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Mathematics --- Mathématiques --- Mathematics. --- Périodiques. --- Math --- Science --- Periodicals.

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A glorious period of Hungarian mathematics started in 1900 when Lipót Fejér discovered the summability of Fourier series.This was followed by the discoveries of his disciples in Fourier analysis and in the theory of analytic functions. At the same time Frederic (Frigyes) Riesz created functional analysis and Alfred Haar gave the first example of wavelets. Later the topics investigated by Hungarian mathematicians broadened considerably, and included topology, operator theory, differential equations, probability, etc. The present volume, the first of two, presents some of the most remarkable results achieved in the twentieth century by Hungarians in analysis, geometry and stochastics. The book is accessible to anyone with a minimum knowledge of mathematics. It is supplemented with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active. A list of all persons referred to in the chapters concludes the volume.

Mathematics. --- History of Mathematics. --- Analysis. --- Geometry. --- Probability Theory and Stochastic Processes. --- Global analysis (Mathematics). --- Mathematics_$xHistory. --- Distribution (Probability theory). --- Mathématiques --- Analyse globale (Mathématiques) --- Géométrie --- Distribution (Théorie des probabilités) --- Mathematics -- History -- 20th century. --- Mathematics -- Hungary -- History -- 20th century. --- Mathematics --- Mathematics - General --- Physical Sciences & Mathematics --- History --- Research --- Math --- History. --- Mathematical analysis. --- Analysis (Mathematics). --- Probabilities. --- History of Mathematical Sciences. --- History of Science. --- Science --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Euclid's Elements --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Annals --- Auxiliary sciences of history --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- 517.1 Mathematical analysis --- Mathematical analysis --- Probability Theory.

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"From nothing I have created a new different world,” wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics. Audience This book is intended for those who teach, study, and do research in geometry and history of mathematics. Cultural historians, physicists, and computer scientists will also find it an important source of information.

Geometry, Non-Euclidean. --- Mathematics. --- Math --- Science --- Non-Euclidean geometry --- Geometry --- Parallels (Geometry) --- Foundations --- Geometry. --- Global differential geometry. --- Cell aggregation --- History of Mathematical Sciences. --- Differential Geometry. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Classical and Quantum Gravitation, Relativity Theory. --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Geometry, Differential --- Mathematics --- Euclid's Elements --- History. --- Differential geometry. --- Manifolds (Mathematics). --- Complex manifolds. --- Gravitation. --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Analytic spaces --- Manifolds (Mathematics) --- Topology --- Differential geometry --- Annals --- Auxiliary sciences of history --- Properties --- Bolyai, János, --- Boi︠a︡i, I︠A︡nosh,