"The most common language of numbers, the decimal system, has not always been used universally. From a purely mathematical point of view, the decimal system has no inherent advantages over other possible systems; its popularity is due to historical and biological, not mathematical factors. In this book, S. V. Fomin discusses the origin, properties, and applications of various number systems, including the decimal, the binary, and the ternary. His presentation offers the student an introduction to mathematical abstraction and then, through its examples, shows him the abstraction at work."

Number Systems

Science & Math

Fomin, S.V.

Mathematics

Univ of Chicago Pr

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 continuous curves in metric spaces — a topic seldom discussed in textbooks.Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.

Elements of the Theory of Functions and Functional Analysis, Vol. I: Metric and Normed Spaces

Kolmogorov, A.N.

Dover Publications

Book by Dalecky, Yu.L., Fomin, S.V.

Measures and Differential Equations in Infinite-Dimensional Space (Mathematics and its Applications)

Dalecky, Yu.L.

Springer

Multiple Integrals Field Theory and Series

Budak, B. M.

Volosov (tr)

MIR PUBLISHER

Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with "simple. " Part II is devoted to "abstract ergodic theory. " It includes the construc tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.

Ergodic Theory (Grundlehren der mathematischen Wissenschaften)

Sinai, Y.G.

Cornfeld, I.P.

2012 Reprint of Volumes One and Two, 1957-1961. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. A. N. Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, logic, turbulence, classical mechanics and computational complexity. Later in life Kolmogorov changed his research interests to the area of turbulence, where his publications beginning in 1941 had a significant influence on the field. In classical mechanics, he is best known for the Kolmogorov-Arnold-Moser theorem. In 1957 he solved a particular interpretation of Hilbert's thirteenth problem (a joint work with his student V. I. Arnold). He was a founder of algorithmic complexity theory, often referred to as Kolmogorov complexity theory, which he began to develop around this time. Based on the authors' courses and lectures, this two-part advanced-level text is now available in a single volume. Topics include metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, and more. Each section contains exercises. Lists of symbols, definitions, and theorems.

Elements of the Theory of Functions and Functional Analysis [Two Volumes in One]

Martino Fine Books

Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna­ mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with "simple. " Part II is devoted to "abstract ergodic theory. " It includes the construc­ tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.

Ergodic Theory

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

lEt moi, .... si j'avait Sll comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile: ' where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded 0- sense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1re of this series.

See the best price to sell, buy, or rent books by Fomin, S.V.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Fomin, S.V.

See the best price to sell, buy, or rent books by Fomin, S.V.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Number Systems

Elements of the Theory of Functions and Functional Analysis, Vol. I: Metric and Normed Spaces

Measures and Differential Equations in Infinite-Dimensional Space (Mathematics and its Applications)

Multiple Integrals Field Theory and Series

Ergodic Theory (Grundlehren der mathematischen Wissenschaften)

Elements of the Theory of Functions and Functional Analysis [Two Volumes in One]

Ergodic Theory

Measures and Differential Equations in Infinite-Dimensional Space (Mathematics and its Applications)