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D'abord conçu comme outil pédagogique pour les étudiants du premier cycle universitaire, ce manuel d'analyse mathématique servira également de référence à tous ceux qui enseignent les éléments du calcul différentiel et intégral. Introduction à l'analyse présente dans un langage accessible les nombres, les suites, les fonctions continues et différentiables, l'intégration, ainsi que les séries de nombres et de fonctions, Outre de nombreux exemples qui faciliteront l'auto-apprentissage de l'étudiant, on trouvera à la fin de chaque chapitre une sélection judicieuse d'exercices. De courtes notices aideront le lecteur à replacer dans une perspective historique chacune des principales notions abordées
Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik)
Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.
Mathematical Perspectives: Essays on Mathematics and its Historical Development is a collection of 13 biographical essays on the historical advances of science. This collection is originally meant to comprise an issue of the journal Historia Mathematica in honor of Professor Kurt R. Biermann's 60th birthday. This 12-chapter text includes essays on studies and commentaries on the problem of "figures of equal perimeter by various authors in antiquity, including Zenodorus, Theon, and Pappus. Other essays explore the comparison of the areas of polygons with equal perimeter; the concept of function; history of mathematics; the development of mathematical physics in France; and the history of Logicism and Formalism. The remaining chapters deal with essays on an early version of Gauss' Disquisitiones Arithmeticae, ideal numbers, a mathematical-philosophilica theory of probability, and historical examples of problem of number sequence interpolation. This book will be of value to mathematicians, historians, and researchers.
The first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning.
"Papers presented to J.E. Littlewood on his 80th birthday" issued as 3d ser., v. 14 A, 1965.
Logic, Methodology and Philosophy of Science, Proceeding of the 1960 International Congress
This concise, well-written handbook provides a distillation of real variable theory with a particular focus on the subject's significant applications to differential equations and Fourier analysis. Ample examples and brief explanations---with very few proofs and little axiomatic machinery---are used to highlight all the major results of real analysis, from the basics of sequences and series to the more advanced concepts of Taylor and Fourier series, Baire Category, and the Weierstrass Approximation Theorem. Replete with realistic, meaningful applications to differential equations, boundary value problems, and Fourier analysis, this unique work is a practical, hands-on manual of real analysis that is ideal for physicists, engineers, economists, and others who wish to use the fruits of real analysis but who do not necessarily have the time to appreciate all of the theory. Valuable as a comprehensive reference, a study guide for students, or a quick review, "A Handbook of Real Variables" will benefit a wide audience.