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Artículo: AMZ-B0G82GTRWP

Numerical Methods with Artificial Intelligence Applications VOL-1 (AI AND MATH NEW)

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Numerical Methods with Artificial Intelligence Applications Foundations, Algorithms, and Machine Learning Optimization VOL-1 Author: Anshuman Mishra In the modern era of computation, Artificial Intelligence (AI) and Machine Learning (ML) have emerged as transformative forces across science, engineering, industry, healthcare, finance, and social systems. From predictive analytics and autonomous systems to deep learning models and large-scale optimization frameworks, intelligent systems increasingly depend on the ability to approximate, iterate, converge, and optimize under uncertainty and computational constraints. At the heart of these capabilities lies a powerful and indispensable discipline: Numerical Methods. This book, Numerical Methods with Artificial Intelligence Applications: Foundations, Algorithms, and Machine Learning Optimization, is written to bridge the long-standing gap between classical numerical analysis and modern AI-driven computation. While numerical methods have traditionally been taught as a purely mathematical or algorithmic subject, their deep relevance to AI—particularly in optimization, learning, approximation, and large-scale computation—has often remained implicit or fragmented across research papers and specialized texts. This book brings these ideas together in a unified, coherent, and application-oriented framework. Authored by Anshuman Mishra, a seasoned academician with more than eighteen years of teaching and research experience in computer science and programming, this book is designed to serve as a comprehensive resource for undergraduate and postgraduate students, competitive examination aspirants, researchers, and working professionals who seek a strong conceptual and practical understanding of numerical computation in the context of artificial intelligence. Why Numerical Methods Matter in Artificial Intelligence Artificial Intelligence systems do not operate in a world of exact solutions. Neural networks do not solve equations symbolically; instead, they iteratively minimize loss functions. Regression models do not compute closed-form solutions in high dimensions; they rely on gradient-based optimization. Probabilistic models estimate expectations using numerical integration and sampling. Even the training of deep neural networks is fundamentally a large-scale numerical optimization problem governed by approximate gradients, finite precision arithmetic, and convergence constraints. Every major pillar of AI—machine learning, deep learning, reinforcement learning, computer vision, natural language processing, and probabilistic modeling—relies heavily on numerical techniques such as:Root finding for solving stationarity conditionsInterpolation and approximation for function modelingNumerical differentiation for gradient estimationNumerical integration for expectation and evidence computationLinear algebraic solvers for high-dimensional dataOptimization algorithms for learning and decision-makingDespite this reality, many learners encounter numerical methods in isolation, often disconnected from real-world AI applications. Conversely, many AI practitioners use optimization libraries and learning frameworks without fully understanding the numerical principles that govern stability, convergence, accuracy, and performance. This book is written to eliminate that disconnect. Scope and Philosophy of the Book The central philosophy of this book is that Artificial Intelligence is, at its core, a numerical science. Learning, adaptation, prediction, and optimization are not merely conceptual processes; they are computational procedures executed under finite precision, limited resources, and noisy data..

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