Linear Explorations In Modern Mathematics
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Linear Explorations In Modern Mathematics
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-09
Linear Explorations In Modern Mathematics written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-09 with Mathematics categories.
Embark on a Mathematical Odyssey with "Linear Explorations in Modern Mathematics": Unraveling the Enigmatic Realm of Linear Algebra Journey into the captivating world of linear algebra, where abstract concepts unveil hidden structures and patterns that govern our universe. Discover the elegance of matrix operations, the interplay between eigenvalues and eigenvectors, and the beauty of orthogonal projections. This comprehensive guide provides a thorough exploration of linear algebra, guiding you from the fundamentals to advanced concepts with clarity and precision. Delve into the intricacies of linear transformations, vector spaces, and matrices, gaining a deeper understanding of the underlying principles that shape our world. Within these pages, you'll encounter a wealth of engaging examples and real-world applications, demonstrating the practical relevance of linear algebra across diverse fields, from engineering and economics to computer science and physics. Witness the power of linear algebra in action as you solve complex problems, model intricate phenomena, and gain insights into the workings of the universe. "Linear Explorations in Modern Mathematics" is not just a textbook; it's an invitation to embark on an intellectual adventure, where you'll challenge your assumptions, expand your perspectives, and cultivate your problem-solving abilities. Through the study of linear algebra, you'll develop a refined mathematical mindset, enabling you to tackle complex challenges with confidence and creativity. Whether you're a student seeking a deeper understanding of linear algebra, a professional seeking to enhance your skills, or simply a curious mind eager to explore the enigmatic realm of mathematics, this book is your gateway to unlocking the secrets of linear algebra. Open its pages and embark on a transformative journey that will reshape your perception of the world. Key Features: * Comprehensive coverage of linear algebra concepts, from basic to advanced * Engaging examples and real-world applications across various disciplines * Clear and concise explanations, making complex topics accessible * A focus on developing problem-solving skills and critical thinking * A valuable resource for students, professionals, and lifelong learners If you like this book, write a review!
Contemporary Mathematics A Comprehensive Exploration
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-04-07
Contemporary Mathematics A Comprehensive Exploration written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-07 with Mathematics categories.
Embark on a captivating mathematical journey with "Contemporary Mathematics: A Comprehensive Exploration," a book that unveils the wonders of the mathematical world in a clear and engaging manner. Discover the beauty and elegance of mathematical concepts as you delve into the fundamental building blocks of the discipline, including sets, logic, functions, and relations. Explore the fascinating realm of numbers, from the familiar natural numbers to the complex and mysterious world of complex numbers. Investigate the geometry of points, lines, and planes, and unravel the secrets of angles and triangles through trigonometry. Delve into the realm of linear algebra, where vectors and matrices provide powerful tools for solving complex problems. Uncover the dynamic world of calculus, where limits, derivatives, and integrals unlock the secrets of change and motion. Venture into the realm of probability and statistics, where you will learn to quantify uncertainty and make informed decisions based on data. Throughout this comprehensive exploration, you will encounter a diverse range of applications that demonstrate the practical power of mathematics. From its role in physics, engineering, and computer science to its impact on economics, finance, and medicine, mathematics plays a vital and indispensable role in shaping our world. "Contemporary Mathematics: A Comprehensive Exploration" is the perfect guide for students seeking a deeper understanding of mathematical concepts, professionals seeking to expand their knowledge, and individuals with a curious mind who want to unlock the secrets of the universe. Prepare to be captivated as you embark on this intellectual adventure and discover the profound impact that mathematics has on our understanding of the world. If you like this book, write a review!
Concepts Of Modern Mathematics
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Author : Ian Stewart
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Concepts Of Modern Mathematics written by Ian Stewart and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.
Explorations In Mathematical Physics
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Author : Don Koks
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-15
Explorations In Mathematical Physics written by Don Koks and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-15 with Science categories.
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
Unveiling Differential Equations A Modern Exploration
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-08
Unveiling Differential Equations A Modern Exploration written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-08 with Mathematics categories.
In this comprehensive and engaging book, readers will embark on a journey into the captivating world of differential equations, uncovering their power and beauty. From the fundamental concepts to advanced applications, this book provides a comprehensive exploration of differential equations, making it an invaluable resource for students, researchers, and professionals alike. With clear and concise explanations, the book delves into the various types of differential equations, including first-order equations, second-order equations, and systems of differential equations. It also delves into the analytical and numerical methods used to solve these equations, providing readers with a thorough understanding of the techniques involved. The book's strength lies in its focus on applications. It showcases how differential equations are used to model and analyze a wide range of real-world phenomena, from the motion of planets to the flow of fluids to the growth of populations. These applications bring the abstract concepts of differential equations to life, demonstrating their relevance and impact across various disciplines. Furthermore, the book explores some of the more advanced topics in differential equations, such as chaos theory and fractals. These topics may seem abstract at first, but they have profound implications for our understanding of the world around us. The book presents these topics in an accessible manner, making them accessible to readers with a variety of backgrounds. Whether you are a student seeking a deeper understanding of differential equations, a researcher looking to expand your knowledge, or simply someone with a curious mind, this book is for you. With its comprehensive coverage, engaging writing style, and abundance of real-world examples, this book is your gateway to unlocking the secrets of differential equations. If you like this book, write a review!
Mathematics For Machine Learning
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Author : Marc Peter Deisenroth
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-23
Mathematics For Machine Learning written by Marc Peter Deisenroth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Computers categories.
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 component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
When Life Is Linear
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Author : Tim Chartier
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-01-07
When Life Is Linear written by Tim Chartier and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-07 with Computers categories.
From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. When Life is Linear introduces concepts of matrix algebra with an emphasis on application, particularly in the fields of computer graphics and data mining. Readers will learn to make an image transparent, compress an image and rotate a 3D wireframe model. In data mining, readers will use linear algebra to read zip codes on envelopes and encrypt sensitive information. Chartier details methods behind web search, utilized by such companies as Google, and algorithms for sports ranking which have been applied to creating brackets for March Madness and predict outcomes in FIFA World Cup soccer. The book can serve as its own resource or to supplement a course on linear algebra.
An Intuitive Exploration Of Artificial Intelligence
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Author : Simant Dube
language : en
Publisher: Springer Nature
Release Date : 2021-06-21
An Intuitive Exploration Of Artificial Intelligence written by Simant Dube and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Computers categories.
This book develops a conceptual understanding of Artificial Intelligence (AI), Deep Learning and Machine Learning in the truest sense of the word. It is an earnest endeavor to unravel what is happening at the algorithmic level, to grasp how applications are being built and to show the long adventurous road in the future. An Intuitive Exploration of Artificial Intelligence offers insightful details on how AI works and solves problems in computer vision, natural language understanding, speech understanding, reinforcement learning and synthesis of new content. From the classic problem of recognizing cats and dogs, to building autonomous vehicles, to translating text into another language, to automatically converting speech into text and back to speech, to generating neural art, to playing games, and the author's own experience in building solutions in industry, this book is about explaining how exactly the myriad applications of AI flow out of its immense potential. The book is intended to serve as a textbook for graduate and senior-level undergraduate courses in AI. Moreover, since the book provides a strong geometrical intuition about advanced mathematical foundations of AI, practitioners and researchers will equally benefit from the book.
The Shape Of Algebra In The Mirrors Of Mathematics
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Author : Gabriel Katz
language : en
Publisher: World Scientific
Release Date : 2012
The Shape Of Algebra In The Mirrors Of Mathematics written by Gabriel Katz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
The Shape of Algebra is the authors' attempt to share their mathematical experiences with readers who have more than a passing interest in mathematics, but have only a traditional exposure to elementary algebra. Secondary school and college teachers and students who want to expand their horizons in the field will find a fresh presentation of familiar concepts and some unexpected results. This book serves as a text for an "appreciation" course in modern mathematics designed for non-mathematics majors or for first-year students who are considering the possibility of studying mathematics or related disciplines. It can also serve as a source of computer-supported activities that could supplement traditional courses in algebra, multivariable calculus, and complex variable. This book gives the reader a sense of the visual nature of mathematics. Mathematical experiments with universal mapping software VisuMatica, designed by Vladimir Nodel'man, form the very core of the book. Readers are encouraged to reproduce, play with, and expand on these experiments. Numerous problems are interspersed throughout the text to guide the reader. Our treatment of standard algebra is visual and computational. By introducing visual computational environments like VisuMatica, our book promotes this geometric approach to algebra and makes it accessible to readers a great deal earlier. The book will enable our readers to approach its content on three levels: the first one which requires only some fluency with elementary algebraic manipulations; the second one which also presumes familiarity with the notions of derivatives and tangent lines to plane curves, and the third one which uses some basic concepts of multivariable calculus. All three levels are clearly marked in the text, and will allow for a smooth reading and virtual experiments, regardless of the level that our readers will find comfortable.
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.