings of data science, such as linear algebra, calculus, probability theory, optimization, and discrete mathematics. The mathematical domains are investigated with respect to their importance in machine learning, statistical modeling, deep learning, natural language processing and large-scale data analytics. Some new mathematical techniques are also discussed in the paper in the area of Explainable AI, High dimensional data analysis and Graph based learning. Finally, challenges and future directions are given with the message that solutions which are mathematically informed are needed in today's increasingly complex data environment.