Christiane Rousseau - Böcker

Les auteurs présentent des concepts mathématiques de base, comme les chaînes de Markov, les fonctions itérées, la structure de corps fini, et les développent dans le contexte de problèmes réels tels que la navigation internet, la compression de données et les codes correcteurs d'erreurs. Un des leitmotivs du texte est de montrer comment la modélisation mathématique, la puissance des outils mathématiques et l'abstraction sont toutes cruciales pour l'innovation technologique. Les divers sujets sont présentés avec clarté et les mathématiques toujours discutées à partir de connaissances de base. Chaque chapitre suggère de nombreux exercices, certains élémentaires pour renforcer la compréhension, d'autres plus avancés pour explorer de nouvelles problématiques. Une mise en contexte historique de certains concepts mathématiques ou de l'évolution d'une technologique enrichit le texte.

Of what use is mathematics? Hasn’t everything in mathematics already been disc- ered? Thesearenaturalquestionsoftenaskedbyundergraduates. Theanswersprovided by their professors are often quite brief. Most university courses, pressed for time and rigidly structured, o?er little opportunity to present and study actual applications and real-world examples. Evenmorehigh-schoolstudentsaskthesamequestionswithmoreinsistence. Tea- ers in these schools generally work under even tighter constraints than university prof- sors. If they are able to competently respond to these questions it is probably because they received good answers from their teachers and professors. And if they do not have the answers, then whose fault is it? The genesis of this text It is impossible to introduce this text without ?rst discussing the course in which it originated. The course “Mathematics and Technology” was created at the Universit´ e de Montr´ eal and taught for the ?rst time in the winter semester of 2001. It was created after observing that most courses in the department neglect to present real applications. Sinceitscreationthecoursehasbeenopentobothundergraduatemathematicsstudents and future high-school teachers. Since no appropriate text or manual for the course we envisioned existed, we were led to write our own course notes, from which we taught. We got so caught up in writing these notes that they quickly grew to the size of a textbook, containing much more material than could possibly be taught in one semester. Despite the two of us being career mathematicians, we must admit that we both knew little or nothing about most of the applications presented in the following chapters.

A number of recent significant developments in the theory of differential equations are presented in an elementary fashion, many of which are scattered throughout the literature and have not previously appeared in book form, the common denominator being the theory of planar vector fields (real or complex). A second common feature is the study of bifurcations of dynamical systems. Moreover, the book links fields that have developed independently and signposts problems that are likely to become significant in the future. The following subjects are covered: new tools for local and global properties of systems and families of systems, nonlocal bifurcations, finiteness properties of Pfaffian functions and of differential equations, geometric interpretation of the Stokes phenomena, analytic theory of ordinary differential equations and complex foliations, applications to Hilbert's 16th problem. Readership: Graduate students, postdocs and researchers in dynamical systems with a minimum background of a one-year course on nonlinear differential equations. 'Skeletal metastases are both a common and devastating consequence of a spectrum of cancers.Significant advances have occurred in our understanding of the pathobiology of this process. This text provides a comprehensive review of current investigative findings and their clinical implications.' Steven T. Rosen, M.D. Series Editor

A number of recent significant developments in the theory of differential equations are presented in an elementary fashion, many of which are scattered throughout the literature and have not previously appeared in book form, the common denominator being the theory of planar vector fields (real or complex). A second common feature is the study of bifurcations of dynamical systems. Moreover, the book links fields that have developed independently and signposts problems that are likely to become significant in the future. The following subjects are covered: new tools for local and global properties of systems and families of systems, nonlocal bifurcations, finiteness properties of Pfaffian functions and of differential equations, geometric interpretation of the Stokes phenomena, analytic theory of ordinary differential equations and complex foliations, applications to Hilbert's 16th problem. Readership: Graduate students, postdocs and researchers in dynamical systems with a minimum background of a one-year course on nonlinear differential equations. 'Skeletal metastases are both a common and devastating consequence of a spectrum of cancers.Significant advances have occurred in our understanding of the pathobiology of this process. This text provides a comprehensive review of current investigative findings and their clinical implications.' Steven T. Rosen, M.D. Series Editor

Of what use is mathematics? Hasn’t everything in mathematics already been disc- ered? Thesearenaturalquestionsoftenaskedbyundergraduates. Theanswersprovided by their professors are often quite brief. Most university courses, pressed for time and rigidly structured, o?er little opportunity to present and study actual applications and real-world examples. Evenmorehigh-schoolstudentsaskthesamequestionswithmoreinsistence. Tea- ers in these schools generally work under even tighter constraints than university prof- sors. If they are able to competently respond to these questions it is probably because they received good answers from their teachers and professors. And if they do not have the answers, then whose fault is it? The genesis of this text It is impossible to introduce this text without ?rst discussing the course in which it originated. The course “Mathematics and Technology” was created at the Universit´ e de Montr´ eal and taught for the ?rst time in the winter semester of 2001. It was created after observing that most courses in the department neglect to present real applications. Sinceitscreationthecoursehasbeenopentobothundergraduatemathematicsstudents and future high-school teachers. Since no appropriate text or manual for the course we envisioned existed, we were led to write our own course notes, from which we taught. We got so caught up in writing these notes that they quickly grew to the size of a textbook, containing much more material than could possibly be taught in one semester. Despite the two of us being career mathematicians, we must admit that we both knew little or nothing about most of the applications presented in the following chapters.