Topology

This book presents basic concepts from the emerging field of computational topology, now being used to solve problems in diverse fields.

This 2003 book connects topology and algebra using modern techniques.

Collection of papers summarising the state of the art.

Articles from leading researchers to introduce the reader to cutting-edge topics in integrable systems theory.

This book studies the geometric theory of polynomials and rational functions in the plane.

This book tells the story of the first computer exploration of Klein''s vision of infinitely repeated reflections, featuring extraordinary images.

A modern, comprehensive review of abstract regular polytopes.

Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.

The second of two volumes offering a modern account of Kaehlerian geometry and Hodge theory for researchers in algebraic and differential geometry.

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students.

A quick introduction to foliations and Lie groupoids with numerous examples and exercises to aid the reader.

A self-contained introduction to typical properties of volume preserving homeomorphisms.

This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.

Accessible and pedagogical introduction to the theory of harmonic maps, covering recent results and applications.

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

Fields-medal winner Donaldson reviews current work, including his own, on the theory of Floer.

This 2001 book presents a general theory as well as a constructive methodology to solve ''observation problems''.

Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability.

Appropriate for both students and professionals, this volume starts with the first principles of topology and advances to general analysis.

Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities.

An elementary text that can be understood by anyone with a background in high school geometry, Invitation to Combinatorial Topology offers a stimulating initiation to important topological ideas.

This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology.

'Homology' as a concept became increasingly elusive during the course of the 20th century.

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations.

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations.

Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics.

Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics.

Carl Friedrich Gauss, the "e;foremost of mathematicians,"e; was a land surveyor.

Carl Friedrich Gauss, the "e;foremost of mathematicians,"e; was a land surveyor.

Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research.

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

This self-contained text is an excellent introduction to Lie groups and their actions on manifolds.

Many nonlinear problems in physics, engineering, biology and social sciences can be reduced to finding critical points of functionals.

This book examines interactions of polyhedral discrete geometry and algebra.

In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics.

From reviews of the first edition:"e;In the world of mathematics, the 1980's might well be described as the "e;decade of the fractal"e;.

This book provides a modern treatment of Lie's geometry of spheres, its applications and the study of Euclidean space.

Aimed at advanced undergraduates and graduate students, this book is about the interplay between algebraic topology and the theory of infinite discrete groups.

Braids and braid groups, the focus of this text, have been at the heart of important mathematical developments over the last two decades.

Praise for George Francis's A Topological Picturebook:Bravo to Springer for reissuing this unique and beautiful book!

This book offers the most comprehensive survey to date of the theory of semiparallel submanifolds.

This book offers readers a taste of the "e;unreasonable effectiveness"e; of Morse theory.

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

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.