Download or read book Category Theory for the Sciences written by David I. Spivak and published by MIT Press. This book was released on 2014-10-17 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Download or read book Science and Mathematics written by Jayant V. Narlikar and published by Taylor & Francis. This book was released on 2021-11-29 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an engaging and comprehensive introduction to scientific theories and the evolution of science and mathematics through the centuries. It discusses the history of scientific thought and ideas and the intricate dynamic between new scientific discoveries, scientists, culture and societies. Through stories and historical accounts, the volume illustrates the human engagement and preoccupation with science and the interpretation of natural phenomena. It highlights key scientific breakthroughs from the ancient to later ages, giving us accounts of the work of ancient Greek and Indian mathematicians and astronomers, as well as of the work of modern scientists like Descartes, Newton, Planck, Mendel and many more. The author also discusses the vast advancements which have been made in the exploration of space, matter and genetics and their relevance in the advancement of the scientific tradition. He provides great insights into the process of scientific experimentation and the relationship between science and mathematics. He also shares amusing anecdotes of scientists and their interactions with the world around them. Detailed and accessible, this book will be of great interest to students and researchers of science, mathematics, the philosophy of science, science and technology studies and history. It will also be useful for general readers who are interested in the history of scientific discoveries and ideas.
Download or read book Mathematics And Science written by Ronald E Mickens and published by World Scientific. This book was released on 1990-08-23 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this review volume is to present the opinions of a number of distinguished individuals who have given careful thought as to why mathematics is so “unreasonably effective” when applied to the analysis of the natural sciences.
Download or read book Philosophy of Mathematics and Natural Science written by Hermann Weyl and published by Princeton University Press. This book was released on 2009-05-17 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: History of mathematics.
Download or read book Mathematics And The Natural Sciences The Physical Singularity Of Life written by Giuseppe Longo and published by World Scientific. This book was released on 2011-03-04 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of “order” and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics, guides most of the work.The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations.Since biology is particularly complex and not as well understood at a theoretical level, we propose a “unification by concepts” which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are “big bags of molecules”. The main question though is to understand which “theory” can help better understand these bags of molecules. They are, indeed, rather “singular”, from the physical point of view. Technically, we express this singularity through the concept of “extended criticality”, which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level./a
Download or read book Science Seti and Mathematics written by Carl L. DeVito and published by Berghahn Books. This book was released on 2013-11-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is as much a part of our humanity as music and art. And it is our mathematics that might be understandable, even familiar, to a distant race and might provide the basis for mutual communication. This book discusses, in a conversational way, the role of mathematics in the search for extraterrestrial intelligence. The author explores the science behind that search, its history, and the many questions associated with it, including those regarding the nature of language and the philosophical/psychological motivation behind this search.
Download or read book Masters of Theory written by Andrew Warwick and published by University of Chicago Press. This book was released on 2011-04-15 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the the Susan Elizabeth Abrams Prize in History of Science. When Isaac Newton published the Principia three centuries ago, only a few scholars were capable of understanding his conceptually demanding work. Yet this esoteric knowledge quickly became accessible in the nineteenth and early twentieth centuries when Britain produced many leading mathematical physicists. In this book, Andrew Warwick shows how the education of these "masters of theory" led them to transform our understanding of everything from the flight of a boomerang to the structure of the universe. Warwick focuses on Cambridge University, where many of the best physicists trained. He begins by tracing the dramatic changes in undergraduate education there since the eighteenth century, especially the gradual emergence of the private tutor as the most important teacher of mathematics. Next he explores the material culture of mathematics instruction, showing how the humble pen and paper so crucial to this study transformed everything from classroom teaching to final examinations. Balancing their intense intellectual work with strenuous physical exercise, the students themselves—known as the "Wranglers"—helped foster the competitive spirit that drove them in the classroom and informed the Victorian ideal of a manly student. Finally, by investigating several historical "cases," such as the reception of Albert Einstein's special and general theories of relativity, Warwick shows how the production, transmission, and reception of new knowledge was profoundly shaped by the skills taught to Cambridge undergraduates. Drawing on a wealth of new archival evidence and illustrations, Masters of Theory examines the origins of a cultural tradition within which the complex world of theoretical physics was made commonplace.
Download or read book Mathematics and the Theory of Science written by Kristian Frederik Vilhelm Kroman and published by . This book was released on 1920 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Science Music And Mathematics The Deepest Connections written by Michael Edgeworth Mcintyre and published by World Scientific. This book was released on 2021-11-03 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. From a lifetime's thinking, he offers this extraordinary synthesis exposing the deepest connections between science, music, and mathematics, while avoiding equations and technical jargon. He begins with perception psychology and the dichotomization instinct and then takes us through biological evolution, human language, and acausality illusions all the way to the climate crisis and the weaponization of the social media, and beyond that into the deepest parts of theoretical physics — demonstrating our unconscious mathematical abilities.He also has an important message of hope for the future. Contrary to popular belief, biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is more than a simple competition between selfish genes. Rather, he suggests, in some ways it is more like turbulent fluid flow, a complex process spanning a vast range of timescales.Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has worked on problems as diverse as the Sun's magnetic interior, the Antarctic ozone hole, jet streams in the atmosphere, and the psychophysics of violin sound. He has long been interested in how different branches of science can better communicate with each other and with the public, harnessing aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication.
Download or read book Number Theory in Science and Communication written by M.R. Schroeder and published by Springer Science & Business Media. This book was released on 2006-01-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory in Science and Communication introductes non-mathematicians to the fascinating and diverse applications of number theory. This best-selling book stresses intuitive understanding rather than abstract theory. This revised fourth edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.
Download or read book Computer Science with MATHEMATICA written by Roman Maeder and published by Cambridge University Press. This book was released on 2000-02-28 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory course shows scientists and engineers how Mathematica can be used to do scientific computations.
Download or read book Mathematics Science and Epistemology Volume 2 Philosophical Papers written by Imre Lakatos and published by Cambridge University Press. This book was released on 1980-10-16 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics together with some critical essays on contemporary philosophers of science.
Download or read book Category Theory in Physics Mathematics and Philosophy written by Marek Kuś and published by Springer Nature. This book was released on 2019-11-11 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.
Download or read book General Systems Theory Mathematical Foundations written by and published by Academic Press. This book was released on 1975-03-21 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Download or read book The Logical Structure of Mathematical Physics written by Joseph D. Sneed and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about scientific theories of a particular kind - theories of mathematical physics. Examples of such theories are classical and relativis tic particle mechanics, classical electrodynamics, classical thermodynamics, statistical mechanics, hydrodynamics, and quantum mechanics. Roughly, these are theories in which a certain mathematical structure is employed to make statements about some fragment of the world. Most of the book is simply an elaboration of this rough characterization of theories of mathematical physics. It is argued that each theory of mathematical physics has associated with it a certain characteristic mathematical struc ture. This structure may be used in a variety of ways to make empirical claims about putative applications of the theory. Typically - though not necessarily - the way this structure is used in making such claims requires that certain elements in the structure play essentially different roles. Some playa "theoretical" role; others playa "non-theoretical" role. For example, in classical particle mechanics, mass and force playa theoretical role while position plays a non-theoretical role. Some attention is given to showing how this distinction can be drawn and describing precisely the way in which the theoretical and non-theoretical elements function in the claims of the theory. An attempt is made to say, rather precisely, what a theory of mathematical physics is and how you tell one such theory from anothe- what the identity conditions for these theories are.
Download or read book The Education of T C MITS written by Lillian R. Lieber and published by Paul Dry Books. This book was released on 2007-06-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whether you are stumped by the "commutative law" in algebra or a whiz at multiplying three-digit numbers in your head, this book opens the door to the wonders of mathematical imagining. By using simple language and intriguing illustrations drawn by her husband, Hugh, Lillian Lieber presents subtle mathematical concepts in an easy-to-understand way. Over sixty years after its release, this whimsical exploration of how to think in a mathematical mood will continue to delight math-lovers of all ages. Barry Mazur's new introduction is a tribute to the Liebers' influence on generations of mathematicians.
