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This book provides the first systematic treatment of model risk, outlining the tools needed to quantify model uncertainty, to study its effects, and, in particular, to determine the best upper and lower risk bounds for various risk aggregation functionals of interest....
Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first...
In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But...
Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C8-schemes', which allow differential geometers to study a huge range of singular spaces,...
Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task,...
This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic...
Optimal mass transport has emerged in the past three decades as an active field with wide-ranging connections to the calculus of variations, PDEs, and geometric analysis. This graduate-level introduction covers the field's theoretical foundation and key ideas in...
Equivariant cohomology has become an indispensable tool in algebraic geometry and in related areas including representation theory, combinatorial and enumerative geometry, and algebraic combinatorics. This text introduces the main ideas of the subject for first- or...
This monograph provides a mathematically rigorous overview of optimal fractionation in cancer radiotherapy, which seeks to address the fundamental tradeoff of maximizing tumor-kill while protecting nearby healthy tissue from toxic effects. Most mathematical research on...
The first book on the explicit birational geometry of complex algebraic threefolds arising from the minimal model program, this text is sure to become an essential reference in the field of birational geometry. Threefolds remain the interface between low and...
Projective geometry is the geometry of vision, and this book introduces students to this beautiful subject from an analytic perspective, emphasising its close relationship with linear algebra and the central role of symmetry. Starting with elementary and familiar...
The Riemann hypothesis (RH) may be the most important outstanding problem in mathematics. This third volume on equivalents to RH comprehensively presents recent results of Nicolas, Rogers–Tao–Dobner, Polymath15, and Matiyasevich. Particularly interesting are derivations...
How should we treat the liar and kindred paradoxes? A Theory of Truth argues that we should diverge from classical logic, and presents a new formal theory of truth. The theory does not incorporate contradictions and is not substructural, but deviates from classical...
The book is designed for undergraduates, graduates, and researchers of mathematics studying fixed point theory or nonlinear analysis. It deals with the fixed point theory for not only single-valued maps but also set-valued maps.The text is divided into three parts:...
Written by Sheldon Ross and Erol Peköz, this text familiarises you with advanced topics in probability while keeping the mathematical prerequisites to a minimum. Topics covered include measure theory, limit theorems, bounding probabilities and expectations, coupling and...
Covering an exceptional range of topics, this text provides a unique overview of the Maurer—Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various...
The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new...
Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone...
Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an...
Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as...
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