Books [Haubold J Hans] Special Functions: Fractional Calculus and the Pathway for Entropy
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Historically, the notion of entropy emerged in conceptually very distinct contexts. This book deals with the connection between entropy, probability, and fractional dynamics as they appeared, for example, in solar neutrino astrophysics since the 1970's (Mathai and Rathie 1975, Mathai and Pederzoli 1977, Mathai and Saxena 1978, Mathai, Saxena, and Haubold 2010).
The original solar neutrino problem, experimentally and theoretically, was resolved through the discovery of neutrino oscillations and was recently enriched by neutrino entanglement entropy. To reconsider possible new physics of solar neutrinos, diffusion entropy analysis...
Books [Jean Camille Walrand] Probability in Electrical Engineering and Computer Science (EECS)
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This revised textbook motivates and illustrates the techniques of applied probability by applications in electrical engineering and computer science (EECS). The author presents information processing and communication systems that use algorithms based on probabilistic models and techniques, including web searches, digital links, speech recognition, GPS, route planning, recommendation systems, classification, and estimation. He then explains how these applications work and, along the way, provides the readers with the understanding of the key concepts and methods of applied probability. Python labs enable the readers to experiment and...
Books [Karl Johan Astrom, Richard M. Murray] Feedback Systems: An Introduction for Scientists and Engineers
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This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems.
Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce...
Books [Eduardo D. Sontag] Mathematical Control Theory: Deterministic Finite Dimensional Systems
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Mathematics is playing an ever more important role in the physical and biologi cal sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein force the...
Books [John Doyle, Bruce Francis, Allen Tannenbaum] Feedback Control Theory
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An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering.
The opening chapters constitute a basic treatment of feedback design. Topics...
Books [Milorad D. Cakic Dragan J. Cvetkovic Goran S. Nikolic] Fourier Transforms - High-tech Application and Current Trends
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The main purpose of this book is to provide a modern review about recent advances in Fourier transforms as the most powerful analytical tool for high-tech application in electrical, electronic, and computer engineering, as well as Fourier transform spectral techniques with a wide range of biological, biomedical, biotechnological, pharmaceutical, and nanotechnological applications. The confluence of Fourier transform methods with high tech opens new opportunities for detection and handling of atoms and molecules using nanodevices, with potential for a large variety of scientific and technological applications.
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Books [Tsukasa Hokimoto] Advances in Statistical Methodologies and Their Application to Real Problems
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In recent years, statistical techniques and methods for data analysis have advanced significantly in a wide range of research areas. These developments enable researchers to analyze increasingly large datasets with more flexibility and also more accurately estimate and evaluate the phenomena they study. We recognize the value of recent advances in data analysis techniques in many different research fields. However, we also note that awareness of these different statistical and probabilistic approaches may vary, owing to differences in the datasets typical of different research fields. This book provides a cross-disciplinary forum for...
Books [Stephan Fackler] Mathematical Foundations of Quantum Mechanics
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Books [Valter Moretti] Mathematical Foundations of Quantum Mechanics: An Advanced Short Course
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Books [Frederick W. Byron, Robert W. Fuller] Mathematics of Classical and Quantum Physics
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This textbook is designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Organized around the central concept of a vector space, the book includes numerous physical applications in the body of the text as well as many problems of a physical nature. It is also one of the purposes of this book to introduce the physicist to the language and style of mathematics as well as the content of those particular subjects with contemporary relevance in physics.
Chapters 1 and 2 are devoted to the mathematics of classical physics. Chapters 3, 4 and 5 — the backbone of the book —...
Books [Johan Hoffman, Claes Johnson] Computational Turbulent Incompressible Flow: Applied Mathematics: Body and Soul 4
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This book, Volume 4 of the book series of the Body and Soul mathematics education reform program, presents a unified new approach to computational simulation of turbulent flow starting from the general basis of calculus and linear algebra covered in Volumes 1 through 3. The book puts the Body and Soul computational finite element methodology in the form of General Galerkin (G2) up against the challenge of computing turbulent solutions of the inviscid Euler equations and the Navier-Stokes equations with small viscosity. It shows that direct application of G2 without any turbulence or wall modeling, allows reliable computation on a PC...
Books [Teiko Heinosaari, Mario Ziman] Guide to Mathematical Concepts of Quantum Theory
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Books [Avi Wigderson] Mathematics and Computation: A Theory Revolutionizing Technology and Science
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From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy
Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific...
Books [Etienne E Kerre, John Mordeson] Fuzzy Mathematics
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This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear...
Books [Denny Burzynski] Mathematics for Game Developers
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Books [Ved Prakash Gupta, Prabha Mandayam, V. S. Sunder] The Functional Analysis of Quantum Information Theory
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This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds...
Books [Jean Gallier, Jocelyn Quaintance] Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Machine Learning
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This book provides the mathematical fundamentals of linear algebra to practicers in computer vision, machine learning, robotics, applied mathematics, and electrical engineering. By only assuming a knowledge of calculus, the authors develop, in a rigorous yet down to earth manner, the mathematical theory behind concepts such as: vectors spaces, bases, linear maps, duality, Hermitian spaces, the spectral theorems, SVD, and the primary decomposition theorem. At all times, pertinent real-world applications are provided. This book includes the mathematical explanations for the tools used which we believe that is adequate for computer...
Books [Seongjai Kim] Mathematical Foundations of Machine Learning
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Books [Gerald Teschl] Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators
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Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem...
Books [Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong] Mathematics for Machine Learning
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The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal...
Books [David Logan] Applied Mathematics, 4 edition
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Praise for the Third Edition
“Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference.”
―MAA Reviews
Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and natural sciences.
The Fourth Edition covers both standard and modern topics, including...
Books [Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger] Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
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This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different Artificial Neural Network (ANN) architectures (such as fully-connected feedforward ANNs, convolutional ANNs, recurrent ANNs, residual ANNs, and ANNs with batch normalization) and different optimization algorithms (such as the basic Stochastic Gradient Descent (SGD) method, accelerated methods, and adaptive methods).
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Books [Jeremy Pickles] Applied Mathematics by Example
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Mathematics is an exceptionally useful subject, having numerous applications in business, computing, engineering and medicine to name but a few. `Applied mathematics’ refers to the study of the physical world using mathematics.
This book approaches the subject from an oft-neglected historical perspective. A particular aim is to make accessible to students Newton’s vision of a single system of law governing the falling of an apple and the orbital motion of the moon.
The book and its associated volume of practice problems give an excellent introduction to applied mathematics.
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Books [Alan Parks] Introduction to Applied Mathematics, Fourth Edition
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An introduction to applied mathematics, including calculus, for students of the social and life sciences. Exact and numerical calculation on a variety of mathematical models. Recursion, equilibria, differentiation, integration, linear algebra, linear and non-linear optimization. Separate online problems document available.
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Books [Manas Joshi] The AI Expedition: From Basics to Brilliance
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Artificial intelligence is reshaping the technology, introducing new advancements and opportunities, guiding us into a future filled with extraordinary progress and possibilities. "The AI Expedition: From Basics to Brilliance" is your essential guide to navigating this fascinating world, offering a deep dive into the core algorithms that power AI, and unraveling the mysteries that lie at the heart of this revolutionary technology.
Designed to be a comprehensive yet accessible exploration of AI, this book takes readers on an enriching journey from the foundational concepts to the most advanced techniques. Whether you are a student, a...
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