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PrefaceMathematics is the oldest of all sciences. Its foundations are visible in math-ematical texts originating in the ancient Egyptian, Mesopotamian, Indian,Chinese, Greek and Islamic worlds. Since the very beginning, when mathematics was conceived for fulﬁllingvery basic needs like numbering, counting and measuring simple-shaped ar-eas, this discipline has evolved in a boisterous way thus producing signiﬁcantresults that have strongly marked the evolution of mankind. Through the centuries, mathematical ideas and achievements have beenorganized and shaped into fundamental branches like arithmetic, numbertheory, algebra, geometry, and trigonometry, as well as related sciences likeastronomy, mechanics and physics. The development of the discipline then bloomed in the 16th century, whenmathematical innovations started to interact with new scientiﬁc discoveries;and its growth has never ceased thereafter. Nowadays, mathematics is the most inﬂuential and pervasive of all sciencesin our society, because of its exclusive potential of establishing connectionsamong virtually all possible manifestation of our knowledge. As a matter offact, it is used throughout the world as an essential tool in many ﬁelds. Inparticular, applied mathematics tranfers mathematical knowledge into otherﬁelds, oﬀering new possibilities to manage the growing complexity of our realworld. Beautiful though they may be, mathematical results are not merelymuseum-pieces, but form a vital underpinning for every branch of quanti-tative knowledge, including all domains of science and engineering. Mathe-matics is in constant and vigorous development, driven both by its internaldynamics and by the demands of other disciplines, henceforth impacting thewhole of our daily life. By gathering diﬀerent contributions from several world-famous scientistsfrom mathematics and related sciences, this book highlights the way mathe-matics deeply permeates and fertilizes our society.
VIII Preface In particular, here will we face the role of mathematics in applied sciencesshowing results in diﬀerent ﬁelds in industry, environment, life sciences andarchitecture. This book has the ambition to excite the readers interest showing howmathematics is also hidden in the natural world around us, independentlyof mankind presence and interference: there are maths schemes in any prey-predator interaction, Boltzmanns equations hidden in clouds, Navier-StokesEquations concealed in a waterfall, free boundary problems to be solved in amelting iceberg. Though this work will face maths problems that are not always elemen-tary, yet it is not intended for mathematicians only. The rigorous, nonethelessreadable, exposition, the intriguing examples, the stimulating demonstrationsof the deep connections among science, technology, architecture, human sci-ences and mathematics will fascinate even those who, not being scientists orexperts of this discipline, have always felt attracted by the noblest and mostfundamental of modern sciences.The Editors, and the Publisher as well, would like to thank all the authors andthe people who actively contributed to the success of this project, in particularLuca Paglieri, for his accuracy and concern in supporting the MATHKNOWexperience since the very beginning.
List of ContributorsRalph Abraham Fernando BlascoUniversity of California Departamento de Matem´tica aSanta Cruz, CA, USA Aplicada a los Recursos Naturalesrha@ucsc.edu ETSI Montes Universidad Polit´cnica de Madrid e Madrid, Spain firstname.lastname@example.orgGiacomo AlettiDipartimento di Matematica“F. Enriques”Universit` degli Studi di Milano a Paola CausinMilano, Italy Dipartimento di Matematicaaletti@mat.unimi.it “F. Enriques” Universit` degli Studi di Milano a Milano, Italy email@example.comNadia AmbrosettiDipartimento di Informatica eComunicazioneFacolt` di Scienze Matematiche, a Andrew CrumeyFisiche e Naturali School of English Literature,Universit` degli Studi di Milano a Language and LinguisticsMilano, Italy Newcastle Universitynadia.firstname.lastname@example.org Newcastle upon Tyne, UK Andrew.Crumey@ncl.ac.ukPaolo BiscariDipartimento di Matematica Guido ChiesaPolitecnico di Milano Movie DirectorMilano, Italy Padova, Italypaolo.email@example.com firstname.lastname@example.org
X List of ContributorsMichele Emmer Claudio ProcesiUniversit` degli studi “La Sapienza” a Universit` degli studi “La Sapienza” aDipartimento di Matematica Istituto di Matematica“G. Castelnuovo” “G. Castelnuovo”Roma, Italy Roma, Italyemmer@mat.uniroma1.it Alﬁo QuarteroniMassimo Fornasier MOX, Dipartimento di MatematicaJohann Radon Institute for “F. Brioschi”Computational and Applied Politecnico di MilanoMathematics (RICAM) Milano, ItalyLinz, Austria email@example.com CMCS-IACS Ecole Polytechnique F´d´rale de e eRoberto Lucchetti LausanneDipartimento di Matematica Lausanne, SwitzerlandPolitecnico di MilanoMilano, Italy Renzo L. Ricca Dipartimento di MatematicaGiulio Magli ApplicataFacolt` di Architettura Civile a Universit` Milano-Bicocca aPolitecnico di Milano Milano, ItalyMilano, Italy and Institute for Scientiﬁc Interchange Torino, ItalyPeter Markowich firstname.lastname@example.orgDAMTP www.matapp.unimib.it/~riccaCentre for Mathematical SciencesCambridge, UK Riccardo SaccoGiovanni Naldi Dipartimento di MatematicaDipartimento di Matematica “F. Brioschi”“F. Enriques” Politecnico di MilanoUniversit` degli Studi di Milano a Milano, ItalyMilano, Italy email@example.com@mat.unimi.it Matteo SempliceLuca Paglieri Dipartimento di MatematicaMOX, Dipartimento di Matematica “F. Enriques”“F. Brioschi” Universit` degli Studi di Milano aPolitecnico di Milano Milano, ItalyMilano, Italy firstname.lastname@example.org
List of Contributors XIAmin Shokrollahi Tobias WallisserEcole Polytechnique F´d´rale de e e Staatliche Akademie der BildendenLausanne K¨nste Stuttgart uLausanne, Switzerland Stuttgart, Germanyamin.email@example.com Sarah WolfLaura Tedeschini Lalli Potsdam Institute for ClimateDipartimento di Matematica Impact Research (PIK)Universit` Roma Tre a Potsdam, GermanyRoma, Italy firstname.lastname@example.org