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Mathematician for All Seasons
by Aleksander Weron Irena Szymaniec Hugo SteinhausRobert G. BurnsThis 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.
A Mathematician Like Me
by Dr Shini SomaraStriking illustrations and an empowering story combine to introduce young readers to the world of maths, creative thinking and problem-solving.Setting off on a camping adventure with her cousin, Aliyah soon discovers that numbers are everywhere, whether it's counting out money at the shops, planning trips on the train or even stargazing in a forest. As Aliyah solves some sums of her own, she learns about the brilliant mathematicians who have helped us understand our world. Soon she can't wait to become a maths whizz too!With pages encouraging kids to play maths games with their friends, this brilliant picture book written by engineer and TV presenter Dr Shini Somara unlocks a love of numbers and creative thinking, and celebrates women in STEM.Also available in the series:- A Scientist Like Me- A Coder Like Me- An Engineer Like Me
A Mathematician Plays The Stock Market
by John Allen PaulosIn A Mathematician Plays the Stock Market best-selling author John Allen Paulos demonstrates what the tools of mathematics can tell us about the vagaries of the stock market. Employing his trademark stories, vignettes, paradoxes, and puzzles (and even a film treatment), Paulos addresses every thinking reader's curiosity about the market: Is it efficient? Is it rational? Is there anything to technical analysis, fundamental analysis, and other supposedly time-tested methods of picking stocks? How can one quantify risk? What are the most common scams? What light do fractals, network theory, and common psychological foibles shed on investor behavior? Are there any approaches to investing that truly outperform the major indexes? Can a deeper knowledge of mathematics help beat the odds?All of these questions are explored with the engaging erudition that made Paulos's A Mathematician Reads the Newspaper and Innumeracy favorites with both armchair mathematicians and readers who want to think like them. Paulos also shares the cautionary tale of his own long and disastrous love affair with WorldCom. In the tradition of Burton Malkiel's A Random Walk Down Wall Street and Jeremy Siegel's Stocks for the Long Run, this wry and illuminating book is for anyone, investor or not, who follows the markets-or knows someone who does.
A Mathematician's Apology
by G. H. HardyG. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician … the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his idiosyncrasies and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.
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.
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.
Mathematics, Administrative and Economic Activities in Ancient Worlds (Why the Sciences of the Ancient World Matter #5)
by Cécile Michel Karine ChemlaThis book focuses on the ancient Near East, early imperial China, South-East Asia, and medieval Europe, shedding light on mathematical knowledge and practices documented by sources relating to the administrative and economic activities of officials, merchants and other actors. It compares these to mathematical texts produced in related school contexts or reflecting the pursuit of mathematics for its own sake to reveal the diversity of mathematical practices in each of these geographical areas of the ancient world. Based on case studies from various periods and political, economic and social contexts, it explores how, in each part of the world discussed, it is possible to identify and describe the different cultures of quantification and computation as well as their points of contact. The thirteen chapters draw on a wide variety of texts from ancient Near East, China, South-East Asia and medieval Europe, which are analyzed by researchers from various fields, including mathematics, history, philology, archaeology and economics. The book will appeal to historians of science, economists and institutional historians of the ancient and medieval world, and also to Assyriologists, Indologists, Sinologists and experts on medieval Europe.
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 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 Claus Michelsen Astrid Beckmann Viktor Freiman Uffe Thomas Jankvist Annie SavardThis 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 null 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.
Mathematics and the Real World
by Zvi ArtsteinIn this accessible and illuminating study of how the science of mathematics developed, a veteran math researcher and educator looks at the ways in which our evolutionary makeup is both a help and a hindrance to the study of math.Artstein chronicles the discovery of important mathematical connections between mathematics and the real world from ancient times to the present. The author then describes some of the contemporary applications of mathematics--in probability theory, in the study of human behavior, and in combination with computers, which give mathematics unprecedented power.The author concludes with an insightful discussion of why mathematics, for most people, is so frustrating. He argues that the rigorous logical structure of math goes against the grain of our predisposed ways of thinking as shaped by evolution, presumably because the talent needed to cope with logical mathematics gave the human race as a whole no evolutionary advantage. With this in mind, he offers ways to overcome these innate impediments in the teaching of math.
The Mathematics and Topology of Fullerenes
by Franco Cataldo Ottorino Ori Ante GraovacThe Mathematics and Topology of Fullerenes presents a comprehensive overview of scientific and technical innovations in theoretical and experimental studies. Topics included in this multi-author volume are: Clar structures for conjugated nanostructures; counting polynomials of fullerenes; topological indices of fullerenes; the wiener index of nanotubes; toroidal fullerenes and nanostars; C60 Structural relatives: a topological study; local combinatorial characterization of fullerenes; computation of selected topological indices of C60 and C80 Fullerenes via the Gap Program; 4valent- analogues of fullerenes; a detailed atlas of Kekule structures of C60. The Mathematics and Topology of Fullerenes is targeted at advanced graduates and researchers working in carbon materials, chemistry and physics.
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 as a Laboratory Tool
by John Milton Toru OhiraThis introductory textbook is based on the premise that the foundation of good science is good data. The educational challenge addressed by this introductory textbook is how to present a sampling of the wide range of mathematical tools available for laboratory research to well-motivated students with a mathematical background limited to an introductory course in calculus.
Mathematics as a Laboratory Tool: Dynamics, Delays and Noise
by John Milton Toru OhiraThe second edition of Mathematics as a Laboratory Tool reflects the growing impact that computational science is having on the career choices made by undergraduate science and engineering students. The focus is on dynamics and the effects of time delays and stochastic perturbations (“noise”) on the regulation provided by feedback control systems. The concepts are illustrated with applications to gene regulatory networks, motor control, neuroscience and population biology. The presentation in the first edition has been extended to include discussions of neuronal excitability and bursting, multistability, microchaos, Bayesian inference, second-order delay differential equations, and the semi-discretization method for the numerical integration of delay differential equations. Every effort has been made to ensure that the material is accessible to those with a background in calculus. The text provides advanced mathematical concepts such as the Laplace and Fourier integral transforms in the form of Tools. Bayesian inference is introduced using a number of detective-type scenarios including the Monty Hall problem.
The Mathematics Behind Biological Invasions
by Mark A. Lewis Sergei V. Petrovskii Jonathan R. PottsThis book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecology.
A Mathematics Boot Camp for Science and Engineering Students
by Ying MaMany students have difficulty applying mathematical techniques to solve problems in science and engineering, even after completing Calculus I and II. Students who are beginning the core coursework in their field of study often need additional guidance on practicing, learning, and improving their problem-solving skills for application. The objectives of A Mathematics Boot Camp for Science and Engineering Students are to offer a solution to this issue and are specifically designed to address common errors in mathematical problem-solving for undergraduate science and engineering students. Teaches readers how to apply math skills as they transition to coursework in their chosen field of study Includes strategies and recommendations for quick improvement in problem-solving skills Emphasizes the physical meanings of the problem, which helps students develop a deep understanding of their field of study Features a broad range of example problems with detailed and easy-to-follow solutions for students to learn problem-solving techniques and additional exercise problems for further practice and improvement Bridges the gap between the knowledge of mathematical techniques and the ability to apply those techniques to solve real-world problems This concise and practical text offers "basic training" in mathematical problem-solving skills for undergraduate students in science and engineering disciplines. A Solutions Manual is available to qualifying adopting professors.
The Mathematics Companion: Mathematical Methods for Physicists and Engineers, 2nd Edition
by Anthony C. Fischer-CrippsEverything You Need to Know about Mathematics for Science and EngineeringUpdated and expanded with new topics, The Mathematics Companion: Mathematical Methods for Physicists and Engineers, 2nd Edition presents the essential core of mathematical principles needed by scientists and engineers. Starting from the basic concepts of trigonometry, the book
Mathematics for Biological Scientists
by Mike Aitken Bill Broadhurst Stephen HladkyMathematics for Biological Scientists is a new undergraduate textbook which covers the mathematics necessary for biology students to understand, interpret and discuss biological questions.The book's twelve chapters are organized into four themes. The first theme covers the basic concepts of mathematics in biology, discussing the mathematics used in biological quantities, processes and structures. The second theme, calculus, extends the language of mathematics to describe change. The third theme is probability and statistics, where the uncertainty and variation encountered in real biological data is described. The fourth theme is explored briefly in the final chapter of the book, which is to show how the 'tools' developed in the first few chapters are used within biology to develop models of biological processes.Mathematics for Biological Scientists fully integrates mathematics and biology with the use of colour illustrations and photographs to provide an engaging and informative approach to the subject of mathematics and statistics within biological science.