Geometry

The problem of enumerating maps (a map is a set of polygonal "e;countries"e; on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, .

This book is a tribute to the memory of Yuri Ivanovich Manin, who passed away on January 7, 2023.

Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view.

The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject.

The author presents deterministic chaos from the standpoint of theoretical computer arithmetic, leading to universal properties described by symbolic dynamics.

In his "e;Geometrie"e; of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry.

In this modern treatment of the topic, Rolland Trapp presents an accessible introduction to the topic of multivariable calculus, supplemented by the use of fully interactive three-dimensional graphics throughout the text.

This volume of proceedings contains research results within the framework of the fields of Chaos, Fractals and Complexity, written by experienced professors, young researchers, and applied scientists.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.

This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory' at the ICMAT (Instituto de Ciencias Matematicas, Madrid) in 2014.

The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op- erators in differential geometry.

Although the monograph Progress in Optimization I: Contributions from Aus- tralasia grew from the idea of publishing a proceedings of the Fourth Optimiza- tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed to a refereed volume in optimization.

Within traditional decision theory, common decision principles -- e.

This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties.

This book is an exposition of the theoretical foundations of hyperbolic manifolds.

This book contains numerous selected contemporary topics, primarily in Hilbert space, although related extended material in Banach spaces and Riemannian manifolds is also included.

Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.

Tough Test Questions?

The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century.

Two types of seemingly unrelated extension problems are discussed in this book.

Provides an introduction to critical point theory and shows how it solves many difficult problems.

A broad introduction, perfect for a one-year graduate course.

Dieses nunmehr in 5.

Aside from the obvious statement that it should be a theory capable of unifying general relativity and quantum field theory, not much is known about the true nature of quantum gravity.

This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry.

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions.

This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense.

A NATO Advanced Study Institute entitled "e;Algebraic K-theory: Connections with Geometry and Topology"e; was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987.

This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.

Gathering and updating results scattered in journal articles over thirty years, this self-contained monograph gives a comprehensive introduction to the subject.

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays.

This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation.

Homogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems.

Hideki Omori is widely recognized as one of the world's most creative and original mathematicians.

This book arose from a conference on "e;Singularities and Computer Algebra"e; which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel's 70th birthday.

This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry.

This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation.

This monograph covers topics in the cohomology of monoids up through recent developments.

Einstein's equations stem from General Relativity.

This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems.

Both a reference and an introduction on the main results about topological geometries on surfaces.

Projective geometry is a very classical part of mathematics and one might think that the subject is completely explored and that there is nothing new to be added.

In this book we study sprays and Finsler metrics.

The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1.

This book is an extension to Arno van den Essen's Polynomial Automorphisms and the Jacobian Conjecture published in 2000.