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Author: Gregory L. Naber Publisher: Courier Corporation ISBN: 0486153444 Category : Mathematics Languages : en Pages : 276
Book Description
Extensive development of such topics as elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, and the Stone-Weierstrass Theorem. New section of solutions to selected problems.
Author: Gregory L. Naber Publisher: Courier Corporation ISBN: 0486153444 Category : Mathematics Languages : en Pages : 276
Book Description
Extensive development of such topics as elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, and the Stone-Weierstrass Theorem. New section of solutions to selected problems.
Author: Jerzy Jezierski Publisher: Springer Science & Business Media ISBN: 140203931X Category : Mathematics Languages : en Pages : 326
Book Description
The notion of a ?xed point plays a crucial role in numerous branches of mat- maticsand its applications. Informationabout the existence of such pointsis often the crucial argument in solving a problem. In particular, topological methods of ?xed point theory have been an increasing focus of interest over the last century. These topological methods of ?xed point theory are divided, roughly speaking, into two types. The ?rst type includes such as the Banach Contraction Principle where the assumptions on the space can be very mild but a small change of the map can remove the ?xed point. The second type, on the other hand, such as the Brouwer and Lefschetz Fixed Point Theorems, give the existence of a ?xed point not only for a given map but also for any its deformations. This book is an exposition of a part of the topological ?xed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers. Since both notions are homotopyinvariants, the deformationis used as an essential method, and the assertions of theorems typically state the existence of ?xed or periodic points for every map of the whole homotopy class, we refer to them as homotopy methods of the topological ?xed and periodic point theory.
Author: E. Dierker Publisher: Springer Science & Business Media ISBN: 3642658008 Category : Business & Economics Languages : en Pages : 137
Book Description
In winter 71/72 I held a seminar on general equilibrium theory for a jOint group of students in mathematics and in econo mics at the university of Bonn , w.Germany1~ The economists , how ever , had a mathematical background well above the average • Most of the material treated in that seminar is described in these notes. The connection between smooth preferences and smooth demand func tions [ see Debreu (1972) ] and regular economies based on agents with smooth preferences are not presented here • Some pedagogical difficulties arose from the fact that elementary knowledge of algebraic topology is not assumed although it is helpful and indeed necessary to make some arguments precise • It is only a minor restriction , at present , that functional ana lysis is not used • But with the development of the theory more economic questions will be considered in their natural infinite dimensional setting • Economic knowledge is not required , but especially a reader without economic background will gain much by reading Debreu's classic "Theory of Value" (1959) • Although the formulation of our economic problem uses a map between Euclidean spaces only , we shall also consider ma- folds • Manifolds appear in our situation because inverse images under differentiable mappings between Euclidean spaces are very often differentiable manifolds • ( Under differentiability assump tions , for instance , the graph of the equilibrium set correspon
Author: Li︠u︡dmila Vsevolodovna Keldysh Publisher: American Mathematical Soc. ISBN: 9780821818817 Category : Mathematics Languages : en Pages : 218
Book Description
"This monograph is devoted to a presentation of the foundations of the set--theoretical theory of topological imbeddings in Euclidean space En and of a number of new results in this area." -- Introduction.
Author: Ross Geoghegan Publisher: Springer Science & Business Media ISBN: 0387746110 Category : Mathematics Languages : en Pages : 473
Book Description
This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.
Author: G. Isac Publisher: Springer Science & Business Media ISBN: 1475731418 Category : Mathematics Languages : en Pages : 691
Book Description
Complementarity theory is a new domain in applied mathematics and is concerned with the study of complementarity problems. These problems represent a wide class of mathematical models related to optimization, game theory, economic engineering, mechanics, fluid mechanics, stochastic optimal control etc. The book is dedicated to the study of nonlinear complementarity problems by topological methods. Audience: Mathematicians, engineers, economists, specialists working in operations research and anybody interested in applied mathematics or in mathematical modeling.
Author: Kenneth Hoffman Publisher: Courier Dover Publications ISBN: 0486833658 Category : Mathematics Languages : en Pages : 449
Book Description
Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory. Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings addresses implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a Bibliography, List of Symbols, Index, and an Appendix with background in elementary set theory.
Author: K. Parthasarathy Publisher: Springer Nature ISBN: 9811694842 Category : Mathematics Languages : en Pages : 271
Book Description
This book starts with a discussion of the classical intermediate value theorem and some of its uncommon “topological” consequences as an appetizer to whet the interest of the reader. It is a concise introduction to topology with a tinge of historical perspective, as the author’s perception is that learning mathematics should be spiced up with a dash of historical development. All the basics of general topology that a student of mathematics would need are discussed, and glimpses of the beginnings of algebraic and combinatorial methods in topology are provided. All the standard material on basic set topology is presented, with the treatment being sometimes new. This is followed by some of the classical, important topological results on Euclidean spaces (the higher-dimensional intermediate value theorem of Poincaré–Miranda, Brouwer’s fixed-point theorem, the no-retract theorem, theorems on invariance of domain and dimension, Borsuk’s antipodal theorem, the Borsuk–Ulam theorem and the Lusternik–Schnirelmann–Borsuk theorem), all proved by combinatorial methods. This material is not usually found in introductory books on topology. The book concludes with an introduction to homotopy, fundamental groups and covering spaces. Throughout, original formulations of concepts and major results are provided, along with English translations. Brief accounts of historical developments and biographical sketches of the dramatis personae are provided. Problem solving being an indispensable process of learning, plenty of exercises are provided to hone the reader's mathematical skills. The book would be suitable for a first course in topology and also as a source for self-study for someone desirous of learning the subject. Familiarity with elementary real analysis and some felicity with the language of set theory and abstract mathematical reasoning would be adequate prerequisites for an intelligent study of the book.
Author: Gregory L. Naber
Author: Gregory L. Naber
Author: Lisa R. Goldberg
Author: Jerzy Jezierski
Author: Egbert Dierker
Author: E. Dierker
Author: Li︠u︡dmila Vsevolodovna Keldysh
Author: Ross Geoghegan
Author: G. Isac
Author: Kenneth Hoffman
Author: K. Parthasarathy