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Gives an introduction to the theory of the integral (called the 'generalized Riemann integral' or the 'Henstock-Kurzweil integral') that corrects the ...Savoir plus
The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. The author covers contempo...Savoir plus
Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a...Savoir plus
Presents an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both inte...Savoir plus
Presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to ...Savoir plus
Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and num...Savoir plus
Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel fea...Savoir plus
Provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. It contains ...Savoir plus
Modern topology uses very diverse methods. This book deals with the methods of combinatorial topology, which reduce the study of topological spaces to...Savoir plus
Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a...Savoir plus
Presents an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both inte...Savoir plus
Develops a mathematical theory for finance, based on an intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a...Savoir plus
Presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to ...Savoir plus
Taking into account the remarkable development of dynamical systems, the authors present the core topics that every young mathematician of our time - ...Savoir plus
The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Sc...Savoir plus
This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings th...Savoir plus
Part of the ""AMS in the Graduate Studies in Mathematics"" series, this volume focuses on the qualitative theory of foliations. It explains the fundam...Savoir plus
Takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition abou...Savoir plus
Presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete p...Savoir plus
Defines simplicial homology and cohomology, with various examples and applications. This book introduces Kolmogorov-Alexander multiplication in cohomo...Savoir plus
Presents the concepts and tools to solve problems of analysis, and shows how to apply these concepts to research in a variety of areas. This work cove...Savoir plus
Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book introduces Ricci flow for graduate students an...Savoir plus
Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. This ...Savoir plus