By Ruben Aldrovandi,José Geraldo Pereira
This e-book specializes in the unifying strength of the geometrical language in bringing jointly recommendations from many various parts of physics, starting from classical physics to the theories describing the 4 primary interactions of Nature — gravitational, electromagnetic, powerful nuclear, and vulnerable nuclear.
The e-book presents in one quantity an intensive advent to topology and differential geometry, in addition to many functions to either mathematical and actual difficulties. it really is aimed as an straight forward textual content and is meant for first 12 months graduate students.
In addition to the conventional contents of books on precise and common relativities, this ebook discusses additionally a few fresh advances corresponding to de Sitter invariant distinctive relativity, teleparallel gravity and their implications in cosmology for these wishing to arrive the next point of understanding.
By Gabor Toth
This textbook treats vital and comparable issues in convex geometry: the quantification of symmetry of a convex set—measures of symmetry—and the measure to which convex units that almost reduce such measures of symmetry are themselves approximately symmetric—the phenomenon of balance. by means of accumulating the subject’s middle principles and highlights round Grünbaum’s basic suggestion of degree of symmetry, it paints a coherent photo of the topic, and courses the reader from the fundamentals to the state of the art. The exposition takes quite a few paths to ends up in order to improve the reader’s snatch of the team spirit of rules, whereas interspersed feedback improve the fabric with a behind-the-scenes view of corollaries and logical connections, substitute proofs, and allied effects from the literature. various illustrations elucidate definitions and key structures, and over 70 exercises—with tricks and references for the more challenging ones—test and sharpen the reader’s comprehension.
The presentation contains: a uncomplicated path masking foundational notions in convex geometry, the 3 pillars of the combinatorial concept (the theorems of Carathéodory, Radon, and Helly), severe units and Minkowski degree, the Minkowski–Radon inequality, and, to demonstrate the final conception, a research of convex our bodies of continuous width; proofs of F. John’s ellipsoid theorem; a remedy of the steadiness of Minkowski degree, the Banach–Mazur metric, and Groemer’s balance estimate for the Brunn–Minkowski inequality; very important specializations of Grünbaum’s summary degree of symmetry, equivalent to Winternitz degree, the Rogers–Shepard quantity ratio, and Guo’s Lp -Minkowski degree; a development via the writer of a brand new series of measures of symmetry, the kth suggest Minkowski degree; and finally, an exciting program to the moduli house of sure distinctive maps from a Riemannian homogeneous house to
spheres—illustrating the huge mathematical relevance of the book’s subject.
By Christoph J. Scriba,Peter Schreiber
Lange bevor die Schrift entwickelt wurde, hat der Mensch geometrische Strukturen wahrgenommen und systematisch verwendet: ob beim Weben oder Flechten einfacher zweidimensionaler Muster oder beim Bauen mit dreidimensionalen Körpern. Das Buch liefert einen faszinierenden Überblick über die geometrischen Vorstellungen und Erkenntnisse der Menschheit von der Urgesellschaft bis hin zu den mathematischen und künstlerischen Ideen des 20. Jahrhunderts.
By Peter Petersen
Intended for a 365 days path, this article is newly up to date for Kindle and serves as a unmarried resource, introducing readers to the real ideas and theorems, whereas additionally containing adequate history on complicated themes to entice these scholars wishing to focus on Riemannian geometry. this is often one of many few Works to mix either the geometric components of Riemannian geometry and the analytic elements of the speculation. The ebook will entice a readership that experience a simple wisdom of normal manifold concept, together with tensors, varieties, and Lie groups.
Important revisions to the 3rd version include:
- a big addition of distinctive and enriching workouts scattered through the text;
- inclusion of an elevated variety of coordinate calculations of connection and curvature;
- addition of common formulation for curvature on Lie teams and submersions;
- integration of variational calculus into the textual content taking into account an early remedy of the sector theorem utilizing an explanation by way of Berger;
- incorporation of numerous fresh effects approximately manifolds with optimistic curvature;
- presentation of a brand new simplifying method of the Bochner process for tensors with software to sure topological amounts with normal decrease curvature bounds.
From studies of the 1st edition:
"The e-book could be hugely urged to all mathematicians who are looking to get a extra profound concept concerning the finest achievements in Riemannian geometry. it truly is one of many few entire assets of this type."
―Bernd Wegner, ZbMATH
By Siavash Shahshahani
Based on writer Siavash Shahshahani's wide educating adventure, this quantity provides an intensive, rigorous path at the idea of differentiable manifolds. aimed toward complex undergraduates and graduate scholars in arithmetic, the treatment's necessities comprise a robust history in undergraduate arithmetic, together with multivariable calculus, linear algebra, easy summary algebra, and aspect set topology. greater than 2 hundred routines supply scholars plentiful chance to gauge their abilities and achieve extra insights.
The four-part remedy starts with a unmarried bankruptcy dedicated to the tensor algebra of linear areas and their mappings. half II brings in neighboring issues to discover integrating vector fields, Lie bracket, external by-product, and Lie spinoff. half III, regarding manifolds and vector bundles, develops the most physique of the path. the ultimate bankruptcy presents a glimpse into geometric buildings through introducing connections on the tangent package deal as a device to implant the second one by-product and the spinoff of vector fields at the base manifold. appropriate old and philosophical asides improve the mathematical textual content, and valuable Appendixes provide supplementary material.
By Goro Kato
If you haven't heard approximately cohomology, the guts of Cohomology could be suited to you. The e-book supplies basic notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived different types are defined in trouble-free type. purposes to sheaf cohomology. additionally, the e-book examines cohomological points of D-modules and of the computation of zeta capabilities of the Weierstrass family.
By Izrail M. Gelfand,Mikhail Kapranov,Andrei Zelevinsky
"This publication revives and significantly expands the classical concept of resultants and discriminants. lots of the major new result of the e-book were released previous in additional than a dozen joint papers of the authors. The ebook properly enhances those unique papers with many examples illustrating either outdated and new result of the theory."—Mathematical Reviews
By Zhilin Li
Using easy-to-understand language, the writer specializes in geometric ameliorations, with each one bankruptcy surveying a specific spatial function. After an creation to the fundamental operations required for geometric alterations in addition to a few mathematical and theoretical history, the e-book describes algorithms for a category of element features/clusters. It then examines algorithms for person line beneficial properties, corresponding to the aid of information issues, smoothing (filtering), and scale-driven generalization, by means of a dialogue of algorithms for a category of line gains together with contours, hydrographic (river) networks, and transportation networks. the writer additionally addresses algorithms for person zone good points, a category of region beneficial properties, and numerous displacement operations. the ultimate bankruptcy in brief covers algorithms for 3-D surfaces and three-D features.
Providing a radical remedy of low-level algorithms, Algorithmic starting place of Multi-Scale Spatial illustration provides the mathematical foundation for multi-scale representations of spatial data.
By Leonid Vainerman
The publication comprises seven refereed study papers on in the community compact quantum teams and groupoids by means of prime specialists within the respective fields. those contributions are in keeping with talks offered at the social gathering of the assembly among mathematicians and theoretical physicists held in Strasbourg from February 21 to February 23, 2002. themes lined are: a variety of structures of in the community compact quantum teams and their multiplicative unitaries; duality concept for in the neighborhood compact quantum teams; combinatorial quantization of flat connections linked to SL(2,c); quantum groupoids, in particular coming from intensity 2 Extensions of von Neumann algebras, C*-algebras and earrings. Many mathematical effects are inspired via difficulties in theoretical physics. old feedback set the implications awarded in standpoint. Directed at examine mathematicians and theoretical physicists in addition to graduate scholars, the amount will provide an outline of a box of study within which nice growth has been accomplished within the previous couple of years, with new ties to many different components of arithmetic and physics.
By A. Kashiwara,A. Matsuo,K. Saito,I. Satake
As the interplay of arithmetic and theoretical physics keeps to accentuate, the theories built in arithmetic are being utilized to physics, and conversely. This e-book facilities round the concept of primitive varieties which presently performs an energetic and key position in topological box idea (theoretical physics), yet used to be initially constructed as a mathematical suggestion to outline a "good interval mapping" for a kin of analytic structures.
The invited papers during this quantity are expository in nature through individuals of the Taniguchi Symposium on "Topological box concept, Primitive kinds and comparable issues" and the edges Symposium bearing an analogous name, either held in Kyoto. The papers mirror the huge study of a few of the world's prime mathematical physicists, and will function an exceptional source for researchers in addition to graduate scholars of either disciplines.