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Elsevier

Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Introduction to Homological Algebra, 85

    • 1st Edition
    • Joseph J. Rotman
    • English
    An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author’s attempt to make it lovable. This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and Ⓧ; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences. This book will be of interest to practitioners in the field of pure and applied mathematics.

  • III: Scattering Theory

    • 1st Edition
    • Volume 3
    • Michael Reed + 1 more
    • English
    Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.

  • Differential Geometry, Lie Groups, and Symmetric Spaces

    • 1st Edition
    • Volume 80
    • Sigurdur Helgason
    • English
    The present book is intended as a textbook and reference work on three topics in the title. Together with a volume in progress on "Groups and Geometric Analysis" it supersedes my "Differential Geometry and Symmetric Spaces," published in 1962. Since that time several branches of the subject, particularly the function theory on symmetric spaces, have developed substantially. I felt that an expanded treatment might now be useful.

  • Rings of Differential Operators

    • 1st Edition
    • Volume 21
    • J.-E. Björk
    • English

  • Bifurcation of Maps and Applications

    • 1st Edition
    • Volume 36
    • English

  • Transmutation and Operator Differential Equations

    • 1st Edition
    • Volume 37
    • English

  • Approximation Theory and Functional Analysis

    Proceedings of the International Symposium on Approximation Theory, Universidade Estadual de Campinas (UNICAMP) Brazil, August 1-5, 1977
    • 1st Edition
    • Volume 35
    • English

  • Developing Mathematics in Third World Countries

    Proceedings of the international conference held in Khartoum, March 6-9, 1978
    • 1st Edition
    • Volume 33
    • English

  • Probabilities and Potential, A

    • 1st Edition
    • Volume 29
    • C. Dellacherie + 1 more
    • English

  • Formal Groups and Applications

    • 1st Edition
    • Volume 78
    • English

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