Category «Geometry And Topology»

Download E-books Kreisgeometrie: Eine elementare Einführung (Springer-Lehrbuch) (German Edition) PDF

Die Kreisgeometrie eignet sich in idealer Weise, den Reichtum der Geometrie zu erschließen. Ausgehend von den klassischen, über 2000 Jahre alten Sätzen der Kreisgeometrie spannt der Autor den Bogen bis in die Neuzeit, in der neue, vor allem von Jacob Steiner entwickelte Werkzeuge der Kreisgeometrie einen enormem Schub brachten. Damit gelingt es ihm, ein breites Themenspektrum anzusprechen, das nicht nur viele berühmte Sätze, sondern auch zahlreiche kaum bekannte Resultate umfasst.

Um die Beweisideen und deren geometrischen Kern obvious zu machen, steht bei allen Beweisen die geometrische Argumentation im Vordergrund.

Über 250 Abbildungen und ein lockerer, aber präziser Schreibstil begleiten den Leser bei dieser faszinierenden Reise durch die Kreisgeometrie.

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Download E-books Convex Sets and Their Applications (Dover Books on Mathematics) PDF

By Steven R. Lay

Suitable for complicated undergraduates and graduate scholars, this article introduces the wide scope of convexity. It leads scholars to open questions and unsolved difficulties, and it highlights different purposes. writer Steven R. Lay, Professor of arithmetic at Lee collage in Tennessee, reinforces his teachings with a variety of examples, plus workouts with tricks and answers.
The first 3 chapters shape the root for all that follows, beginning with a overview of the basics of linear algebra and topology. additionally they survey the advance and purposes of relationships among hyperplanes and convex units. next chapters are rather self-contained, each one targeting a selected point or program of convex units. themes comprise characterizations of convex units, polytopes, duality, optimization, and convex services. tricks, strategies, and references for the routines seem behind the book.

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Download E-books Categorical Methods in Computer Science With Aspects from Topology PDF

By Hartmut Ehrig (auth.), H. Ehrig, H. Herrlich, H. -J. Kreowski, G. Preuß (eds.)

This quantity includes chosen papers of the foreign Workshop on "Categorical equipment in desktop technology - with elements from Topology" and of the "6th foreign info variety Workshop" held in August/September 1988 in Berlin. The 23 papers of this quantity are grouped into 3 elements: Part 1 contains papers on express foundations and basic innovations from classification thought in laptop technology. Part 2 provides purposes of specific the way to algebraic specification languages and methods, information forms, information bases, programming, and strategy necessities. Part 3 includes papers on categorial facets from topology which as a rule be aware of certain adjoint events like cartesian closeness, Galois connections, reflections, and coreflections that are of becoming curiosity in specific topology and computing device science.

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Download E-books The Physics of Phase Space: Nonlinear Dynamics and Chaos, Geometric Quantization,and Wigner Function (Lecture Notes in Physics) PDF

The idea that of part house performs a decisive function within the examine of the transition from classical to quantum physics. this can be relatively the case in components equivalent to nonlinear dynamics and chaos, geometric quantization and the examine of a number of the semi-classical theories, that are the atmosphere of the current quantity. a lot of the content material is dedicated to the research of the Wigner distribution. This quantity supplies the 1st entire survey of the development made by means of either mathematicians and physicists. it is going to function an outstanding reference for additional examine.

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Download E-books Partially Ordered Rings and Semi-Algebraic Geometry (London Mathematical Society Lecture Note Series) PDF

By Gregory W. Brumfiel

The aim of this particular e-book is to set up in simple terms algebraic foundations for the improvement of sure elements of topology. a few topologists search to appreciate geometric houses of options to finite platforms of equations or inequalities and configurations which in a few experience really ensue within the genuine global. Others learn areas developed extra abstractly utilizing endless restrict procedures. Their target is to figure out simply how comparable or diversified those summary areas are from these that are finitely defined. in spite of the fact that, as topology is generally taught, even the 1st, extra concrete form of challenge is approached utilizing the language and techniques of the second one style. Professor Brumfiel's thesis is this is senseless and, actually, deceptive philosophically. He develops a kind of algebra, in part ordered jewelry, within which it is smart to speak about strategies of equations and inequalities and to match geometrically the ensuing areas. the significance of this procedure is essentially that it clarifies this kind of geometrical questions one desires to ask and solution approximately these areas which would have actual value.

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Download E-books Embeddings and Immersions (Translations of Mathematical Monographs Reprint) PDF

By Masahisa Adachi

This e-book covers basic options within the idea of C-imbeddings and C-immersions, emphasizing transparent intuitive knowing and containing many figures and diagrams. Adachi starts off with an creation to the paintings of Whitney and of Haefliger on C-imbeddings and C-manifolds. The Smale-Hirsch theorem is gifted as a generalization of the category of C-imbeddings via isotopy and is prolonged via Gromov's paintings at the topic, together with Gromov's convex integration thought. ultimately, as an program of Gromov's paintings, the writer introduces Haefliger's type theorem of foliations on open manifolds. additionally defined this is the Adachi's paintings with Landweber at the integrability of virtually advanced constructions on open manifolds. This ebook will be an outstanding textual content for upper-division undergraduate or graduate classes.

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Download E-books Lessons in Geometry, Vol. 1: Plane Geometry (Monograph Book) PDF

By Jacques Hadamard

This can be a e-book within the culture of Euclidean artificial geometry written by way of one of many 20th century's nice mathematicians. the unique viewers used to be pre-college academics, however it comes in handy besides to proficient highschool scholars and school scholars, particularly, to arithmetic majors attracted to geometry from a extra complex perspective. The textual content starts off the place Euclid starts off, and covers all of the fundamentals of aircraft Euclidean geometry. yet this article does even more. it really is straight away pleasingly vintage and unusually glossy. the issues (more than 450 of them) are well-suited to exploration utilizing the fashionable instruments of dynamic geometry software program. therefore, the current version incorporates a CD of dynamic recommendations to pick difficulties, created utilizing Texas tools' TI-NspireTM studying software program. The TI-NspireTM files show connections between difficulties and--through the loose trial software program incorporated at the CD--will enable the reader to discover and have interaction with Hadamard's Geometry in new methods. the fabric additionally contains introductions to numerous complex themes. The exposition is spare, giving purely the minimum heritage wanted for a scholar to discover those themes. a lot of the worth of the ebook lies within the difficulties, whose suggestions open worlds to the engaged reader. And so this booklet is within the Socratic culture, in addition to the Euclidean, in that it calls for of the reader either engagement and interplay. A imminent better half quantity that comes with recommendations, extensions, and school room actions with regards to the issues can in simple terms start to open the treasures provided through this paintings. we're simply lucky that one of many maximum mathematical minds of contemporary occasions has made this attempt to teach to readers many of the possibilities that the highbrow culture of Euclidean geometry has to provide.

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Download E-books Monoidal Topology: A Categorical Approach to Order, Metric and Topology (Encyclopedia of Mathematics and its Applications) PDF

Monoidal Topology describes an energetic study quarter that, after a number of earlier proposals on how you can axiomatize 'spaces' by way of convergence, started to emerge initially of the millennium. It combines Barr's relational presentation of topological areas by way of ultrafilter convergence with Lawvere's interpretation of metric areas as small different types enriched over the prolonged actual half-line. accordingly, outfitted with a quantale V (replacing the reals) and a monad T (replacing the ultrafilter monad) laxly prolonged from set maps to V-valued family, the publication develops a specific thought of (T,V)-algebras that's encouraged at the same time by way of its metric and topological roots. The ebook highlights specifically the prestigious position of equationally outlined constructions in the given lax-algebraic context and offers a number of new effects starting from topology and technique idea to area concept. all of the invaluable pre-requisites so as and classification thought are awarded within the e-book.

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