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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with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active.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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Szemerédi's influence on today's mathematics, especially in combinatorics, additive number theory, and theoretical computer science, is enormous. This volume is a celebration of Szemerédi's achievements and personality, on the occasion of his seventieth birthday. It exemplifies his extraordinary vision and unique way of thinking. A number of colleagues and friends, all top authorities in their fields, have contributed their latest research papers to this volume. The topics include extension and applications of the regularity lemma, the existence of k-term arithmetic progressions in various subsets of the integers, extremal problems in hypergraphs theory, and random graphs, all of them beautiful, Szemerédi type mathematics. It also contains published accounts of the first two, very original and highly successful Polymath projects, one led by Tim Gowers and the other by  Terry Tao.

Combinatorial analysis. --- Graph theory. --- Number theory. --- Szemerédi, E. --- Number study --- Numbers, Theory of --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorics --- Extremal problems --- Szemerédi, E. -- Bibliography. --- Mathematics. --- Algebra. --- Field theory (Physics). --- Discrete mathematics. --- Combinatorics. --- Discrete Mathematics. --- Graph Theory. --- Number Theory. --- Field Theory and Polynomials. --- Algebra --- Combinatorial analysis --- Topology --- Mathematical analysis --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Algebraic fields. --- Polynomials. --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- Szemeredi, E.

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Mathematics --- Combinatorial analysis --- Set theory --- Analyse combinatoire --- Théorie des ensembles --- Congresses --- Congrès --- Erdos, Paul, --- Erdős, Paul, --- Erdos, Paul --- Erdős, Paul, --- Congresses. --- Erdős, Pál --- Théorie des ensembles --- Congrès --- Combinatorial analysis - Congresses --- Set theory - Congresses --- Erdős, Paul, - 1913-1996 --- Combinatoire --- Colloque