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Introduction to Differential and Algebraic Topology
Topology as a subject, in our opinion, plays a central role in university education. It is not really possible to design courses in differential geometry, mathematical analysis, differential equations, mechanics, functional analysis that correspond to the temporary state of these disciplines without involving topological concepts. Therefore, it is essential to acquaint students with topo logical research methods already in the first university courses. This textbook is one possible version of an introductory course in topo logy and elements of differential geometry, and it absolutely reflects both the authors' personal preferences and experience as lecturers and researchers. It deals with th...
History: fiction or science?. Chronology 1
The author contends that all generaly accepted historical chronology prior to the 16th century is inaccurate, often off by many hundreds or even thousands of years. Volume 1 of a proposed seven volumes.
Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating
Today the methods of applied statistics have penetrated very different fields of knowledge, including the investigation oftexts ofvarious origins. These "texts" may be considered as signal sequences of different kinds, long genetic codes, graphic representations (which may be coded and represented by a "text"), as well as actual narrative texts (for example, historical chronicles, originals, documents, etc. ). One ofthe most important problems arising here is to recognize dependent text, i. e. , texts which have a measure of "resemblance", arising from some kind of "common origin". For instance, in pattern-recognition problems, it is essential to identify from a large set of "patterns" a pat...
Coordination Chemistry
First published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.
Topology and Its Applications
The Proceedings of an international topology conference - this book covrs various aspects of general algebraic, and low-dimensional topology.
Variational Problems in Topology
Many of the modern variational problems of topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clear explanation of some of these problems (both solved and unsolved), using current methods of analytical topology. His book falls into three interrelated sections. The first gives an elementary introduction to some of the most important concepts of topology used in modern physics and mechanics: homology and cohomology, and fibration. The second investigates the significant role of Morse theory in modern aspects of the topology of smooth manifolds, particularly those of three and four dime...
Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem
Plateau's problem is a scientific trend in modern mathematics that unites several different problems connected with the study of minimal surfaces. In its simplest version, Plateau's problem is concerned with finding a surface of least area that spans a given fixed one-dimensional contour in three-dimensional space--perhaps the best-known example of such surfaces is provided by soap films. From the mathematical point of view, such films are described as solutions of a second-order partial differential equation, so their behavior is quite complicated and has still not been thoroughly studied. Soap films, or, more generally, interfaces between physical media in equilibrium, arise in many applie...
Lectures on Algebraic Topology
Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.
Introduction to Geometry of Manifolds with Symmetry
One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the three-dimensional Euclidean space as the only possible mathematical description of real physical space. Apriorization of geometrical notions and identification of physical 3 space with its mathematical modellR were characteristic for these views. The discovery of non-Euclidean geometries led mathematicians to the understanding that Euclidean geometry is nothing more than one of many logically admissible geometrical systems. Relativity theory amended our understanding of the problem of space by amalgamating space and time...
