Category: Geometry

By Vladimir Rovenski, Pawel Walczak

This quantity has been divided into components: Geometry and functions. The geometry component to the publication relates basically to geometric flows, laminations, critical formulae, geometry of vector fields on Lie teams and osculation; the articles within the purposes component quandary a few specific difficulties of the speculation of dynamical platforms, together with mathematical difficulties of liquid flows and a learn of cycles for non-dynamical systems.

This paintings is predicated at the moment overseas workshop entitled "Geometry and Symbolic Computations," hung on may perhaps 15-18, 2013 on the college of Haifa and is devoted to modeling (using symbolic calculations) in differential geometry and its functions in fields resembling laptop technology, tomography and mechanics. it's meant to create a discussion board for college kids and researchers in natural and utilized geometry to advertise dialogue of recent cutting-edge in geometric modeling utilizing symbolic courses similar to Maple™ and Mathematica® , in addition to presentation of latest results.

By Andrzej Lasota, Józef Myjak, Tomasz Szarek (auth.), Christoph Bandt, Umberto Mosco, Martina Zähle (eds.)

Fractal geometry is used to version complex usual and technical phenomena in a number of disciplines like physics, biology, finance, and drugs. on the grounds that such a lot convincing types comprise a component of randomness, stochastics enters the world in a normal means. This e-book files the institution of fractal geometry as a considerable mathematical conception. As within the earlier volumes, which seemed in 1998 and 2000, top specialists recognized for transparent exposition have been chosen as authors. They survey their box of workmanship, emphasizing contemporary advancements and open difficulties. major issues contain multifractal measures, dynamical structures, stochastic strategies and random fractals, harmonic research on fractals.

By Glen D. Anderson

A unified view of conformal invariants from the viewpoint of functions in geometric functionality conception and purposes and quasiconformal mappings within the aircraft and in area.

By Jürgen Jost

This validated reference paintings maintains to steer its readers to a couple of the most popular themes of latest mathematical examine. the former version already brought and defined the tips of the parabolic tools that had discovered a brilliant good fortune within the paintings of Perelman on the examples of closed geodesics and harmonic types. It additionally mentioned additional examples of geometric variational difficulties from quantum box thought, one other resource of profound new rules and strategies in geometry.

The sixth version encompasses a systematic therapy of eigenvalues of Riemannian manifolds and a number of other additions. additionally, the whole fabric has been reorganized for you to enhance the coherence of the e-book.

By Beverly Nance

By John Stillwell (auth.), S. Axler, K.A. Ribet (eds.)

For millennia easy methods to educate geometry was once the Euclidean strategy, and in lots of respects, this is often nonetheless the case. yet within the Nineteen Fifties the cry "Down with triangles!" was once heard in France and new geometry books seemed, jam-packed with linear algebra yet with out diagrams. was once this the hot correct strategy? Or was once the perfect method nonetheless anything else, possibly transformation groups?

The 4 Pillars of Geometry methods geometry in 4 other ways, spending chapters on every one. This makes the topic obtainable to readers of all mathematical tastes, from the visible to the algebraic. not just does every one technique provide a unique view; the combo of viewpoints yields insights no longer on hand in so much books at this point. for instance, it truly is proven how algebra emerges from projective geometry, and the way the hyperbolic aircraft emerges from the true projective line.

The writer starts with Euclid-style building and axiomatics, then proceeds to linear algebra whilst it turns into handy to interchange tortuous arguments with uncomplicated calculations. subsequent, he makes use of projective geometry to give an explanation for why gadgets glance the best way they do, in addition to to provide an explanation for why geometry is entangled with algebra. And finally, the writer introduces transformation groups---not merely to elucidate the diversities among geometries, but in addition to show geometries which are suddenly the same.

All readers are bound to locate whatever new during this appealing textual content, that's abundantly supplemented with figures and workouts. This booklet could be worthwhile for an undergraduate geometry path, a capstone direction, or a path aimed toward destiny highschool teachers.

John Stillwell is Professor of arithmetic on the college of San Francisco. he's the writer of numerous extremely popular books released by means of Springer, together with parts of quantity thought (2003), arithmetic and Its historical past (Second version, 2002), Numbers and Geometry (1998) and parts of Algebra (1994).

By Angelo Alessandro Mazzotti

This is the one e-book devoted to the Geometry of Polycentric Ovals. It contains challenge fixing structures and mathematical formulation. For someone attracted to drawing or spotting an oval, this booklet offers the entire priceless development and calculation instruments. greater than 30 easy building difficulties are solved, with references to Geogebra animation movies, plus the answer to the body challenge and strategies to the Stadium Problem.

A bankruptcy (co-written with Margherita Caputo) is devoted to completely new hypotheses at the undertaking of Borromini’s oval dome of the church of San Carlo alle Quattro Fontane in Rome. one other one provides the case learn of the Colosseum for instance of ovals with 8 centres.

The e-book is exclusive and new in its sort: unique contributions upload as much as approximately 60% of the entire booklet, the remainder being taken from released literature (and usually from different paintings by means of an analogous author).

The basic viewers is: architects, photograph designers, commercial designers, structure historians, civil engineers; in addition, the systematic approach during which the e-book is organised can make it a better half to a textbook on descriptive geometry or on CAD.

By Rolf Berndt

Symplectic geometry is a primary subject of present study in arithmetic. certainly, symplectic equipment are key materials within the examine of dynamical structures, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie teams. This publication is a real advent to symplectic geometry, assuming just a normal heritage in research and familiarity with linear algebra. It begins with the fundamentals of the geometry of symplectic vector areas. Then, symplectic manifolds are outlined and explored. as well as the fundamental vintage effects, corresponding to Darboux's theorem, more moderen effects and ideas also are integrated the following, akin to symplectic ability and pseudoholomorphic curves. those rules have revolutionized the topic. the most examples of symplectic manifolds are given, together with the cotangent package deal, Kähler manifolds, and coadjoint orbits. additional valuable rules are conscientiously tested, similar to Hamiltonian vector fields, the Poisson bracket, and connections with touch manifolds. Berndt describes a few of the shut connections among symplectic geometry and mathematical physics within the final chapters of the booklet. particularly, the instant map is outlined and explored, either mathematically and in its relation to physics. He additionally introduces symplectic aid, that is a major software for lowering the variety of variables in a actual approach and for developing new symplectic manifolds from outdated. the ultimate bankruptcy is on quantization, which makes use of symplectic easy methods to take classical mechanics to quantum mechanics. This part incorporates a dialogue of the Heisenberg team and the Weil (or metaplectic) illustration of the symplectic staff. numerous appendices offer history fabric on vector bundles, on cohomology, and on Lie teams and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a transparent and concise creation to the most important tools and purposes of the topic, and calls for just a minimal of must haves. This ebook will be a great textual content for a graduate path or as a resource for somebody who needs to profit approximately symplectic geometry.

By George Gasper

A superb reference at the topic. fabric on generalized hypergeometric features (starting with Gauss' hypergeometric functionality) is gifted by means of the q analogy's. the cloth is complex and is easily written with a decent and readable typeface. The advent to q sequence will fulfill the newbie. The record of approximately 500 references protecting the complete topic is definitely worth the rate alone.

Lorenz H. Menke, Jr.

By Paul B. Yale

This e-book is an creation to the geometry of Euclidean, affine, and projective areas with distinctive emphasis at the very important teams of symmetries of those areas. the 2 significant targets of the textual content are to introduce the most principles of affine and projective areas and to enhance facility in dealing with changes and teams of differences. on account that there are lots of reliable texts on affine and projective planes, the writer has targeting the n-dimensional cases.
Designed for use in complex undergraduate arithmetic or physics classes, the publication makes a speciality of "practical geometry," emphasizing themes and methods of maximal use in all components of arithmetic. those subject matters include:
Algebraic and Combinatoric Preliminaries
Isometries and Similarities
An advent to Crystallography
Fields and Vector Spaces
Affine Spaces
Projective Spaces
Special gains comprise a spiral method of symmetry; a evaluation of the algebraic must haves; proofs which don't seem in different texts, reminiscent of the Polya-Burnside theorem; an in depth bibliography; and a wide selection of routines including feedback for term-paper subject matters. additionally, designated emphasis is put on the geometric value of cosets and conjugates in a bunch.