• Download E-books Topologie: Eine anschauliche Einführung in die geometrischen und algebraischen Grundlagen (Aufbaukurs Mathematik) (German Edition) PDF

    By Erich Ossa

    Das Ziel des Buches ist eine umfassende Einführung sowohl in die geometrische wie die algebraische Topologie. Dabei werden lediglich gute Kenntnisse aus dem 1. Studienjahr in der Mathematik vorausgesetzt, die über die research und lineare Algebra kaum hinausgehen; alle weiteren Hilfsmittel, wie die Grundbegriffe der mengentheoretischen Topologie, die Theorie der topologischen Gruppen und die algebraischen Grundlagen werden ebenfalls ausführlich dargestellt. Im Vordergrund stehen jedoch nicht die hieraus hervorgehenden technischen Apparate, sondern die geometrischen Fragestellungen, die erst den Anlass zu ihrer Entwicklung gaben.
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  • Download E-books Topologie I: Erster Band. Grundbegriffe der Mengentheoretischen Topologie Topologie der Komplexe · Topologische Invarianzsätze und Anschliessende ... Abbildungen von Polyedern (German Edition) PDF

    By Paul Alexandroff

    Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer e-book documents mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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  • Download E-books Lectures on Algebraic Topology PDF

    By Albrecht Dold

    Springer is reissuing a specific few hugely winning books in a brand new, reasonably cheap softcover version to cause them to simply obtainable to more youthful generations of scholars and researchers. Springer-Verlag all started publishing books in better arithmetic in 1920. it is a reprint of the second one Edition.

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  • Download E-books Lectures on Dynamical Systems, Structural Stability and Their Applications PDF

    By K K Lee

    The communique of information on nonlinear dynamical structures, among the mathematicians engaged on the analytic process and the scientists operating totally on the functions and numerical simulations has been under perfect. This quantity hopes to bridge the distance among books written at the topic by means of mathematicians and people written through scientists. the second one aim of this quantity is to attract realization to the necessity for cross-fertilization of data among the actual and organic scientists. The 3rd goal is to supply the reader with a private consultant at the examine of world nonlinear dynamical structures.
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  • Download E-books Topological Library: Part 2: Characteristic Classes and Smooth Structures on Manifolds (Series on Knots and Everything) (Series on Knots and Everything (Hardcover)) PDF

    This can be the second one of a three-volume set gathering the unique and now-classic works in topology written through the 1950s-1960s. the unique tools and buildings from those works are accurately documented for the 1st time during this ebook. No present booklet covers the gorgeous ensemble of equipment created in topology ranging from nearly 1950, that's, from Serre's celebrated singular homologies of fiber areas.
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  • Download E-books Modern Geometry: Introduction to Homology Theory Pt. 3: Methods and Applications (Graduate Texts in Mathematics) PDF

    During the last fifteen years, the geometrical and topological tools of the speculation of manifolds have assumed a imperative position within the so much complex components of natural and utilized arithmetic in addition to theoretical physics. the 3 volumes of "Modern Geometry - equipment and functions" comprise a concrete exposition of those tools including their major functions in arithmetic and physics. This 3rd quantity, provided in hugely available languages, concentrates in homology concept. It comprises introductions to the modern equipment for the calculation of homology teams and the class of manifesto. either scientists and scholars of arithmetic in addition to theoretical physics will locate this booklet to be a important reference and textual content.
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  • Download E-books Elementary Topology PDF

    This textbook on effortless topology encompasses a precise creation to common topology and an creation to algebraic topology through its such a lot classical and straight forward phase founded on the notions of basic team and protecting house. The booklet is customized for the reader who's decided to paintings actively. The proofs of theorems are separated from their formulations and are collected on the finish of every bankruptcy. This makes the publication appear like a natural challenge ebook and encourages the reader to imagine via each one formula. A reader who prefers a extra conventional type can both locate the proofs on the finish of the bankruptcy or bypass them altogether. This variety additionally caters to the professional who wishes a instruction manual and prefers formulations no longer overshadowed by way of proofs. lots of the proofs are basic and simple to find. The ebook will be necessary and relaxing for readers with particularly diverse backgrounds and pursuits. The textual content is dependent in the sort of method that you'll be able to ascertain what to anticipate from every bit and the way to take advantage of it. there's center fabric, which makes up a comparatively small a part of the e-book. The middle fabric is interspersed with examples, illustrative and coaching difficulties, and appropriate discussions. The reader who has mastered the middle fabric acquires a powerful history in basic topology and should believe at domestic within the surroundings of summary arithmetic. With virtually no necessities (except genuine numbers), the e-book can function a textual content for a direction on basic and starting algebraic topology.
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  • Download E-books Topology, Geometry and Gauge fields: Foundations (Texts in Applied Mathematics) PDF

    Like every books on a topic as enormous as this, this e-book has to have a point-of-view to lead the choice of subject matters. Naber takes the view that the rekindled curiosity that arithmetic and physics have proven in one another of past due could be fostered, and that this is often top comprehensive by way of permitting them to cohabit. The ebook weaves jointly rudimentary notions from the classical gauge idea of physics with the topological and geometrical ideas that turned the mathematical versions of those notions. The reader is requested to hitch the writer on a few obscure concept of what an electromagnetic box should be, to be keen to just accept a number of the extra common pronouncements of quantum mechanics, and to have a great history in actual research and linear algebra and a few of the vocabulary of recent algebra. In go back, the ebook deals an day trip that starts off with the definition of a topological house and reveals its means finally to the moduli area of anti-self-dual SU(2) connections on S4 with instanton quantity -1.
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  • Download E-books Homotopy Limit Functors on Model Categories and Homotopical Categories (Mathematical Surveys and Monographs) PDF

    The aim of this monograph, that is aimed toward the graduate point and past, is to acquire a deeper knowing of Quillen's version different types. A version class is a class including 3 extraordinary periods of maps, referred to as vulnerable equivalences, cofibrations, and fibrations. version different types became a typical device in algebraic topology and homological algebra and, more and more, in different fields the place homotopy theoretic rules have gotten vital, equivalent to algebraic $K$-theory and algebraic geometry. The authors' procedure is to outline the concept of a homotopical type, that's extra common than that of a version class, and to contemplate version different types as exact situations of this. A homotopical class is a class with just a unmarried individual category of maps, referred to as susceptible equivalences, topic to a suitable axiom. this permits one to outline ``homotopical'' types of such uncomplicated express notions as preliminary and terminal items, colimit and restrict functors, cocompleteness and completeness, adjunctions, Kan extensions, and common houses. There are primarily self-contained components, and half II logically precedes half I. half II defines and develops the idea of a homotopical classification and will be regarded as the beginnings of one of those ``relative'' type conception. the result of half II are utilized in half I to procure a deeper figuring out of version different types. The authors exhibit specifically that version different types are homotopically cocomplete and entire in a feeling more advantageous than simply the requirement of the life of small homotopy colimit and restrict functors. A reader of half II is thought to have just some familiarity with the above-mentioned express notions. those that learn half I, and particularly its introductory bankruptcy, also needs to recognize anything approximately version different types.
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  • Download E-books Applications of Contact Geometry and Topology in Physics PDF

    Even though touch geometry and topology is in short mentioned in V I Arnol'd's booklet "Mathematical equipment of Classical Mechanics "(Springer-Verlag, 1989, 2d edition), it nonetheless continues to be a website of study in natural arithmetic, e.g. see the new monograph by means of H Geiges "An creation to touch Topology" (Cambridge U Press, 2008). a few makes an attempt to exploit touch geometry in physics have been made within the monograph "Contact Geometry and Nonlinear Differential Equations" (Cambridge U Press, 2007). regrettably, even the superb type of this monograph isn't enough to draw the eye of the physics neighborhood to this kind of difficulties. This ebook is the 1st severe try to switch the prevailing established order. In it we exhibit that, actually, all branches of theoretical physics will be rewritten within the language of touch geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum pcs, and so on. The booklet is written within the kind of well-known Landau-Lifshitz (L-L) multivolume path in theoretical physics. which means its readers are anticipated to have stable history in theoretical physics (at least on the point of the L-L course). No past wisdom of specialised arithmetic is needed. All wanted new arithmetic is given within the context of mentioned actual difficulties. As within the L-L path a few problems/exercises are formulated alongside the way in which and, back as within the L-L direction, those are continuously supplemented by means of both strategies or by way of tricks (with distinctive references). in contrast to the L-L path, notwithstanding, a few definitions, theorems, and feedback also are provided. this is often performed with the aim of stimulating the curiosity of our readers in deeper examine of themes mentioned within the textual content.

    Readership: Researchers and execs in utilized arithmetic and theoretical physics.

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