In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties will help students gain a rounded understanding of the subject.
In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Stude...
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via sheaf cohomology theory, and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find this...
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie ...
The textbook Geometry, published in French by CEDICjFernand Nathan and in English by Springer-Verlag (scheduled for 1985) was very favorably re ceived. Nevertheless, many readers found the text too concise and the exercises at the end of each chapter too difficult, and regretted the absence of any hints for the solution of the exercises. This book is intended to respond, at least in part, to these needs. The length of the textbook (which will be referred to as B] throughout this book) and the volume of the material covered in it preclude any thought of publishing an expanded version, but we...
The textbook Geometry, published in French by CEDICjFernand Nathan and in English by Springer-Verlag (scheduled for 1985) was very favorably re ceived...
This book is meant as a text for a first year graduate course in analysis. Any standard course in undergraduate analysis will constitute sufficient preparation for its understanding, for instance, my Undergraduate Anal- ysis. I assume that the reader is acquainted with notions of uniform con- vergence and the like. In this third edition, I have reorganized the book by covering inte- gration before functional analysis. Such a rearrangement fits the way courses are taught in all the places I know of. I have added a number of examples and exercises, as well as some material about integration on...
This book is meant as a text for a first year graduate course in analysis. Any standard course in undergraduate analysis will constitute sufficient pr...
Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. The new edition of this text includes two additional chapters, one on the gauge group of a bundle and the other on the differential forms representing characteristic classes of complex vector bundles on manifolds.
Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical educa...
The 20 years since the publication of this book have been an era of continuing growth and development in the field of algebraic topology. New generations of young mathematicians have been trained, and classical problems have been solved, particularly through the application of geometry and knot theory. Diverse new resources for introductory coursework have appeared, but there is persistent interest in an intuitive treatment of the basic ideas. This second edition has been expanded through the addition of a chapter on covering spaces. By analysis of the lifting problem it introduces the funda-...
The 20 years since the publication of this book have been an era of continuing growth and development in the field of algebraic topology. New generati...
Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: AMathematical Sketchbook provides a brief but rigorous introduction to the abstract theory of computation, sometimes also referred to as recursion theory. It develops major themes in computability theory, such as Rice's theorem and the recursion theorem, and provides a systematic account of Blum's complexity theory as well as an introduction to the theory of computable real numbers and functions. The book is intended as a university text, but it may also be used...
Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: AMathematical Sketchboo...
Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions.
From the reviews:
"Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route." --MATHEMATICAL REVIEWS
Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material fo...
. . . both Gauss and lesser mathematicians may be justified in rejoic- ing that there is one science number theory] at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean. - G. H. Hardy, A Mathematician's Apology, 1940 G. H. Hardy would have been surprised and probably displeased with the increasing interest in number theory for application to "ordinary human activities" such as information transmission (error-correcting codes) and cryptography (secret codes). Less than a half-century after Hardy wrote the words quoted above, it...
. . . both Gauss and lesser mathematicians may be justified in rejoic- ing that there is one science number theory] at any rate, and that their own, ...
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject...
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of th...