Topology

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.

"e;From nothing I have created a new different world,"e; wrote Janos Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today.

If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of literature in the original language.

The second part of the book concludes with Plancherel's theorem in Chapter 8.

This book is not an intellectual history or popular summary of recent work on consciousness in humans.

A Course on Borel sets provides a thorough introduction to Borel sets and measurable selections and acts as a stepping stone to descriptive set theory by presenting important techniques such as universal sets, prewellordering, scales, etc.

This book is a self-contained introduction to fiber spaces and differential operators on smooth manifolds that is accessible to graduate students specializing in mathematics and physics.

This book is an introduction to manifolds at the beginning graduate level.

This text is an elementary introduction to differential geometry.

Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications.

This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations.

This is an introductory text for a first course in algebraic topology.

Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations.

The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non- linear functional analysis, emphasizing developments related to the Leray- Schauder theory.

Manifolds are everywhere.

This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations.

'The book is an engaging and influential collection of significant contributions from an assembly of world expert leaders and pioneers from different fields, working at the interface between topology and physics or applications of topology to physical systems .

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces.

This book provides a comprehensive and up-to-date introduction to Hodge theory-one of the central and most vibrant areas of contemporary mathematics-from leading specialists on the subject.

This definitive synthesis of mathematician Gregory Margulis's research brings together leading experts to cover the breadth and diversity of disciplines Margulis's work touches upon.

Geomodeling applies mathematical methods to the unified modeling of the topology, geometry, and physical properties of geological objects.

Optimal Solution of Nonlinear Equations is a text/monograph designed to provide an overview of optimal computational methods for the solution of nonlinear equations, fixed points of contractive and noncontractive mapping, and for the computation of the topological degree.

Historically, science has sought to reduce complex problems to their simplest components, but more recently it has recognized the merit of studying complex phenomena in situ.

This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time.

There are many proposed aims for scientific inquiry--to explain or predict events, to confirm or falsify hypotheses, or to find hypotheses that cohere with our other beliefs in some logical or probabilistic sense.

In this book, two seemingly unrelated fields -- algebraic topology and robust control -- are brought together.

The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics.

Based on Fields medal winning work of Michael Freedman, this book explores the disc embedding theorem for 4-dimensional manifolds.

An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming.

How is a subway map different from other maps?

How is a subway map different from other maps?

This book is a new edition of "e;Tensors and Manifolds: With Applications to Mechanics and Relativity"e; which was published in 1992.

Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results.

The standard starting point in cosmology is the cosmological principle; the assumption that the universe is spatially homogeneous and isotropic.

The standard starting point in cosmology is the cosmological principle; the assumption that the universe is spatially homogeneous and isotropic.

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors.

The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics.

The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics.

This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property.

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics.

One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting.

Banach spaces and algebras are a key topic of pure mathematics.

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves.

The theory of Riemann surfaces occupies a very special place in mathematics.

Rational homotopy is a very powerful tool for differential topology and geometry.

This edited collection of chapters, authored by leading experts, provides a complete and essentially self-contained construction of 3-fold and 4-fold klt flips.

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years.

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years.

This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut.