Anil Gupta*
Department of Applied Mathematics, Banaras Hindu University, Varanasi, India
Received: 01-Mar-2025, Manuscript No. JSMS-25-169986; Editor assigned: 4-Mar-2025, Pre-QC No. JSMS-25-169986 (PQ); Reviewed: 20-Mar-2025, QC No JSMS-25-169986; Revised: 26-Mar- 2025, Manuscript No. JSMS-25-169986 (R); Published: 30-Mar-2025, DOI: 10.4172/RRJ Stats Math Sci. 11.01.003
Citation: Anil Gupta, Department of Applied Mathematics, Banaras Hindu University, Varanasi, India. RRJ Mater Sci. 2025.11.003.
Copyright: © 2025 Anil Gupta, this is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Computational mathematics leverages algorithms and numerical methods to solve real-world problems across sciences and engineering. With the rise of high-performance computing, computational techniques enable breakthroughs in simulation, data analysis, and algorithmic design. This article discusses five major research directions: numerical analysis, scientific computing, big data algorithms, cryptographic computation, and computer vision.
Advances in Computational Mathematics
Numerical Analysis: Numerical analysis ensures accuracy and stability in solving equations computationally. Finite difference and finite element methods remain central to engineering and physics problems [1].
Scientific Computing: Scientific computing integrates mathematics with computational hardware, enabling large-scale simulations in climate modeling, structural analysis, and plasma physics [2].
Algorithms for Big Data: Mathematical algorithms like matrix factorization and sparse optimization underpin big data analysis. Efficient computational strategies reduce complexity and improve scalability [3].
Cryptographic Computation: Computational number theory supports encryption techniques, ensuring secure transactions in banking and communication. Research now explores quantum-resistant algorithms [4].
Computer Vision: Mathematical models drive computer vision applications in image recognition, autonomous vehicles, and medical imaging. Linear algebra and optimization play vital roles in training deep learning models.
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