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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...
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...
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...
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...
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...
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...
The main subject of this introductory book is simple random walk on the integer lattice, with special attention to the two-dimensional case. This fascinating mathematical object is the point of departure for an intuitive and richly illustrated tour of related topics at...
This is the first 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...
Written in a conversational tone, this classroom-tested text introduces the fundamentals of linear programming and game theory, showing readers how to apply serious mathematics to practical real-life questions by modelling linear optimization problems and strategic...
Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known...
This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the...
Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical...
Build the skills for determining appropriate error limits for quantities that matter with this essential toolkit. Understand how to handle a complete project and how uncertainty enters into various steps. Provides a systematic, worksheet-based process to determine error...
Probability theory has diverse applications in a plethora of fields, including physics, engineering, computer science, chemistry, biology and economics. This book will familiarize students with various applications of probability theory, stochastic modeling and random...
The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by S.V. Stratila and L. Zsidó) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and...
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