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Mathematical and Computational Modeling
by Roderick MelnikIllustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-the-art achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts also features: Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, industrial, and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.
Mathematical and Computational Modelling Across the Scales: Lecture Notes of the XX Jacques-Louis Lions Spanish-French School, Barcelona, Spain, July 3-7, 2023 (SEMA SIMAI Springer Series #39)
by Pedro Diez Matteo GiacominiMany physical and engineering systems deal with micro-, meso-, macro-, and multi-scale phenomena. The accurate description and the reliable simulation of such phenomena entail major challenges from the point of view of both mathematical modelling and computational engineering. This book covers a selection of challenges related to "Mathematical and Computational Modelling Across the Scales”, stemming from the lecture notes of the XX edition of the Jacques-Louis Lions Spanish-French School in Numerical Simulations in Physics & Engineering. The thematic focus is broad, encompassing mathematical models of complex physical problems, theoretical results on their derivation, and development of numerical methods for their efficient simulation. The contributions of the book include: uncertainty quantification for phenomena at different scales such as epidemic dynamics, medical imaging, and geophysical exploration; structural health monitoring integrating small-scale sensor data in large-scale computational models; frontier numerical methods for the simulation of geophysical and heliophysical dynamics accounting for multi-scale, heterogeneous media; multi-physics, multi-scale models for the mechanobiology of atheroma plaques formation; locomotion models for swimming at the micro-scale; mathematical foundations of quantum mechanics phenomena at the micro-scale. The book is addressed to scientists and engineers, from both academia and industry, interested in the mathematical modelling and numerical simulation of a variety of complex systems in physics and engineering characterised by multiple scales.
Mathematical and Numerical Foundations of Turbulence Models and Applications
by Tomás Chacón Rebollo Roger LewandowskiWith applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.
Mathematical and Numerical Modeling in Porous Media: Applications in Geosciences (Multiphysics Modeling)
by Martín A. Díaz Viera Pratap N. Sahay Theo M. Nieuwenhuizen Manuel Coronado Arturo Ortiz TapiaPorous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete
Mathematical and Numerical Modeling of the Cardiovascular System and Applications (SEMA SIMAI Springer Series #16)
by Gianluigi Rozza Daniele Boffi Simone Scacchi Luca F. Pavarino Christian VergaraThe book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. It covers a wide range of topics, from the assimilation of clinical data to the development of mathematical and computational models, including with parameters, as well as their efficient numerical solution, and both in-vivo and in-vitro validation. It also considers applications of relevant clinical interest. This book is intended for graduate students and researchers in the field of bioengineering, applied mathematics, computer, computational and data science, and medicine wishing to become involved in the highly fascinating task of modeling the cardiovascular system.
Mathematical and Physical Fundamentals of Navigation and Positioning with Earth's Natural Fields (Navigation: Science and Technology #13)
by An Li Yang Li Lei Yan Wanfeng JiThis book covers various fields relevant to navigation, including Earth's magnetic field, gravity field, topography, celestial polarization field, electrostatic field, and relativistic celestial field effects. It introduces the principles and applications of navigation positioning using various natural field navigation and terrain-assisted methods, including gravity field navigation positioning, geomagnetic field navigation positioning, terrain-assisted navigation positioning, polarization field navigation positioning, electrostatic field navigation positioning, and relativistic effect verification. This book comprehensively introduces the algorithm principles and engineering implementation approaches, providing basic theoretical support for precision navigation positioning and deep space exploration. Based on the principles of gravity, geomagnetic, and terrain-assisted navigation positioning, corresponding to the universal gravitational force and Earth's rotation in Newtonian mechanics, it combines polarization field navigation positioning with the energy field effect of solar incident light waves, as well as electrostatic field navigation positioning with relativistic effect verification. This forms a relatively complete theoretical technical system and abstracts the mathematical essence of each link in the geomagnetic, gravity, and terrain navigation positioning systems. Taking mechanism exploration and algorithm implementation as the basic approach, it has confirmed the theoretical correctness and practical feasibility of natural field navigation positioning through verification with actual measurement data. This book is mainly targeted at professionals, researchers, students, and readers interested in deep space, deep Earth, deep sea, and polar exploration, as well as those working in the field of navigation positioning. It is of reference value in deep space, deep Earth, and deep sea exploration.
Mathematical and Statistical Applications in Food Engineering
by Anoop Singh Surajbhan SevdaWritten by experts from all over the world, the book comprises the latest applications of mathematical and models in food engineering and fermentation. It provides the fundamentals on statistical methods to solve standard problems associated with food engineering and fermentation technology. Combining theory with a practical, hands-on approach, this book covers key aspects of food engineering. Presenting cuttingedge information, the book is an essential reference on the fundamental concepts associated with food engineering.
Mathematical and Statistical Applications in Life Sciences and Engineering
by Mahima Ranjan Adhikari Avishek Adhikari Yogendra Prasad ChaubeyThe book includes articles from eminent international scientists discussing a wide spectrum of topics of current importance in mathematics and statistics and their applications. It presents state-of-the-art material along with a clear and detailed review of the relevant topics and issues concerned. The topics discussed include message transmission, colouring problem, control of stochastic structures and information dynamics, image denoising, life testing and reliability, survival and frailty models, analysis of drought periods, prediction of genomic profiles, competing risks, environmental applications and chronic disease control. It is a valuable resource for researchers and practitioners in the relevant areas of mathematics and statistics.
Mathematical and Statistical Approaches for Anaerobic Digestion Feedstock Optimization (SpringerBriefs in Energy)
by Federico Moretta Giulia BozzanoThis book examines biomass mixture modeling and optimization. The book discusses anaerobic digestion and related fermentative processes and explains their compositional dynamics. Early chapter examine macromolecules, elemental fractions, and their direct influence on methane production. Supported by an extensive data bank of substrates obtained from research, the book points out correlations that enable the estimation of global methane production for diverse biomass mixtures. Furthermore, it provides valuable insights into discerning the optimal composition capable of yielding the utmost methane output.The book integrates cutting-edge machine learning techniques and shows how the programming language Python and Julia can be used for analysis and to optimize processes. It has many graphs, figures, and visuals.
Mathematical and Theoretical Neuroscience: Cell, Network And Data Analysis (Springer INdAM #24)
by Giovanni Naldi Thierry NieusThis volume gathers contributions from theoretical, experimental and computational researchers who are working on various topics in theoretical/computational/mathematical neuroscience. The focus is on mathematical modeling, analytical and numerical topics, and statistical analysis in neuroscience with applications. The following subjects are considered: mathematical modelling in Neuroscience, analytical and numerical topics; statistical analysis in Neuroscience; Neural Networks; Theoretical Neuroscience. The book is addressed to researchers involved in mathematical models applied to neuroscience.
Mathematical, Computational and Experimental T Cell Immunology
by Carmen Molina-París Grant LytheMathematical, statistical, and computational methods enable multi-disciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. This volume collects a representative sample of studies in T cell immunology that illustrate the benefits of modelling-experimental collaborations and which have proven valuable or even ground-breaking. Studies include thymic selection, T cell repertoire diversity, T cell homeostasis in health and disease, T cell-mediated immune responses, T cell memory, T cell signalling and analysis of flow cytometry data sets. Contributing authors are leading scientists in the area of experimental, computational, and mathematical immunology. Each chapter includes state-of-the-art and pedagogical content, making this book accessible to readers with limited experience in T cell immunology and/or mathematical and computational modelling.
Mathematician for All Seasons
by Hugo SteinhausRobert G. Burns Irena Szymaniec Aleksander WeronThis book presents, in his own words, the life of Hugo Steinhaus (1887-1972), noted Polish mathematician of Jewish background, educator, and mathematical popularizer. A student of Hilbert, a pioneer of the foundations of probability and game theory, and a contributor to the development of functional analysis, he was one of those instrumental to the extraordinary flowering of Polish mathematics before and after World War I. In particular, it was he who "discovered" the great Stefan Banach. Exhibiting his great integrity and wit, Steinhaus's personal story of the turbulent times he survived - including two world wars and life postwar under the Soviet heel - cannot but be of consuming interest. His recounting of the fearful years spent evading Nazi terror is especially moving. The steadfast honesty and natural dignity he maintained while pursuing a life of demanding scientific and intellectual enquiry in the face of encroaching calamity and chaos show him to be truly a mathematician for all seasons. The present work will be of great interest not only to mathematicians wanting to learn some of the details of the mathematical blossoming that occurred in Poland in the first half of the 20th century, but also to anyone wishing to read a first-hand account of the history of those unquiet times in Europe - and indeed world-wide - by someone of uncommon intelligence and forthrightness situated near an eye of the storm.
Mathematicians Fleeing from Nazi Germany: Individual Fates and Global Impact
by Reinhard Siegmund-SchultzeThe emigration of mathematicians from Europe during the Nazi era signaled an irrevocable and important historical shift for the international mathematics world. Mathematicians Fleeing from Nazi Germany is the first thoroughly documented account of this exodus. In this greatly expanded translation of the 1998 German edition, Reinhard Siegmund-Schultze describes the flight of more than 140 mathematicians, their reasons for leaving, the political and economic issues involved, the reception of these emigrants by various countries, and the emigrants' continuing contributions to mathematics. The influx of these brilliant thinkers to other nations profoundly reconfigured the mathematics world and vaulted the United States into a new leadership role in mathematics research. Based on archival sources that have never been examined before, the book discusses the preeminent emigrant mathematicians of the period, including Emmy Noether, John von Neumann, Hermann Weyl, and many others. The author explores the mechanisms of the expulsion of mathematicians from Germany, the emigrants' acculturation to their new host countries, and the fates of those mathematicians forced to stay behind. The book reveals the alienation and solidarity of the emigrants, and investigates the global development of mathematics as a consequence of their radical migration. An in-depth yet accessible look at mathematics both as a scientific enterprise and human endeavor, Mathematicians Fleeing from Nazi Germany provides a vivid picture of a critical chapter in the history of international science.
Mathematicians at war
by Laurent Mazliak Rossana TazzioliNumerous scientists have taken part in the war effort during World War I, but few gave it the passionate energy of the prominent Italian mathematician Volterra. As a convinced supporter of the cause of Britain and France, he struggled vigorously to carry Italy into the war in May 1915 and then developed a frenetic activity to support the war effort, going himself to the front, even though he was 55. This activity found an adequate echo with his French colleagues Borel, Hadamard and Picard. The huge correspondence they exchanged during the war, gives an extraordinary view of these activities, and raises numerous fundamental questions about the role of a scientist, and particularly a mathematician during WW I. It also offers a vivid documentation about the intellectual life of the time ; Volterra's and Borel's circles in particular were extremely wide and the range of their interests was not limited to their field of specialization. The book proposes the complete transcription of the aforementioned correspondence, annotated with numerous footnotes to give details on the contents. It also offers a general historical introduction to the context of the letters and several complements on themes related to the academic exchanges between France and Italy during the war.
Mathematics And 21st Century Biology
by National Research Council of the National AcademiesThe exponentially increasing amounts of biological data along with comparable advances in computing power are making possible the construction of quantitative, predictive biological systems models. This development could revolutionize those biology-based fields of science. To assist this transformation, the U.S. Department of Energy asked the National Research Council to recommend mathematical research activities to enable more effective use of the large amounts of existing genomic information and the structural and functional genomic information being created. The resulting study is a broad, scientifically based view of the opportunities lying at the mathematical science and biology interface. The book provides a review of past successes, an examination of opportunities at the various levels of biological systems— from molecules to ecosystems—an analysis of cross-cutting themes, and a set of recommendations to advance the mathematics-biology connection that are applicable to all agencies funding research in this area.
Mathematics Applied to Engineering, Modelling, and Social Issues (Studies in Systems, Decision and Control #200)
by John N. Mordeson Hemen Dutta Frank T. SmithThis book presents several aspects of research on mathematics that have significant applications in engineering, modelling and social matters, discussing a number of current and future social issues and problems in which mathematical tools can be beneficial. Each chapter enhances our understanding of the research problems in a particular an area of study and highlights the latest advances made in that area. The self-contained contributions make the results and problems discussed accessible to readers, and provides references to enable those interested to follow subsequent studies in still developing fields. Presenting real-world applications, the book is a valuable resource for graduate students, researchers and educators. It appeals to general readers curious about the practical applications of mathematics in diverse scientific areas and social problems.
Mathematics Minus Fear: How to Make Math Fun and Beneficial to Your Everyday Life
by Lawrence PotterForget your classroom nightmares and discover how numbers can enhance and illuminate your world!How can math help you bet on horses or win in Vegas? What's the foolproof way to solve Sudoku? How can probability teach you to calculate your chances of survival in Russian roulette?In this irreverent and entertaining guide to mathematics, Lawrence Potter takes the fear out of everything from long division to percentages. Using fascinating puzzles and surprising examples, he shows us how math is connected with the world we encounter every day, from how the VAT works to why weather forecasts are wrong, from winning at Monopoly to improving your mental arithmetic. Along the way you'll also discover who invented numbers, whether animals can count, and what nuns have to do with multiplication.
Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures
by Steven J. BramsVoters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly. One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.
Mathematics and Explanation (Elements in the Philosophy of Mathematics)
by Christopher PincockThis Element answers four questions. Can any traditional theory of scientific explanation make sense of the place of mathematics in explanation? If traditional monist theories are inadequate, is there some way to develop a more flexible, but still monist, approach that will clarify how mathematics can help to explain? What sort of pluralism about explanation is best equipped to clarify how mathematics can help to explain in science and in mathematics itself? Finally, how can the mathematical elements of an explanation be integrated into the physical world? Some of the evidence for a novel scientific posit may be traced to the explanatory power that this posit would afford, were it to exist. Can a similar kind of explanatory evidence be provided for the existence of mathematical objects, and if not, why not?
Mathematics and Its Connections to the Arts and Sciences: 15 Years of Interdisciplinary Mathematics Education (Mathematics Education in the Digital Era #19)
by Viktor Freiman Annie Savard Claus Michelsen Astrid Beckmann Uffe Thomas JankvistThis book celebrates the 15th anniversary of the bi-annual symposium series Mathematics and its Connections to the Arts and Sciences (MACAS), which was first held in 2005 following the continued collaboration of an international group of researchers from ICME Topic Study Group 21. The MACAS-conferences bring together scientists and educators who are interested in the connection between mathematics, arts and science in educational curriculum, while emphasizing on, as well as researching about, the role of mathematics. By pooling together these different approaches and viewpoints between mathematics, arts and sciences, this book reveals possible synergies and paths for collaborations. In view of the challenges of the 21st century, a modern approach to education with a focus on multi- and interdisciplinarity is more important than ever. The role of mathematics assumes a key role in this approach as it is connected to all other disciplines, such as STEM education, physics, chemistry, biology, aesthetics and language, and can serve as a bridge between them. This book discusses, amongst others, the curricular approaches to integrate mathematics and other disciplines, the importance of mathematical modelling and the interdisciplinarity ways for learning and studying of mathematics, as well as the intercultural dimensions of mathematics and mathematics in the digital era. All topics will be presented from very different perspectives and regarding very different contexts, including digitization, culture and sustainability. This unique collection will serve as a very valuable and compact source for all above mentioned scientists and educators, as well as for use in advanced teacher education courses.
Mathematics and Metaphilosophy (Elements in the Philosophy of Mathematics)
by Justin Clarke-DoaneThis Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap's pragmatism, transposed to the key of realism.
Mathematics and Music: Composition, Perception, and Performance
by James S. Walker Gary W. DonMathematics and Music: Composition, Perception, and Performance, Second Edition includes many new sections and more consistent expectations of a student’s experience. The new edition of this popular text is more accessible for students with limited musical backgrounds and only high school mathematics is required. The new edition includes more illustrations than the previous one and the added sections deal with the XronoMorph rhythm generator, musical composition, and analyzing personal performance. The text teaches the basics of reading music, explaining how various patterns in music can be described with mathematics, providing mathematical explanations for musical scales, harmony, and rhythm. The book gives students a deeper appreciation showing how music is informed by both its mathematical and aesthetic structures. Highlights of the Second Edition: Now updated for more consistent expectations of students’ backgrounds More accessible for students with limited musical backgrounds Full-color presentation Includes more thorough coverage of spectrograms for analyzing recorded music Provides a basic introduction to reading music Features new coverage of building and evaluating rhythms
Mathematics and Philosophy at the Turn of the First Millennium: Abbo of Fleury on Calculus (Global Perspectives on the History of Natural Philosophy)
by Clelia V. CrialesiAt the turn of the first millennium, scientific and philosophical knowledge was far from dormant. Arithmetic, with its diverse calculation techniques and number theory, served as a bridge to philosophy, theology, and the study of the physical world. Even something as simple as a series of multiplication tables could unlock a profound knowledge of both the divine realm and natural phenomena. Such is the case with Abbo of Fleury’s Commentary on the Calculus.Mathematics and Philosophy at the Turn of the First Millennium sheds light on Abbo’s original philosophical system anchored in two central doctrines, which serve as a compass to navigate it: the theory of unity (henology) and the theory of composition. Yet, the Commentary on the Calculus covers much more. The present study, thus, explores an eclectic range of topics – from water clocks to barleycorns, constellations to human voice, synodic month to the human lifespan, and numbers to God. Abbo’s work is an ambitious attempt to tie together the study of both the visible and invisible realms, what can be measured and what cannot, what can be quantified and what exceeds quantification.Scholars and students of the history of philosophy and mathematics will be introduced to a pivotal figure from an often overlooked era. They will be provided with fresh insights into the spread of Neopythagorean doctrines in the early Middle Ages, as they learn how these ideas were transmitted through arithmetic texts and harmonised with theology and natural philosophy. They will also get to know the medieval fraction system and calculus practices.
Mathematics and Science Education Around the World: What Can We Learn From the Survey of Mathematics and Science Opportunities (SMSO) and the Third International Mathematics and Science Study (TIMSS)?
by "SMSO to TIMSS" Writing CommitteeThe National Academies Press (NAP)--publisher for the National Academies--publishes more than 200 books a year offering the most authoritative views, definitive information, and groundbreaking recommendations on a wide range of topics in science, engineering, and health. Our books are unique in that they are authored by the nation's leading experts in every scientific field.
Mathematics and the Physical World
by Morris Kline"Kline is a first-class teacher and an able writer. . . . This is an enlarging and a brilliant book." - Scientific American"Dr. Morris Kline has succeeded brilliantly in explaining the nature of much that is basic in math, and how it is used in science." - San Francisco ChronicleSince the major branches of mathematics grew and expanded in conjunction with science, the most effective way to appreciate and understand mathematics is in terms of the study of nature. Unfortunately, the relationship of mathematics to the study of nature is neglected in dry, technique-oriented textbooks, and it has remained for Professor Morris Kline to describe the simultaneous growth of mathematics and the physical sciences in this remarkable book. In a manner that reflects both erudition and enthusiasm, the author provides a stimulating account of the development of basic mathematics from arithmetic, algebra, geometry, and trigonometry, to calculus, differential equations, and the non-Euclidean geometries. At the same time, Dr. Kline shows how mathematics is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other phenomena. Historical and biographical materials are also included, while mathematical notation has been kept to a minimum. This is an excellent presentation of mathematical ideas from the time of the Greeks to the modern era. It will be of great interest to the mathematically inclined high school and college student, as well as to any reader who wants to understand - perhaps for the first time - the true greatness of mathematical achievements.