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Mathematical logic --- Topology --- Harmonic analysis. Fourier analysis --- Ergodic theory. Information theory --- Operational research. Game theory --- Fourieranalyse --- stochastische analyse --- wiskunde --- logica --- kansrekening --- topologie --- informatietheorie

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A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov. Each chapter treats one of Kolmogorov's research themes, or a subject that was invented as a consequence of his discoveries. His contributions are presented, his methods, the perspectives he opened to us, the way in which this research has evolved up to now, along with examples of recent applications and a presentation of the current prospects. This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than present detailed proofs, the main ideas are described. A bibliography is provided for those who wish to understand the technical details. One can see that sometimes very simple reasoning (with the right interpretation and tools) can lead in a few lines to very substantial results. The Kolmogorov Legacy in Physics was published by Springer in 2004 (ISBN 978-3-540-20307-0).

Kolmogorov complexity. --- Mathematics --- History --- Kolmogorov, A. N. --- Complexity, Kolmogorov --- Kolmogorov-Chaitin complexity --- Electronic data processing --- Machine theory --- Kolmogorov, Andreĭ Nikolaevich, --- Kolmogoroff, A., --- Колмогоров, А. Н. --- Logic, Symbolic and mathematical. --- Distribution (Probability theory. --- Differentiable dynamical systems. --- Fourier analysis. --- Topology. --- Mathematical Logic and Foundations. --- Probability Theory and Stochastic Processes. --- Dynamical Systems and Ergodic Theory. --- Fourier Analysis. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Analysis, Fourier --- Mathematical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism --- Mathematical logic. --- Probabilities. --- Dynamics. --- Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov. Each chapter treats one of Kolmogorov's research themes, or a subject that was invented as a consequence of his discoveries. His contributions are presented, his methods, the perspectives he opened to us, the way in which this research has evolved up to now, along with examples of recent applications and a presentation of the current prospects. This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than present detailed proofs, the main ideas are described. A bibliography is provided for those who wish to understand the technical details. One can see that sometimes very simple reasoning (with the right interpretation and tools) can lead in a few lines to very substantial results. The Kolmogorov Legacy in Physics was published by Springer in 2004 (ISBN 978-3-540-20307-0).

Mathematical logic --- Topology --- Harmonic analysis. Fourier analysis --- Ergodic theory. Information theory --- Operational research. Game theory --- Fourieranalyse --- stochastische analyse --- wiskunde --- logica --- kansrekening --- topologie --- informatietheorie

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Mathématiques

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"Cet ouvrage complet et pédagogique, destiné aussi bien aux étudiants de Licence (Bac) et Maîtrise en Sciences économiques et de gestion qu'aux professionnels de la gestion de portefeuille et de l'asset management, se positionne comme une référence en matière d'analyse de la stratégie de gestion de portefeuille et de l'examen de la performance de cette gestion. Un soin particulier a été apporté dans la clarté et la mise en perspective critique de l'exposition des bases de la théorie moderne de portefeuille et de l'efficience des marchés, en précisant l'état de la science et de l'art en la matière. Ensuite, l'ouvrage passe en revue les classes d'instruments financiers susceptibles d'intégrer un portefeuille de valeurs mobilières, à savoir les actions, les titres à revenus fixes, les produits dérivés et les actifs alternatifs, avec leurs principes de valorisation et leurs propriétés dans le cadre de la gestion d'actifs. Les stratégies de gestion de portefeuille par classes homogènes ou dans une optique d'allocation d'actifs font l'objet d'un examen minutieux. Cette analyse est complétée par une partie importante consacrée à l'évaluation de la performance de portefeuille, permettant d'établir un lien concret entre la mise en oeuvre des principes de gestion et le contrôle de leur qualité. Les innovations récentes en matière de stratégie et d'évaluation de la performance de portefeuille sont décrites avec objectivité et sans complaisance, mettant en exergue leurs avantages et faiblesses potentiels."--Page 4 de la couverture.

Portfolio management --- Investments --- Mathematical models --- Decision making --- Mathematical m --- Options (finances) --- Obligations (finances) --- Gestion de portefeuille --- Stocks --- Portfolios --- Actions de sociétés --- Management --- Actions (Titres de société) --- Marché financier --- Analyse financière --- Actifs financiers --- Modèles mathématiques --- Évaluation --- Capital market --- Investment analysis --- 339.40 --- Vermogenbeheer. financiële analyse (algemeenheden). --- Actions (Titres de société) --- Marché financier --- Analyse financière --- Évaluation --- Modèles mathématiques --- Textbooks --- Options (Finance) --- Bonds --- Stocks. --- Management. --- Vermogenbeheer. financiële analyse (algemeenheden) --- Gestion de portefeuille. --- Actions de sociétés. --- Portfolio management - Mathematical models --- Investments - Decision making - Mathematical models