Analysis Situs
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Author | : Vincenzo de Risi |
Publisher | : Springer Science & Business Media |
Total Pages | : 658 |
Release | : 2007-08-08 |
Genre | : Science |
ISBN | : 3764379863 |
This book reconstructs, from both historical and theoretical points of view, Leibniz’s geometrical studies, focusing in particular on the research Leibniz carried out in his final years. The work’s main purpose is to offer a better understanding of the philosophy of space and in general of the mature Leibnizean metaphysics. This is the first ever, comprehensive historical reconstruction of Leibniz’s geometry.
Author | : |
Publisher | : American Mathematical Soc. |
Total Pages | : 250 |
Release | : |
Genre | : |
ISBN | : 0821852345 |
Author | : Frederick Converse Beach |
Publisher | : |
Total Pages | : 1104 |
Release | : 1906 |
Genre | : Encyclopedias and dictionaries |
ISBN | : |
Author | : Hermann Weyl |
Publisher | : |
Total Pages | : 380 |
Release | : 1922 |
Genre | : Relativity (Physics) |
ISBN | : |
Author | : William S. Massey |
Publisher | : Springer Science & Business Media |
Total Pages | : 452 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 038797430X |
This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.
Author | : David E. Rowe |
Publisher | : Birkhäuser |
Total Pages | : 500 |
Release | : 2018-06-18 |
Genre | : Mathematics |
ISBN | : 1493977083 |
Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.
Author | : Marcelo Dascal |
Publisher | : Springer Science & Business Media |
Total Pages | : 528 |
Release | : 2008-08-09 |
Genre | : Philosophy |
ISBN | : 1402086687 |
Gottfried Wilhelm Leibniz was an outstanding contributor to many fields of human knowledge. The historiography of philosophy has tagged him as a “rationalist”. But what does this exactly mean? Is he a “rationalist” in the same sense in Mathematics and Politics, in Physics and Jurisprudence, in Metaphysics and Theology, in Logic and Linguistics, in Technology and Medicine, in Epistemology and Ethics? What are the most significant features of his “rationalism”, whatever it is? For the first time an outstanding group of Leibniz researchers, some acknowledged as leading scholars, others in the beginning of a promising career, who specialize in the most significant areas of Leibniz’s contributions to human thought and action, were requested to spell out the nature of his rationalism in each of these areas, with a view to provide a comprehensive picture of what it amounts to, both in its general drive and in its specific features and eventual inner tensions. The chapters of the book are the result of intense discussion in the course of an international conference focused on the title question of this book, and were selected in view of their contribution to this topic. They are clustered in thematically organized parts. No effort has been made to hide the controversies underlying the different interpretations of Leibniz’s “rationalism” – in each particular domain and as a whole. On the contrary, the editor firmly believes that only through a variety of conflicting interpretive perspectives can the multi-faceted nature of an oeuvre of such a magnitude and variety as Leibniz’s be brought to light and understood as it deserves.
Author | : S.P. Novikov |
Publisher | : Springer Science & Business Media |
Total Pages | : 326 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662105799 |
This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.
Author | : Oswald Veblen |
Publisher | : |
Total Pages | : 218 |
Release | : 1931 |
Genre | : Parapsychology |
ISBN | : |
'Analysis situs' is the name used by Poincaré when he was creating, at the end of the 19th century, the area of mathematics known today as topology. These lectures contain what is probably the first text where Poincaré's results and ideas were summarized, and an attempt to systematically present this difficult new area of mathematics was made. Of the two streams of topology existing at that time, point set topology and combinatorial topology, it is the latter to which this book is almost totally devoted. The first four chapters present, in detail, the notion and properties (introduced by Poincaré) of the incidence matrix of a cell decomposition of a manifold. The author's main goal is to show how to reproduce main topological invariants of a manifold and their relations in terms of the incidence matrix.
Author | : Mahima Ranjan Adhikari |
Publisher | : Springer Nature |
Total Pages | : 488 |
Release | : 2023-03-15 |
Genre | : Mathematics |
ISBN | : 9811665508 |
This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.