Maciej (Professor of Mathematical Physics Dunajski Professor of Mathematical Physics Department of Applied Mathematics and Theoretical Physics University of Cambridge)
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‘A Concise Introduction to the Theory of Integration’ was once a best-selling Birkhauser title which published 3 editions. This manuscript is a substantial revision of the material. Chapter one now in
The book provides a self-contained and accessible introduction to integrable systems. It starts with an introduction to integrability of ordinary and partial differential equations, and goes on to exp
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 topolo
This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculati
Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and wit
This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. Additionally, the aim is to show how the theory is combined with the study of operators
This nicely written manuscript takes a gentler approach than other functional analysis graduate texts, and includes an improved approach along with a better choice of topics. The concise treatment ma
This book is intended as a textbook to be used in a first graduate level course, and covers the fundamental principals of optimization in finite dimensions. It develops the necessary background mater
This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals.Providing a useful and quick intro
In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects o
A central problem in additive number theory is the growth of sumsets. If A is a finite or infinite subset of the integers and the lattice points, or more generally, of any abelian group or semigroup G
This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view
One of my favorite graduate courses at Berkeley is Math 251, a one-semester course in ring theory offered to second-year level graduate students. I taught this course in the Fall of 1983, and more rec
Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of com
An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pu
