Published: May 2025
Format: Paperback
ISBN: 9781009267267
Thomas Morel tells the story of subterranean geometry, a forgotten discipline that developed in the silver mines of early modern Europe. Mining and metallurgy were of great significance to the rulers of early modern Europe, required for the silver bullion that fuelled warfare and numerous other uses. Through seven lively case studies, he illustrates how geometry was used in metallic mines by practitioners using esoteric manuscripts. He describes how an original culture of accuracy and measurement paved the way for technical and scientific innovations, and fruitfully brought together the world of artisans, scholars and courts. Based on a variety of original manuscripts, maps and archive material, Morel recounts how knowledge was crafted and circulated among practitioners in the Holy Roman Empire and beyond. Specific chapters deal with the material culture of surveying, map-making, expertise and the political uses of quantification. By carefully reconstructing the religious, economic and cultural context of mining cities, Underground Mathematics contextualizes the rise of numbered information, practical mathematics and quantification in the early modern period.
Provides inter-disciplinary perspectives on the historical development of quantitative knowledge
Presents the history of mathematics in a non-technical way providing numerous illustrations and real-life examples
Situates itself within current debates on the history of science and technology and the relationship between theory and practice and artisanal and elite culture
Introduction
1. Of scholars and miners
2. A mathematical culture: the art of setting limits
3. The mines and the court
4. Writing it down: innovation, secrecy, and print
5. 'So fair a subterraneous city': mapping the underground
6. How to teach it?: finding the right direction
7. 'One of geometry's nicest applications': crafting the Deep-George tunnel (1771?1799)
Conclusion.
Series: Cambridge Monographs on Applied and Computational Mathematics
Published: June 2025
Format: Hardback
ISBN: 9781009566537
Scientific computing plays a critically important role in almost all areas of engineering, modeling, and forecasting. The method of finite differences (FD) is a classical tool that is still rapidly evolving, with several key developments barely yet in the literature. Other key aspects of the method, in particular those to do with computations that require high accuracy, often 'fall through the cracks' in many treatises. Bengt Fornberg addresses that failing in this book, which adopts a practical perspective right across the field and is aimed at graduate students, scientists, and educators seeking a follow-up to more typical curriculum-oriented textbooks. The coverage extends from generating FD formulas and applying them to solving ordinary and partial differential equations, to numerical integration, evaluation of infinite sums, approximation of fractional derivatives, and computations in the complex plane.
Provides general perspectives and practical considerations that are aimed towards making computational implementations simple and effective
Contains an abundance of illustrations highlighting not just computational results, but also algorithmic concepts
Supplemented by seven appendices and an extensive collection of references
1. Introduction to finite difference methods
2. Brief summary of pseudospectral methods
3. FD approximations for ordinary differential equations
4. Grid-based FD approximations for partial differential equations
5. Mesh-free FD approximations
6. FD in the complex plane
7. FD-based methods for quadrature and infinite sums
8. Fractional-order derivatives
A. Polynomial interpolation
B. Splines
C. Fourier transforms, Fourier series, and the FFT algorithm
Published: June 2025
Format: Hardback
ISBN: 9781009514729
Hardback
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
Makes minimal assumptions about the background of the reader and provides access ramps for students of different STEM backgrounds through focus boxes
Is fully up to date with the latest developments in a fast-moving field, exploring the physical systems that can be used as qubits and the quantum technologies that can be built with them
Features nearly 300 unique exercises that are designed to build fluency in solving quantum information problems from scratch, including exercises from a wide range of topics such as linear algebra, number theory, and computer science
Offers extensive learning support including a detailed glossary, suggestions for further reading, and solutions to selected problems
Preface
1. Welcome to quantum computing
2. Quantum mechanics for quantum computers
3. Two qubits and entanglement
4. Quantum algorithms
5. Period finding and Shor's algorithm
6. Realizations of qubits: general discussion
7. Realizations of qubits: examples
8. The physics of two-qubit gates
9. Device characterization
10. Variations on the DiVincenzo criteria
Series: Institute of Mathematical Statistics Monographs
Published: June 2025
Format: Hardback
ISBN: 9781009288446
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, continuous time MCMC, and new techniques for convergence assessment. A particular focus is on cutting-edge methods that are scalable with respect to either the amount of data, or the data dimension, motivated by the emerging high-priority application areas in machine learning and AI. Examples are woven throughout the text to demonstrate how scalable Bayesian learning methods can be implemented. This text could form the basis for a course and is sure to be an invaluable resource for researchers in the field.
Focuses on scalable Bayesian inference techniques for large datasets, making it highly relevant for modern data science and machine learning challenges
Covers cutting-edge MCMC techniques like non-reversible MCMC and piecewise deterministic Markov processes (PDMPs)
Provides practical examples to demonstrate how scalable Bayesian learning methods can be implemented
Preface
1. Background
2. Reversible MCMC and its Scaling
3. Stochastic Gradient MCMC Algorithms
4. Non-Reversible MCMC
5. Continuous-Time MCMC
6. Assessing and Improving MCMC
References
Index.
Series: Cambridge Tracts in Theoretical Computer Science
Published: July 2025
Format: Hardback
ISBN: 9781009613286
Petri nets are one of the most popular tools for modeling distributed systems. This book provides a modern look at the theory behind them, by studying three classes of nets that model (i) sequential systems, (ii) non-communicating parallel systems, and (iii) communicating parallel systems. A decidable and causality respecting behavioral equivalence is presented for each class, followed by a modal logic characterization for each equivalence. The author then introduces a suitable process algebra for the corresponding class of nets and proves that the behavioral equivalence proposed for each class is a congruence for the operator of the corresponding process algebra. Finally, an axiomatization of the behavioral congruence is proposed. The theory is introduced step by step, with ordinary-language explanations and examples provided throughout, to remain accessible to readers without specialized training in concurrency theory or formal logic. Exercises with solutions solidify understanding, and the final chapter hints at extensions of the theory.
Provides a uniform presentation of the theories of sequential and distributed computation
Introduces the theory step by step using ordinary-language explanations and examples throughout
Includes exercises to further develop understanding, with solutions in the Appendix
1. Introduction
2. Sequential systems
3. Non-communicating parallel systems
4. Communicating systems
5. Other equivalences for Petri nets
6. Conclusion
Appendix. Solutions to selected exercises
References
Glossary
Index.
Series: Cambridge Monographs on Applied and Computational Mathematics
Published: September 2025
Format: Hardback
ISBN: 9781009123204
Unlock the potential of computational fluid dynamics with this essential guide for master's and graduate students, and researchers. It explores the immersed boundary method (IBM), a revolutionary approach for simulating flows in complex geometries. With a focus on fluid/structure interaction, it examines theoretical principles and practical implementations, offering insights into tackling intricate geometries and enhancing simulation accuracy. The book features a series of numerical examples that increase in complexity, and is accompanied by the source code, allowing readers to replicate results and deepen their understanding. Whether you're wanting to refine your skills or embark on new research, this introduction will empower you to master the art of complex flow simulations.
Describes the theory and practical implementation of a computational technique that is being used in many different fields of computational science
An accurate and up-to-date reference providing an entry point to the immense literature in the field
Gives a frank and explicit examination of many subtle problems that can arise with immersed boundaries if not properly implemented
Accompanied by the source files of a flow solver in which several of the methods described in the book are implemented, tested and validated
1. Introduction
2. Introduction to flow simulations
3. Computational geometry and grid generation
4. Forcing methods
5. Moving boundaries
6. Computation of hydrodynamic loads
7. Fluid?structure interaction
8. Turbulence and wall models within IBMs
9. Advanced IBM applications
10. Numerical examples
References