Geometrie der Raumzeit: Eine mathematische Einführung in die by Rainer Oloff

By Rainer Oloff

Die Relativitätstheorie ist in ihren Kernaussagen nicht mehr umstritten, gilt aber noch immer als kompliziert und nur schwer verstehbar. Das liegt unter anderem an dem aufwendigen mathematischen Apparat, der schon zur Formulierung ihrer Ergebnisse und erst recht zum Nachvollziehen der Argumentation notwendig ist. In diesem Lehrbuch werden die mathematischen Grundlagen der Relativitätstheorie systematisch entwickelt, das ist die Differentialgeometrie auf Mannigfaltigkeiten einschließlich Differentiation und Integration. Die Spezielle Relativitätstheorie wird als Tensorrechnung auf den Tangentialräumen dargestellt. Die zentrale Aussage der Allgemeinen Relativitätstheorie ist die Einstein'sche Feldgleichung, die die Krümmung zur Materie in Beziehung setzt. Ausführlich werden die relativistischen Effekte im Sonnensystem einschließlich der Schwarzen Löcher behandelt. Dieser textual content richtet sich an Studierende der Physik und der Mathematik und setzt nur Grundkenntnisse aus der klassischen Differential- und Integralrechnung und der Linearen Algebra voraus. Für die neue Auflage wurde das Buch durchgesehen und alle bekannt gewordenen Fehler korrigiert.

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Strange Phenomena in Convex and Discrete Geometry by Chuanming Zong (auth.), James J. Dudziak (eds.)

By Chuanming Zong (auth.), James J. Dudziak (eds.)

Convex and discrete geometry is likely one of the so much intuitive topics in arithmetic. you can actually clarify a lot of its difficulties, even the main tough - corresponding to the sphere-packing challenge (what is the densest attainable association of spheres in an n-dimensional space?) and the Borsuk challenge (is it attainable to partition any bounded set in an n-dimensional house into n+1 subsets, each one of that's strictly smaller in "extent" than the whole set?) - in phrases layman can comprehend; and you'll quite make conjectures approximately their options with little education in mathematics.

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Basic Noncommutative Geometry by Masoud Khalkhali

By Masoud Khalkhali

This article presents an advent to noncommutative geometry and a few of its functions. it may be used both as a textbook for a graduate direction or for self-study. it will likely be worthy for graduate scholars and researchers in arithmetic and theoretical physics and all those people who are attracted to gaining an knowing of the topic. One characteristic of this ebook is the wealth of examples and workouts that aid the reader to navigate in the course of the topic. whereas history fabric is supplied within the textual content and in different appendices, a few familiarity with simple notions of sensible research, algebraic topology, differential geometry and homological algebra at a primary 12 months graduate point is helpful.

Developed by way of Alain Connes because the overdue Nineteen Seventies, noncommutative geometry has came across many functions to long-standing conjectures in topology and geometry and has lately made headways in theoretical physics and quantity concept. The ebook begins with a close description of a few of the main pertinent algebrageometry correspondences through casting geometric notions in algebraic phrases, then proceeds within the moment bankruptcy to the assumption of a noncommutative house and the way it truly is built. The final chapters care for homological instruments: cyclic cohomology and Connes–Chern characters in K-theory and K-homology, culminating in a single commutative diagram expressing the equality of topological and analytic index in a noncommutative surroundings. functions to integrality of noncommutative topological invariants are given as well.

Two new sections were further to this moment variation: one matters the Gauss–Bonnet theorem and the definition and computation of the scalar curvature of the curved noncommutative torus, and the second one is a short advent to Hopf cyclic cohomology. The bibliography has been prolonged and a few new examples are provided.

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An Algebraic Geometric Approach to Separation of Variables by Konrad Schöbel

By Konrad Schöbel

Konrad Schöbel goals to put the principles for a consequent algebraic geometric remedy of variable Separation, that's one of many oldest and strongest ways to build particular options for the elemental equations in classical and quantum physics. the current paintings unearths a stunning algebraic geometric constitution at the back of the recognized record of separation coordinates, bringing jointly an exceptional variety of arithmetic and mathematical physics, from the past due nineteenth century concept of separation of variables to trendy moduli house concept, Stasheff polytopes and operads.

"I am fairly inspired by means of his mastery of numerous ideas and his skill to teach truly how they have interaction to provide his results.” (Jim Stasheff)

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Two Reports on Harmonic Maps by James Eells

By James Eells

Harmonic maps among Riemannian manifolds are strategies of platforms of partial differential equations which look in several contexts of differential geometry. They comprise holomorphic maps, minimum surfaces, delta-models in physics. lately, they've got develop into strong instruments within the learn of world homes of Riemannian and Kahlerian manifolds. normal references for this topic are stories, released in 1978 and 1988 via James Eells and Luc Lemaire. This publication provides those experiences in one quantity with a quick complement reporting on a few contemporary advancements within the concept. it really is either an creation to the topic and a resource of reference, supplying an prepared exposition of effects unfold all through greater than 800 papers.

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The Fractal Geometry of Nature by Benoit B. Mandelbrot

By Benoit B. Mandelbrot

Clouds aren't spheres, mountains are usually not cones, and lightening doesn't shuttle in a immediately line. The complexity of nature's shapes differs in variety, no longer simply measure, from that of the shapes of standard geometry, the geometry of fractal shapes.

Now that the sector has extended vastly with many energetic researchers, Mandelbrot offers the definitive evaluation of the origins of his principles and their new functions. The Fractal Geometry of Nature relies on his hugely acclaimed prior paintings, yet has a lot broader and deeper insurance and extra large illustrations.

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The Misbehavior of Markets: A Fractal View of Financial by Benoit Mandelbrot

By Benoit Mandelbrot

Mathematical famous person and inventor of fractal geometry, Benoit Mandelbrot, has spent the prior 40 years learning the underlying arithmetic of area and common styles. What lots of his fans do not understand is that he has additionally been looking at styles of industry swap. within the (Mis)Behavior of Markets, Mandelbrot joins with technology journalist and previous Wall highway magazine editor Richard L. Hudson to bare what a fractal view of the realm of finance appears like. the result's a progressive reevaluation of the traditional instruments and versions of contemporary monetary conception. Markets, we examine, are some distance riskier than we've got desired to think. From the gyrations of IBM's inventory fee and the Dow, to cotton buying and selling, and the dollar-Euro alternate rate--Mandelbrot indicates that the realm of finance will be understood in additional exact, and unstable, phrases than the drained theories of yesteryear. the power to simplify the advanced has made Mandelbrot one of many century's such a lot influential mathematicians. With The (Mis)Behavior of Markets, he places the instruments of upper arithmetic into the palms of each individual concerned with markets, from monetary analysts to economists to 401(k) holders. Markets is not really obvious as "safe bets" back.

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Representation Theories and Algebraic Geometry by Michel Brion (auth.), Abraham Broer, A. Daigneault, Gert

By Michel Brion (auth.), Abraham Broer, A. Daigneault, Gert Sabidussi (eds.)

The 12 lectures awarded in Representation Theories and AlgebraicGeometry specialise in the very wealthy and robust interaction among algebraic geometry and the illustration theories of assorted sleek mathematical constructions, akin to reductive teams, quantum teams, Hecke algebras, limited Lie algebras, and their partners. This interaction has been broadly exploited in the course of fresh years, leading to nice growth in those illustration theories. Conversely, a good stimulus has been given to the improvement of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology.
the diversity of subject matters coated is huge, from equivariant Chow teams, decomposition sessions and Schubert forms, multiplicity loose activities, convolution algebras, normal monomial thought, and canonical bases, to annihilators of quantum Verma modules, modular illustration conception of Lie algebras and combinatorics of illustration different types of Harish-Chandra modules.

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