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In mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as...
The wave equation, a classical partial differential equation, has been studied and applied since the eighteenth century. Solving it in the presence of an obstacle, the scatterer, can be achieved using a variety of techniques and has a multitude of applications. This...
The theory of marked point processes on the real line is of great and increasing importance in areas such as insurance mathematics, queuing theory and financial economics. However, the theory is often viewed as technically and conceptually difficult and has proved to be...
The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and influence. 'Data science' and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of...
Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the...
Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal...
From Bäcklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian...
Algorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book...
From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various...
Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive...
Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years...
The global biodiversity crisis is one of humanity's most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category...
Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on...
After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points...
The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for...
In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several...
Designing engineering components that make optimal use of materials requires consideration of the nonlinear static and dynamic characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through...
This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with...
The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond...
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