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Mathematics and Technology presents technological applications of mathematics making use of elegant mathematical concepts. The selected subjects consist of: public key cryptography, error correcting codes, the global positioning system (GPS) and cartography, image compression using fractals and the JPEG format, digital recording, robot movement, DNA computing, Google's PageRank algorithm, savings and loans, gamma ray surgery and random number generators. The authors highlight how mathematical modeling, together with the power of mathematical tools, have been crucial for innovation in technology. The exposition is clear, straightforward, motivated by excellent examples, and user-friendly. Numerous exercises at the end of every chapter reinforce the material. An engaging quality is the various historical notes accompanying the mathematical development. This book is intended mainly for undergraduate students in pure and applied mathematics, physics and computer science, instructors, and high school teachers. The main prerequisites are linear algebra and Euclidean geometry. A few chapters require multivariable calculus and elementary probability theory. A clear indication of the more difficult topics and relatively advanced references make it also suitable for an independent reader mastering the prerequisites.

Didactics of mathematics --- Mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Computer Science, general. --- Probability Theory and Stochastic Processes. --- Game Theory, Economics, Social and Behav. Sciences. --- Applications of Mathematics. --- Computer science. --- Distribution (Probability theory). --- Mathématiques --- Informatique --- Distribution (Théorie des probabilités) --- Technology --Mathematical models. --- Technology. --- Mathematics --- Technology --- Physical Sciences & Mathematics --- Mathematics - General --- Mathematical models --- Applied science --- Arts, Useful --- Science, Applied --- Useful arts --- Science --- Industrial arts --- Material culture --- Math --- Mathematical models. --- Engineering mathematics. --- Distribution (Probability theory. --- Mathematical and Computational Engineering. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Informatics --- Engineering --- Engineering analysis --- Mathematical analysis --- Applied mathematics. --- Probabilities. --- Game theory. --- Games, Theory of --- Theory of games --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Models, Mathematical --- Simulation methods

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Les auteurs dévoilent les élégants concepts mathématiques cachés derrière des applications technologiques et les replacent dans un contexte historique. Les sujets traités comprennent : la cryptographie à clé publique, les codes correcteurs d'erreurs, le système de positionnement global (GPS) et la cartographie, la compression d'images à l'aide de fractals et à l'aide du format JPEG, la numérisation de la musique, les robots, l'ordinateur à l'ADN, l'algorithme PageRank de Google, l'épargne et l'emprunt, la chirurgie aux rayons gamma, les générateurs de nombres aléatoires. Un des leitmotivs du texte est que la modélisation mathématique, la puissance des outils mathématiques et l'abstraction jouent un rôle crucial dans l'innovation technologique. Les divers sujets sont présentés avec clarté, et les préalables mathématiques sont relativement élémentaires. Chaque chapitre comporte de nombreux exercices, certains élémentaires pour renforcer la compréhension, d'autres plus avancés pour explorer de nouvelles problématiques. Ce livre s'adresse aux étudiants en mathématiques pures et appliquées, en physique, en informatique, ainsi qu'aux futurs maîtres du secondaire. Les préalables sont l'algèbre linéaire, la géométrie euclidienne et, pour quelques chapitres, les probabilités élémentaires ou le calcul à plusieurs variables. Une mise en contexte historique enrichit le texte. Les sections plus difficiles sont clairement indiquées afin que le livre soit accessible à toute personne curieuse maîtrisant les préalables.

Mathematics. --- Technology --- Technology. --- Applied science --- Arts, Useful --- Science, Applied --- Useful arts --- Math --- Mathematical models. --- Algebra. --- Computer science. --- Distribution (Probability theory. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Computer Science, general. --- Game Theory, Economics, Social and Behav. Sciences. --- Probability Theory and Stochastic Processes. --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Informatics --- Mathematics --- Mathematical analysis --- Industrial arts --- Material culture --- Applied mathematics. --- Engineering mathematics. --- Game theory. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Games, Theory of --- Theory of games --- Mathematical models --- Engineering --- Engineering analysis --- Models, Mathematical --- Simulation methods --- Technology - Mathematical models