This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent…
An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.
De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of…
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics,…
This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is…
The formation of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics represent one of the most important developments in 20th-century mathematics. This text takes a…
'Guillemin and HaineaEURO (TM)s goal is to construct a well-documented road map that extends undergraduate understanding of multivariable calculus into the theory of differential forms. Throughout, the authors emphasize connections between different…
Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe w…
Differential geometry is the study of curved spaces using the techniques of calculus. It is a mainstay of undergraduate mathematics education and a cornerstone of modern geometry. It is also the language used by Einstein to express general relativit…
In Dual Models, written in the same enthusiastic style as its predecessors Polyhedron Models and Spherical Models, Magnus J. Wenninger presents the complete set of uniform duals of uniform polyhedral, thus rounding out a significant body of knowledg…
This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers pre…
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 first edition of Introduction to Symple…
This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses.Starting from the very foundations of analysis, it offers a complete first…
A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how…
Stiefel manifolds are an interesting family of spaces much studied by algebraic topologists. These notes, which originated in a course given at Harvard University, describe the state of knowledge of the subject, as well as the outstanding problems.…
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study…
Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it…
How is a subway map different from other maps? What makes a knot knotted? What makes the Moebius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century…
'This book is a useful reference for faculty members involved in contest preparation or teaching Euclidean geometry at the college level.'MAA ReviewsThis new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and adva…
Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's G…
How a simple equation reshaped mathematics Leonhard Euler's polyhedron formula describes the structure of many objects-from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's theorem is so simple…
An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly illustrates how the basics of the subject can be implemented on a computer thro…
Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic found…
This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves.The first par…
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 first part introduces basic objects such as schemes, morphisms, base change, local…
This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and i…
Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topolo…
This is the softcover reprint of the 1971 English translation of the first four chapters of Bourbaki's Topologie Generale. It gives all basics of the subject, starting from definitions. Important classes of topological spaces are studied, and unifor…
This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the stude…
Topology is a branch of pure mathematics that deals with the abstract relationships found in geometry and analysis. Written with the mature student in mind, Foundations of Topology, Second Edition, provides a user-friendly, clear, and concise introd…
Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate cour…
Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related t…
In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and…
Our purpose and main concern in writing this book is to illuminate classical concepts from the noncommutative viewpoint, to make the language and techniques of noncommutative geometry accessible and familiar to practi- tioners of classical mathemati…
The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four…
The topology optimization method solves the basic enginee- ring problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design which is concerned with the optimiz…
Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at t…
This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up t…
When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledg…
This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "A…
A systematic and integrated approach to Cantor Sets and their applications to various branches of mathematics The Elements of Cantor Sets: With Applications features a thorough introduction to Cantor Sets and applies these sets as a bridge between r…
"A First Course in Algebraic Topology" starts with the basic notions of category, functors and homotopy of continuous mappings including relative homotopy. Fundamental groups of circles and torus have been treated along with the fundamental group of…
This book is intended as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes features of the multicomponent case not normally considered by knot theorists, such as longitude…
Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each p…
The theory of foliations of manifolds was created in the forties of the last century by Ch. Ehresmann and G. Reeb [ER44]. Since then, the subject has enjoyed a rapid development and thousands of papers investigating foliations have appeared. A list…
One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and An…
Every eight years since 1961, the University of Georgia has hosted a major international topology conference aimed at disseminating important recent results and bringing together researchers at different stages of their careers. This volume contains…
This book presents 13 peer-reviewed papers as written results from the 2005 workshop "Topology-Based Methods in Visualization" that was initiated to enable additional stimulation in this field. It contains a survey of the state-of-the-art, as well o…