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Fibre Bundles
Fibre bundles play an important role in just about every aspect of modern geometry and topology. Basic properties, homotopy classification, and characteristic classes of fibre …
Compact Lie Groups
Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie …
Lectures on Riemann Surfaces
This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and …
Categories for the Working Mathematician
This new edition includes a number of revisions and additions. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The …
The Arithmetic of Elliptic Curves
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in …
Problems in Analytic Number Theory
This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior …
A Course in Functional Analysis
Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, …
Mathematical Methods of Classical Mechanics
Updated version of a classic text (first published 1974 in Russian, and 1978 in English translation) by a man who for several decades has been universally acknowledged to stand at …
Real and Functional Analysis
This book is meant as a text for a first year graduate course in analysis. Any standard course in undergraduate analysis will constitute sufficient preparation for its …
Introduction to Smooth Manifolds
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 …