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This self-contained guide introduces two pillars of data science, probability theory, and statistics, side by side, in order to illuminate the connections between statistical techniques and the probabilistic concepts they are based on. The topics covered in the book...
One of life's most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our...
A graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC), as applied broadly in the Bayesian computational context. The topics covered have emerged as recently as the last decade and include stochastic gradient MCMC, non-reversible MCMC,...
The K-stability of Fano varieties has been a major area of research over the last decade, ever since the Yau-Tian-Donaldson conjecture was resolved. This is the first book to give a comprehensive algebraic treatment of this emerging field. It introduces all the notions...
Providing a succinct overview of Lindenmayer system (L-system) topology optimization, this book focuses on the methods and theory underlying this novel bioinspired approach. Starting from basic principles, the book outlines how topology optimization can be utilized at...
Oriented matroids appear throughout discrete geometry, with applications in algebra, topology, physics, and data analysis. This introduction to oriented matroids is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure...
Abstract polytopes are partially ordered sets that satisfy some key aspects of the face lattices of convex polytopes. They are chiral if they have maximal symmetry by combinatorial rotations, but none by combinatorial reflections. Aimed at graduate students and...
Primal heuristics guarantee that feasible, high-quality solutions are provided at an early stage of the solving process, and thus are essential to the success of mixed-integer programming (MIP). By helping prove optimality faster, they allow MIP technology to extend to...
Bringing together years of research into one useful resource, this text empowers the reader to creatively construct their own dependence models. Intended for senior undergraduate and postgraduate students, it takes a step-by-step look at the construction of specific...
This text provides an advanced introduction to the modeling of competitive financial markets, encompassing arbitrage and equilibrium pricing of financial contracts, as well as optimal lifetime consumption and portfolio choice. Notable features include its coverage of...
The N-body problem has been investigated since Isaac Newton, however vast tracts of the problem remain open. Showcasing the vibrancy of the problem, this book describes four open questions and explores progress made over the last 20 years. After a comprehensive...
Every four years leading researchers gather to survey the latest developments in all aspects of group theory. Since 1981, the proceedings of these meetings have provided a regular snapshot of the state of the art in group theory and helped to shape the direction of...
Understanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of numbers from whole numbers to fractions to exotic ones like p, are, frankly, really difficult to describe rigorously. Instead of...
The Traveling Salesman Problem (TSP) is a central topic in discrete mathematics and theoretical computer science. It has been one of the driving forces in combinatorial optimization.The design and analysis of better and better approximation algorithms for the TSP has...
Symmetry is one of the most important concepts in mathematics and physics. Emerging from the 2021 LMS-Bath Summer School, this book provides Ph.D. students and young researchers with some of the essential tools for the advanced study of symmetry. Illustrated with...
The theory of definable equivalence relations has been a vibrant area of research in descriptive set theory for the past three decades. It serves as a foundation of a theory of complexity of classification problems in mathematics and is further motivated by the study of...
The third edition of this highly regarded text provides a rigorous, yet entertaining, introduction to probability theory and the analytic ideas and tools on which the modern theory relies.The main changes are the inclusion of the Gaussian isoperimetric inequality plus...
Classical logic – which studies the structural features of purported claims of fact – and modal logic – which studies relations of necessity and possibility – are different but complementary areas of logical thought. In this lively and accessible textbook, Adam...
Albert algebras provide key tools for understanding exceptional groups and related structures such as symmetric spaces. This self-contained book provides the first comprehensive reference onAlbert algebras over fields without any restrictions on the characteristic of...
This comprehensive introduction to global spectral methods for fractional differential equations from leaders of this emerging field is designed to be accessible to graduate students and researchers across math, science, and engineering. The book begins by covering the...
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