Topology

At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies.

What is a number?

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors.

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E.

Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization.

Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications.

The theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify reasons for their existence.

The book treats the theory of attractors for non-autonomous dynamical systems.

Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics.

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject.

Inverse limits provide a powerful tool for constructing complicated spaces from simple ones.

Abstract models for many problems in science and engineering take the form of an operator equation.

This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology.

"e;Descriptive Topology in Selected Topics of Functional Analysis"e; is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis.

This is the Proceedings of the ICM 2010 Satellite Conference on "e;Buildings, Finite Geometries and Groups"e; organized at the Indian Statistical Institute, Bangalore, during August 29 - 31, 2010.

In the Fall of 1975 we started a joint project with the ultimate goal of topo- logically classifying real algebraic sets.

This book gives a treatment of exterior differential systems.

There are many reasons for writing this first volume of strategic activities on fractals.

From the reviews of the first edition: "e;This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate.

Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold.

K -Theory has revolutionized the study of operator algebras in the last few years.

In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications.

A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories.

Many mathematics books suffer from schizophrenia, and this is yet another.

Students of topology rightly complain that much of the basic material in the subject cannot easily be found in the literature, at least not in a convenient form.

In 1992 two successive symposia were held in Japan on algorithms, fractals and dynamical systems.

Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few.

as well as by the list of open problems in the final section of this monograph.

These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79.

As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory.

The creative process of mathematics, both historically and individually, may be described as a counterpoint between theorems and examples.

Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms.

Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space.

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This book is based on lectures I have given to undergraduate and graduate audiences at Oxford and elsewhere over the years.

The work of Max Dehn (1878-1952) has been quietly influential in mathematics since the beginning of the 20th century.

There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J.

In recent years, many students have been introduced to topology in high school mathematics.

Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory.

In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom.

"e;La narraci6n literaria es la evocaci6n de las nostalgias.

The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin- ear analysis during the last three decades.

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns.

This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer- sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987.

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