Download New Trends in Geometry: Their Role in the Natural and Life by Claudio Bartocci, Luciano Boi, Corrado Sinigaglia PDF

By Claudio Bartocci, Luciano Boi, Corrado Sinigaglia

This quantity makes a speciality of the interactions among arithmetic, physics, biology and neuroscience through exploring new geometrical and topological modelling in those fields. one of the highlights are the primary roles performed through multilevel and scale-change ways in those disciplines. the combination of arithmetic with physics, in addition to molecular and telephone biology and the neurosciences, will represent the hot frontier of twenty first century technological know-how, the place breakthroughs usually tend to span throughout conventional disciplines.

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Download Maximum and minimum principles: A unified approach with by M. J. Sewell PDF

By M. J. Sewell

In lots of difficulties of utilized arithmetic, technology, engineering or economics, an power expenditure or its analogue should be approximated via top and decrease bounds. This ebook offers a unified account of the idea required to set up such bounds, via expressing the governing stipulations of the matter, and the limits, when it comes to a saddle useful and its gradients. There are numerous positive aspects, together with a bankruptcy at the Legendre twin transformation and a few of its singularities. Many colossal examples and workouts are incorporated, particularly from the mechanics of fluids, elastic and plastic solids and from optimisation conception. The saddle sensible perspective supplies the publication a large scope. The therapy is easy, the single prerequisite being a simple wisdom of the calculus of adaptations. a part of the publication is predicated on final-year undergraduate classes. this is often constructed into an account in order to curiosity a variety of scholars and execs in utilized arithmetic, engineering, physics and operations examine.

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Download Laplacian on Riemannian manifold by Steven Rosenberg PDF

By Steven Rosenberg

This article on research on Riemannian manifolds is a radical creation to issues lined in complex examine monographs on Atiyah-Singer index conception. the most subject is the research of warmth circulate linked to the Laplacians on differential types. this gives a unified remedy of Hodge thought and the supersymmetric evidence of the Chern-Gauss-Bonnet theorem. specifically, there's a cautious remedy of the warmth kernel for the Laplacian on services. the writer develops the Atiyah-Singer index theorem and its functions (without whole proofs) through the warmth equation procedure. Rosenberg additionally treats zeta services for Laplacians and analytic torsion, and lays out the lately exposed relation among index idea and analytic torsion. The textual content is geared toward scholars who've had a primary path in differentiable manifolds, and the writer develops the Riemannian geometry used from the start. There are over a hundred routines with tricks.

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Download Leibniz on the Parallel Postulate and the Foundations of by Vincenzo De Risi PDF

By Vincenzo De Risi

This ebook deals a normal creation to the geometrical reviews of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. particularly, it makes a speciality of his conception of parallel strains and his makes an attempt to end up the well-known Parallel Postulate. moreover it explains the function that Leibniz’s paintings performed within the improvement of non-Euclidean geometry. the 1st half is an summary of his epistemology of geometry and some of his geometrical findings, which places them within the context of the seventeenth-century stories at the foundations of geometry. It additionally offers a close mathematical and philosophical observation on his writings at the concept of parallels, and discusses how they have been acquired within the eighteenth century in addition to their relevance for the non-Euclidean revolution in arithmetic. the second one half deals a suite of Leibniz’s essays at the idea of parallels and an English translation of them. whereas some of these papers have already been released (in Latin) within the regular Leibniz variations, so much of them are transcribed from Leibniz’s manuscripts written in Hannover, and released the following for the 1st time. The publication presents new fabric at the historical past of non-Euclidean geometry, stressing the formerly missed position of Leibniz in those developments.

This quantity could be of curiosity to historians in arithmetic, philosophy or good judgment, in addition to mathematicians attracted to non-Euclidean geometry.

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Download Elementare Geometrie und Algebra: Basiswissen für Studium by Hans-Wolfgang Henn PDF

By Hans-Wolfgang Henn

Ziel des Buches ist es, zu einem "stimmigen Bild von Mathematik" beizutragen und die Kluft zwischen der Mathematik, die guy in der Schule erlebt hat, und der Mathematik, die guy im Studium kennen lernt, zu ?berbr?cken. Es wird Grundwissen in Geometrie, Arithmetik und Algebra vermittelt. Als foundation f?r die Berufswissenschaft zuk?nftiger Mathematiklehrer ist es insbesondere f?r Bachelorstudieng?nge geeignet. Der Aufbau ist m?glichst wenig formal. Bei Begr?ndungen und Beweisen wird bevorzugt inhaltlich argumentiert. Die Stoffauswahl ist schulbezogen und hat selbstverst?ndlich subjektive Gesichtspunkte. Diese resultieren aus der T?tigkeit des Autors in der Algebraischen Zahlentheorie und Algebraischen Geometrie und aus seinen langj?hrigen Erfahrungen als Gymnasiallehrer und Fachleiter.

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