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Functional Analysis, Calculus of Variations and Optimal Control
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, …
An Introduction to Number Theory
An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of …
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, …
Graph Theory
Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role …
Differential Geometry
This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of …
Quaternion Algebras
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of …
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 …