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Critical coding techniques have developed over the past few decades for data storage, retrieval and transmission systems, significantly mitigating costs for governments and corporations that maintain server systems containing large amounts of data. This book surveys the...
This book provides statistics instructors and students with complete classroom material for a one- or two-semester course on applied regression and causal inference. It is built around 52 stories, 52 class-participation activities, 52 hands-on computer demonstrations,...
An emerging field in statistics, distributional regression facilitates the modelling of the complete conditional distribution, rather than just the mean. This book introduces generalized additive models for location, scale and shape (GAMLSS) – one of the most important...
Discrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years...
What follows from what, and how do we make statements (whether true or false) about which inferences are correct? In this book, Edwin Mares provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. In the...
A large international conference celebrated the 50-year career of Anatole Katok and the body of research across smooth dynamics and ergodic theory that he touched. In this book many leading experts provide an account of the latest developments at the research frontier...
Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and...
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,...
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...
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,...
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...
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