Copyright 2025
ISBN 9781032988252
382 Pages 11 B/W Illustrations
September 4, 2025 by Chapman & Hall
Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.
The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author’s motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems.
・ Approachable for first year undergraduates, but still of interest to more advanced students and postgraduates
・ Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof
・ Draws attention to connections with other areas of mathematics
・ Plenty of exercises for students, both straightforward problems and more in-depth investigations
・ Introduces many concepts that are required in more advanced topics in mathematics
・ Complete solutions to all exercises, and hints for the in-depth investigations
・ Extensive changes to chapters 4 and 5, including defining integral domains as distinct from commutative rings, a more complete discussion of irreducibles, primes and unique factorisation, and more topics in elementary number theory
・ A completely revised chapter 8, giving a more coherent account of quadratic rings and their unique (or non-unique) factorisation properties
・ A thorough correction of typos and errors across all chapters
・ Updates to the bibliography
Preface and Acknowledgements 1 Introduction: The Purpose of This Book 2 Sets and Relations 3 Natural Numbers 4 Integers, Z 5 Foundations of Number Theory 6 Rational Numbers, Q 7 Real Numbers, R 8 Quadratic Extensions: General Concepts and Extensions of Z and Q 9 Complex Numbers, C: A Quadratic Extension of R 10 Yet More Number Systems 11 Where Do We Go from Here? A How to Read Proofs: The Self-Explanation" Strategy Solutions to Exercises and Hints for Investigations Bibliography Index
Copyright 2026
Hardback
ISBN 9781032488851
275 Pages 32 B/W Illustrations
August 20, 2025 by Chapman & Hall
In recent years there has been substantial and growing interest in small area estimation (SAE) that is largely driven by practical demands. Here, the term "small area" typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain.
Keywords in SAE are “borrowing strength”. Because there are insufficient samples from the small areas to produce reliable direct estimates, statistical methods are sought to utilize other sources of information to do better than the direct estimates. A typical way of borrowing strength is via statistical modelling. On the other hand, there is no “free lunch”. Yes, one can do better by borrowing strength, but there is a cost. This is the main topic discussed in this text.
A comprehensive account of methods, applications, as well as some open problems related to robust SAE
Methods illustrated by worked examples and case studies using real data
Discusses some advanced topics including benchmarking, Bayesian approaches, machine learning methods, missing data, and classified mixed model prediction
Supplemented with code and data via a website
Robust Small Area Estimation: Methods, Applications, and Open Problems is primarily aimed at researchers and graduate students of statistics and data science and would also be suitable for geography and survey methodology researchers. The practical approach should help persuade practitioners, such as those in government agencies, to more readily adopt robust SAE methods. It could be used to teach a graduate-level course to students with a background in mathematical statistics.
1. Small Area Estimation: A Brief Overview
2. SAE Methods Built on Weaker Assumptions
3. Outlier Robustness
4. Observed Best Prediction and Its Extensions
5. More Flexible Models
6. Model Selection and Diagnostics
7. Other Topics
Copyright 2026
Hardback
ISBN 9781032649047
248 Pages 47 B/W Illustrations
August 29, 2025 by Chapman & Hall
Change point analysis is a crucial statistical technique for detecting structural breaks within datasets, applicable in diverse fields such as finance and weather forecasting. The authors of this book aim to consolidate recent advancements and broaden the scope beyond traditional time series applications to include biostatistics, longitudinal data analysis, high-dimensional data, and network analysis.
The book introduces foundational concepts with practical data examples from literature, alongside discussions of related machine learning topics. Subsequent chapters focus on mathematical tools for single- and multiple-change point detection along with statistical inference issues, which provide rigorous proofs to enhance understanding but assume readers have foundational knowledge in graduate-level probability and statistics. The book also expands the discussion into threshold regression frameworks linked to subgroup identification in modern statistical learning and apply change point analysis to functional data and dynamic networks?areas not comprehensively covered elsewhere.
1. Overview
2. Single change point
3. Multiple change points
4. Interval estimation
5. Regression models with change points
6. Further Applications
Copyright 2026
Hardback
ISBN 9781032931920
464 Pages 174 B/W Illustrations
September 19, 2025 by Chapman & Hall
Exploratory and Robust Data Analysis: A Modern Applied Statistics Guide Using SPSS and R is an essential resource for students, researchers, and professionals seeking a comprehensive yet practical approach to modern statistical analysis. This book bridges traditional statistical methods with contemporary techniques, emphasizing exploratory and robust data analysis while integrating powerful computational tools such as R and SPSS.
Designed for intermediate-level courses and research applications, the book begins with fundamental concepts in exploratory data analysis, graphical methods, and confirmatory statistical procedures. It then introduces robust statistical methods, including M-estimators, high-breakdown estimators, bootstrap techniques, and Monte Carlo simulations, equipping readers with tools to handle complex and real-world data scenarios. Key topics include regression analysis, multiple linear models, nonparametric regression, and generalized linear models, ensuring broad applicability across disciplines.
What sets this book apart is its emphasis on theoretical foundations and hands-on applications. Annotated computer sessions guide readers through statistical analysis, enabling them to apply techniques effectively while understanding their theoretical underpinnings. This book fosters an analytical mindset that encourages critical thinking and data-driven decision-making by combining classical statistical procedures with modern computational methods.
With real-world datasets, practical exercises, and detailed software integration, this book is an indispensable guide for those looking to master data analysis in an era where statistical rigor and computational efficiency are paramount.
INTRODUCTION. CHAPTER 1 EXPLORATORY DATA ANALYSIS FOR THE LOCATION MODEL CHAPTER 2 COMBINING EXPLORATORY AND CONFIRMATORY DATA ANALYSIS FOR THE LOCATION MODEL. CHAPTER 3 ROBUST ESTIMATION IN THE LOCATION MODEL CHAPTER 4 ROBUST ESTIMATION IN THE LOCATION MODEL: COMPUTER-INTENSIVE METHODS. CHAPTER 5 COMPARING TWO OR MORE GROUPS OF DATA: EXPLORATORY, CLASSICAL INFERENCE, AND OTHER FORMS OF ANALYSIS CHAPTER 6 SIMPLE LINEAR REGRESSION: CLASSICAL, ROBUST, AND NONPARAMETRIC METHODS CHAPTER 7 MULTIPLE LINEAR REGRESSION AND THE GENERAL LINEAR MODEL CHAPTER 8 ANALYSIS OF NON-NORMAL RESPONSE VARIABLES: THE GENERALIZED LINEAR MODEL
Copyright 2026
Hardback
ISBN 9781032979618
512 Pages 31 Color & 2 B/W Illustrations
September 12, 2025 by CRC Press
Mathematical Foundations of Blockchains is a two-volume work on blockchains. Blockchain is a novel paradigm for a distributed ledger. Volume 1 is on the fundamentals of blockchains and consists of an overview of blockchains, essential elements of blockchains, and the mathematics required for understanding the workings of blockchains. Volume 2 develops mathematical models to enhance the understanding of blockchains.
This work can be used by students of electrical engineering, computer science, applied mathematics, and economics. Students in business school can also benefit. It can also be used by professionals and researchers in the field who would like a quick review of the basics of the subject.
Preface List of Commonly Used Sets Part I. Overview of Blockchains 1. Introduction to Blockchains 2. Blockchain Architecture 3. Blockchain Economics, Security, and Applications 4. Bitcoin, Ethereum, and Algorand Blockchains Part II. Essential Elements of Blockchains 5. Consensus Protocols in Distributed Computing Systems 6. Blockchain Cryptography 7. Digital Currencies 8. Introduction to Decentralized Finance 9. Introduction to Game Theory 10. Post-Quantum Cryptography Part III. Mathematics for Blockchains 11. Sets, Functions, and Number Theory 12. Algebra, and Analysis 13. Matrices, Determinants, and Graph Theory 14. Probability Theory 15. Stochastic Processes, and Some Applications Part IV. Miscellaneous Bibliography Index
Copyright 2026
Hardback
ISBN 9781032979649
448 Pages 11 Color & 2 B/W Illustrations
September 12, 2025 by CRC Press
Mathematical Foundations of Blockchains is a two-volume work on blockchains. Blockchain is a novel paradigm for a distributed ledger. Volume 1 is on the fundamentals of blockchains and consists of an overview of blockchains, essential elements of blockchains, and the mathematics required for understanding the workings of blockchains. Volume 2 develops mathematical models to enhance the understanding of blockchains.
This work can be used by students of electrical engineering, computer science, applied mathematics, and economics. Students in business school can also benefit. It can also be used by professionals and researchers in the field who would like a quick review of the basics of the subject.
Preface List of Commonly Used Sets Part I. Blockchain Formalization 1. A High-Level Blockchain Description 2. Blockchain Throughput and Block-Size Depend 3. Double-Spending Attack, Selfish Mining, and Private-Chain Attack 4. Forking, Sharding, and Energy Consumption in Blockchains 5. Robustness of the Nakamoto Consensus Protocol 6. Analysis of Blockchain Economics 7. Game-Theoretic Blockchain Models 8. Blockchains and Trust 9. Tangle Distributed Ledger 10. Decentralized Finance Analysis and Blockchains 11. Blockchains and Differential Privacy 12. Blockchains and the Quantum Revolution Part II. Miscellaneous Acronyms Glossary Bibliography