Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow. Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do...
Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the...
A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent'ev, S. H. Gould, T. Bartha
Mathematics, which originated in antiquity in the needs of daily life, has developed into an immense system of widely varied disciplines. Like the other sciences, it reflects the laws of the material world around us and serves as a powerful instrument for our knowledge and mastery of nature. But the high level of abstraction peculiar to mathematics means that its newer branches are relatively inaccessible to nonspecialists. This abstract character of mathematics gave birth even in antiquity to idealistic notions about its independence of the material world.In recent years, many popular...
Mathematics, which originated in antiquity in the needs of daily life, has developed into an immense system of widely varied disciplines. Like the ...
