Exploring Mathematical Analysis Approximation Theory And Optimization
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Exploring Mathematical Analysis, Approximation Theory, and Optimization
This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.
Mathematical Analysis, Approximation Theory and Their Applications
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Essential Math for AI
Author: Hala Nelson
language: en
Publisher: "O'Reilly Media, Inc."
Release Date: 2023-01-04
Many sectors and industries are eager to integrate AI and data-driven technologies into their systems and operations. But to build truly successful AI systems, you need a firm grasp of the underlying mathematics. This comprehensive guide bridges the current gap in presentation between the unlimited potential and applications of AI and its relevant mathematical foundations. Rather than discussing dense academic theory, author Hala Nelson surveys the mathematics necessary to thrive in the AI field, focusing on real-world applications and state-of-the-art models. You'll explore topics such as regression, neural networks, convolution, optimization, probability, Markov processes, differential equations, and more within an exclusive AI context. Engineers, data scientists, mathematicians, and scientists will gain a solid foundation for success in the AI and math fields.