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How is a subway map different from other maps? What makes a knot knotted? What makes the Möbius strip one-sided? These are questions of topology, the mathematical study of …
K-theory is often considered a complicated `specialist's' theory. This book is an introduction to the basics and provides detailed explanation of the various concepts required for …
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 …
Covering an area of current intense research interest, this book is ideal for all mathematicians, undergraduate or at research level, as an introduction to the field. The book …
This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in …
Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and …
Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook …
An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly …
Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is …
Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical …