Posts in category: Geometry
By Jean Gallier
This publication is an advent to the elemental techniques and instruments wanted for fixing difficulties of a geometrical nature utilizing a working laptop or computer. It makes an attempt to fill the space among normal geometry books, that are basically theoretical, and utilized books on special effects, machine imaginative and prescient, robotics, or computing device learning.
This booklet covers the subsequent themes: affine geometry, projective geometry, Euclidean geometry, convex units, SVD and important part research, manifolds and Lie teams, quadratic optimization, fundamentals of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). a few functional functions of the ideas offered during this publication contain laptop imaginative and prescient, extra particularly contour grouping, movement interpolation, and robotic kinematics.
during this greatly up to date moment variation, extra fabric on convex units, Farkas’s lemma, quadratic optimization and the Schur supplement were additional. The bankruptcy on SVD has been significantly extended and now incorporates a presentation of PCA.
The ebook is definitely illustrated and has bankruptcy summaries and a number of workouts all through. it is going to be of curiosity to a large viewers together with machine scientists, mathematicians, and engineers.
8 subject matters concerning the unit cubes are brought inside of this textbook: go sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. specifically Chuanming Zong demonstrates how deep research like log concave degree and the Brascamp-Lieb inequality can care for the pass part challenge, how Hyperbolic Geometry is helping with the triangulation challenge, how staff earrings can care for Minkowski's conjecture and Furtwangler's conjecture, and the way Graph concept handles Keller's conjecture
By D. J. Saunders
The aim of this booklet is to supply an advent to the speculation of jet bundles for mathematicians and physicists who desire to research differential equations, relatively these linked to the calculus of adaptations, in a contemporary geometric means. one of many issues of the publication is that first-order jets might be regarded as the average generalisation of vector fields for learning variational difficulties in box concept, and such a lot of of the buildings are brought within the context of first- or second-order jets, earlier than being defined of their complete generality. The publication features a evidence of the neighborhood exactness of the variational bicomplex. an information of differential geometry is believed through the writer, even if introductory chapters comprise the mandatory historical past of fibred manifolds, and on vector and affine bundles. Coordinate-free innovations are used all through, even supposing coordinate representations are usually utilized in proofs and whilst contemplating purposes.
By Cortinas G., et al. (eds.)
Due to the fact that its inception 50 years in the past, K-theory has been a device for figuring out a wide-ranging kin of mathematical buildings and their invariants: topological areas, earrings, algebraic kinds and operator algebras are the dominant examples. The invariants variety from attribute periods in cohomology, determinants of matrices, Chow teams of types, in addition to strains and indices of elliptic operators. therefore K-theory is impressive for its connections with different branches of arithmetic. Noncommutative geometry develops instruments which enable one to consider noncommutative algebras within the similar footing as commutative ones: as algebras of services on (noncommutative) areas. The algebras in query come from difficulties in numerous components of arithmetic and mathematical physics; normal examples contain algebras of pseudodifferential operators, team algebras, and different algebras bobbing up from quantum box idea. to review noncommutative geometric difficulties one considers invariants of the suitable noncommutative algebras. those invariants comprise algebraic and topological K-theory, and in addition cyclic homology, came across independently through Alain Connes and Boris Tsygan, which might be appeared either as a noncommutative model of de Rham cohomology and as an additive model of K-theory. There are fundamental and secondary Chern characters which cross from K-theory to cyclic homology. those characters are appropriate either to noncommutative and commutative difficulties and feature purposes starting from index theorems to the detection of singularities of commutative algebraic forms. The contributions to this quantity signify this diversity of connections among K-theory, noncommmutative geometry, and different branches of arithmetic.
By Phillip A Griffiths, Mathematiker USA
By Louis Magnin
Algèbre, géométrie usuelle, calcul des probabilités : trois piliers de l'édifice des mathématiques, qui devraient faire partie du bagage de tout futur enseignant scientifique, comme du citoyen.Ce livre, élaboré à partir d'un cours de los angeles Licence Pluridisciplinaire de Sciences et Technologie de l'université de Bourgogne, s'adresse à des étudiants de moment cycle, qui ne voudraient pas suivre un cycle spécialisé en mathématiques, mais désireraient acquérir une formation générale en mathématiques sur ces sujets, afin de pouvoir préparer des concours ouverts aux titulaires d'une Licence : concours administratifs de l. a. catégorie A, concours de recrutement d'enseignants tels que CERPE (concours externe de recrutement des Professeurs des Écoles) ou CAPLP2 (Certificat d'aptitude au Professorat des lycées professionnels)...Les prérequis sont très limités ; le texte est obtainable aux étudiants ayant suivi un DEUG, un DUT ou même un BTS. Pour autant, il ne néglige pas l. a. rigueur mathématique tout en restant dans le cadre fixé.Chaque chapitre est suivi d'exercices, dont l. a. plupart avec des symptoms formant un véritable corrigé.**
By Otto Mutzbauer
By R. Couty, A. Revuz (auth.), M. Cahen, M. Flato (eds.)
On the social gathering of the 60th birthday of Andre Lichnerowicz a couple of his neighbors, a lot of whom were his scholars or coworkers, made up our minds to have fun this occasion by means of getting ready a jubilee quantity of contributed articles within the major fields of analysis marked by means of Lichnerowicz's paintings, particularly differential geometry and mathematical physics. boundaries of area and time didn't let us to incorporate papers from all Lichnerowicz's neighbors nor from all his former scholars. It used to be both very unlikely to mirror in one ebook the good number of topics tackled by way of Lichnerowicz. despite those obstacles, we are hoping that this booklet displays a few of the current developments of fields during which he labored, and a few of the themes to which he contributed in his lengthy - and never but complete - occupation. This profession was once a great deal marked through the effect of his masters, Elie Cartan who brought him to investigate in arithmetic, in general in geometry and its kin with mathematical physics, and Georges Darmois who constructed his curiosity for mechanics and physics, specially the speculation of relativity and electromagnetism. This par ticular mixture, and his own expertise, made up of him a traditional clinical inheritor and continuator of the French mathematical physics university within the culture of Henri Poincare. a few of his works may also be most sensible certified by means of a brand new box identify, that of actual ma thematics: branches of natural arithmetic fullyyt influenced by way of physics.
By Schreier O., Sperner E.
By K. Goebel, S. Reich, Visit Amazon's Kazimierz Goebel Page, search results, Learn about Author Central, Kazimierz Goebel,