Geometry Algebra And Applications From Mechanics To Cryptography
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Geometry Algebra And Applications From Mechanics To Cryptography
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Author : Marco Castrillón López
language : en
Publisher: Springer
Release Date : 2016-06-30
Geometry Algebra And Applications From Mechanics To Cryptography written by Marco Castrillón López and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-30 with Science categories.
This volume collects contributions written by different experts in honor of Prof. Jaime Muñoz Masqué. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant.
Variant Construction From Theoretical Foundation To Applications
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Author : Jeffrey Zheng
language : en
Publisher: Springer
Release Date : 2018-12-17
Variant Construction From Theoretical Foundation To Applications written by Jeffrey Zheng and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-17 with Technology & Engineering categories.
This open access book presents theoretical framework and sample applications of variant construction. The first part includes the components variant logic, variant measurements, and variant maps, while the second part covers sample applications such as variation with functions, variant stream ciphers, quantum interference, classical/quantum random sequences, whole DNA sequences, and multiple-valued pulse sequences. Addressing topics ranging from logic and measuring foundation to typical applications and including various illustrated maps, it is a valuable guide for theoretical researchers in discrete mathematics; computing-, quantum- and communication scientists; big data engineers; as well as graduate and upper undergraduate students.
Computational Algebra Course And Exercises With Solutions
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Author : Ihsen Yengui
language : en
Publisher: World Scientific
Release Date : 2021-05-17
Computational Algebra Course And Exercises With Solutions written by Ihsen Yengui and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-17 with Mathematics categories.
This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.
Basics Of Representation Theory
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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Basics Of Representation Theory written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
Delve into the captivating world of "Basics of Representation Theory," a comprehensive guide designed for students, researchers, and enthusiasts eager to explore the intricate symmetries and structures that underpin modern mathematics. Our book offers a detailed introduction to foundational concepts, providing a solid understanding of group actions, linear representations, and character theory. From there, it explores the algebraic structures of irreducible representations, breaking down the decomposition into irreducible components and examining the properties of characters. Readers will journey through diverse topics, including the representation theory of symmetric groups, Lie groups, and algebraic groups, as well as advanced topics such as the representation theory of finite groups, the Langlands program, and applications in quantum mechanics and number theory. With a wealth of examples, illustrations, and exercises, "Basics of Representation Theory" ensures a hands-on approach to learning, encouraging practical exploration and problem-solving. The book also includes numerous references and further reading suggestions for those who wish to delve deeper into specific topics. Written in a clear and accessible style, this book caters to all levels, from undergraduate students encountering representation theory for the first time to experienced researchers seeking fresh insights. With its comprehensive coverage and diverse applications, "Basics of Representation Theory" is an invaluable resource for anyone interested in the beauty and depth of this field.
Geometric Algebra Applications Vol Iii
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Author : Eduardo Bayro-Corrochano
language : en
Publisher: Springer Nature
Release Date : 2024-09-26
Geometric Algebra Applications Vol Iii written by Eduardo Bayro-Corrochano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-26 with Computers categories.
The goal of Geometric Algebra Applications Vol. III: Integral Transforms, Machine Learning, and Quantum Computing is to present a unified mathematical treatment of diverse problems in the general domain like Clifford Fourier Transforms, Deep Learning and Geometric Algebra Convolutional Neural Networks, Quaternion Quantum Fourier Transform and Geometric Quantum Computing. Topics and features · Introduces nonspecialists to Clifford, or geometric algebra and by example encourages the reader to learn to compute using geometric entities and geometric formulations. · A study in depth for applications of Lie group theory, Lie algebra, projective geometry, and the algebra of incidence using the conformal geometric algebra. · Features the computing frameworks of the linear model n-dimensional affine plane and the nonlinear model of Euclidean space known as the horosphere, and addresses the relationships of these models to conformal, affine, and projective geometries. · Includes a thorough study of Integral transforms: Quaternion and Clifford Transforms, quaternion analytic signal, monogenic signals, Hilbert transform, Riesz transform, Clifford Fourier Transform, Quaternion Wavelet transforms, Quaternion Quantum Fourier Transform, 3D Radon Transform and Hough-Transform in geometric algebra. · Color image processing using the color model HSV, Quaternion Split rotors and motors, and the space-time Lorentz transform. · Geometric neural computing using Split Quaternions, Geometric Algebra neural networks, Clifford Support Vector Machine and Neuro Control. · Thorough discussion of several tasks of computer vision, graphics, neurocomputing, and robotics. machine learning, Deep Learning and CNNs, and Geometric Quantum Computing using the geometric algebra framework. · 130 exercises and hints for the development of future computer software packages for extensive calculations in geometric algebra. An entire section is dedicated to explaining how one should write the subroutines in C++, Phyton, Matlab, and Maple to carry out efficient geometric computations in the geometric algebra framework. Furthermore, it is shown how program code can be optimized for real-time computations. The book is an essential resource for applied mathematicians, physicists, computer scientists, graphics engineering, AI and Machine Learning researchers, roboticists and mechanical and electrical engineers, neurocomputing researchers, neuroscientists, and quantum computing specialists. It clarifies and demonstrates the importance of geometric computing for building autonomous systems and pushes forward advances in geometric cybernetics research.
From Great Discoveries In Number Theory To Applications
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Author : Michal Křížek
language : en
Publisher: Springer Nature
Release Date : 2021-09-21
From Great Discoveries In Number Theory To Applications written by Michal Křížek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-21 with Mathematics categories.
This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
Essentials Of Abstract Algebra
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Author : Sachin Nambeesan
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Essentials Of Abstract Algebra written by Sachin Nambeesan and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Essentials of Abstract Algebra" offers a deep exploration into the fundamental structures of algebraic systems. Authored by esteemed mathematicians, this comprehensive guide covers groups, rings, fields, and vector spaces, unraveling their intricate properties and interconnections. We introduce groups, exploring their diverse types, from finite to infinite and abelian to non-abelian, with concrete examples and rigorous proofs. Moving beyond groups, we delve into rings, explaining concepts like ideals, homomorphisms, and quotient rings. The text highlights the relevance of ring theory in number theory, algebraic geometry, and coding theory. We also navigate fields, discussing field extensions, Galois theory, and algebraic closures, and exploring connections between fields and polynomial equations. Additionally, we venture into vector spaces, examining subspaces, bases, dimension, and linear transformations. Throughout the book, we emphasize a rigorous mathematical foundation and intuitive understanding. Concrete examples, diagrams, and exercises enrich the learning experience, making abstract algebra accessible to students, mathematicians, and researchers. "Essentials of Abstract Algebra" is a timeless resource for mastering the beauty and power of algebraic structures.
Mastering Algebra
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Author : Sachin Nambeesan
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Mastering Algebra written by Sachin Nambeesan and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Mastering Algebra" is a comprehensive and student-friendly exploration of fundamental principles and advanced applications of algebra, tailored specifically for undergraduate students. We provide a valuable resource for those seeking to deepen their understanding of algebraic theory and its diverse range of applications across various disciplines. Our book starts with foundational concepts such as algebraic manipulation, equation solving, and functions. It then progresses to more advanced topics, including linear algebra, abstract algebra, and algebraic geometry, offering a seamless transition from basic to advanced algebraic theory. What sets this book apart is its emphasis on clarity, coherence, and practical relevance. Each chapter is meticulously crafted to provide clear explanations of complex concepts, supported by illustrative examples and thought-provoking exercises that encourage active learning and critical thinking. Furthermore, "Mastering Algebra" highlights the practical applications of algebra in fields such as physics, computer science, engineering, and economics, demonstrating its importance and versatility in solving real-world problems. Whether you are a mathematics major looking to deepen your understanding of algebraic theory or a student from another discipline seeking to strengthen your quantitative skills, this book is your essential companion on the journey to mastering algebra. Prepare to embark on an enriching intellectual adventure that will empower you to unlock the full potential of algebraic concepts and their applications.
Multivariate Calculus And Geometry Concepts
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Author : Chirag Verma
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Multivariate Calculus And Geometry Concepts written by Chirag Verma and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Multivariate Calculus and Geometry Concepts" is a comprehensive textbook designed to provide students, researchers, and practitioners with a thorough understanding of fundamental concepts, techniques, and applications in multivariate calculus and geometry. Authored by experts, we offer a balanced blend of theoretical foundations, practical examples, and computational methods, making it suitable for both classroom instruction and self-study. We cover a wide range of topics, including partial derivatives, gradients, line and surface integrals, parametric equations, polar coordinates, conic sections, and differential forms. Each topic is presented clearly and concisely, with detailed explanations and illustrative examples to aid understanding. Our emphasis is on developing a conceptual understanding of key concepts and techniques, rather than rote memorization of formulas. We include numerous figures, diagrams, and geometric interpretations to help readers visualize abstract mathematical concepts and their real-world applications. Practical applications of multivariate calculus and geometry are highlighted throughout the book, with examples drawn from physics, engineering, computer graphics, and other fields. We demonstrate how these concepts are used to solve real-world problems and inspire readers to apply their knowledge in diverse areas. We discuss computational methods and numerical techniques used in multivariate calculus and geometry, such as numerical integration, optimization algorithms, and finite element methods. Programming exercises and computer simulations provide hands-on experience with implementing and applying these methods. Our supplementary resources include online tutorials, solution manuals, and interactive simulations, offering additional guidance, practice problems, and opportunities for further exploration and self-assessment. "Multivariate Calculus and Geometry Concepts" is suitable for undergraduate and graduate students in mathematics, engineering, physics, computer science, and related disciplines. It also serves as a valuable reference for researchers, educators, and professionals seeking a comprehensive overview of multivariate calculus and geometry and its applications in modern science and technology.
Mathematical Innovation
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Author : Mr. A. Durai Ganesh
language : en
Publisher: QUILL TECH PUBLICATIONS
Release Date : 2025-06-16
Mathematical Innovation written by Mr. A. Durai Ganesh and has been published by QUILL TECH PUBLICATIONS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-16 with categories.
Mathematical Innovation is a comprehensive and forward-looking exploration of how mathematics drives progress across science, technology, and modern industry. This book presents a rich collection of contemporary theories, applied methodologies, and creative problem-solving approaches that showcase the evolving role of mathematics in solving real-world challenges. Covering both pure and applied mathematics, it bridges classical concepts with emerging fields such as artificial intelligence, data science, optimization, and complex systems. Designed for students, educators, researchers, and professionals, the book highlights interdisciplinary connections and demonstrates how mathematical thinking fuels innovation across diverse domains. Through engaging explanations, illustrative examples, and real-world applications, Mathematical Innovation invites readers to see mathematics not just as a subject, but as a dynamic, essential tool for understanding and shaping the future.