A. N. Kolmogorov Pořadí knih (chronologicky)

This famous little book remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of probability and to historians of modern mathematics. 1956 second edition.

This foundational work in probability theory rigorously establishes key principles, akin to Euclid's approach to geometry. Originally published in 1933, it marked a significant milestone in mathematics, laying the groundwork for modern probability. Kolmogorov's treatise not only introduced essential concepts but also solidified his status as a preeminent figure in the field. This reprint offers a full facsimile of the original edition, preserving the historical significance and intellectual contributions of Kolmogorov's groundbreaking insights.

Focusing on advanced mathematical concepts, this comprehensive two-part text by A. N. Kolmogorov covers essential topics such as metric and normed spaces, measure theory, and Hilbert space. The work reflects Kolmogorov's significant contributions to various fields, including probability theory and turbulence. It includes exercises for practical application and provides lists of symbols, definitions, and theorems, making it a valuable resource for advanced students and researchers in mathematics. The reprint preserves the original edition's integrity without optical recognition software.

The editors initially aimed to create a comprehensive work on the history of nineteenth-century mathematics, transitioning systematically through various disciplines. However, challenges in author selection led to the abandonment of this plan by the second volume. Instead of a unified monograph, the series now offers a collection of books that collectively cover the mathematics of the nineteenth century, though not in the conventional order of disciplines. Unlike the first two volumes, which were organized into chapters, this third volume is divided into four parts, aligning better with the publication's nature. The first book addressed the history of mathematical logic, algebra, number theory, and probability, while the second focused on geometry and analytic function theory. In this third volume, readers will encounter an essay on Chebyshev's theory of function approximation, later termed "constructive function theory" by S. N. Bernshtein. This original essay, authored by the late N. I. Akhiezer (1901-1980), who made significant contributions to this field, is expected to engage not only historians of mathematics but also specialists in constructive function theory.

This multi-authored effort, Mathematics of the nineteenth century (to be fol­ lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics from antiquity to the early nineteenth century, published in three volumes from 1970 to 1972. 1 For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as well. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend, first, to unravel the forces that shape mathe­ matical progress. We examine the interaction of mathematics with the social structure, technology, the natural sciences, and philosophy. Through an anal­ ysis of mathematical history proper, we hope to delineate the relationships among the various mathematical disciplines and to evaluate mathematical achievements in the light of the current state and future prospects of the science. The difficulties confronting us considerably exceeded those encountered in preparing the three-volume edition.

Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.