Published: May 2026
Format: Paperback
ISBN: 9781009711258
This book presents a modern introduction to the field of algorithmic game theory. It places a heavy emphasis on optimization and online learning (a subdiscipline of machine learning), which are tools that increasingly play a central role in both the theory and practice of applying game-theoretic ideas. The book covers the core techniques used in several majorly successful applications, including techniques used for creating superhuman poker AIs, the theory behind the 'pacing' methodology that has become standard in the internet advertising industry, and the application of competitive equilibrium from equal incomes for fair course seat allocation in many business schools. With its focus on online learning tools, this book is an ideal companion to classic texts on algorithmic game theory for graduate students and researchers.
Demonstrates the capabilities of algorithmic game theory (AGT) by covering several hallmark applications, which provides a guiding principle for finding new applications
Presents online learning as a unifying tool that leads to fundamental results in several areas of AGT
Covers recent developments in large-scale game solving
Preface
Notation
Part I. Introductory Material:
1. Introduction and examples
2. Nash equilibrium introduction
3. Auctions and mechanism design introduction
Part II. Game Solving and Regret Minimization:
4. Regret minimization and the minimax theorem
5. Blackwell approachability and regret matching
6. Self-play via regret minimization
7. Optimism and fast convergence of self play
8. Extensive-form games
9. Stackelberg equilibrium and security games
10. Fixed-point theorems and equilibrium existence
Part III. Fair Allocation and Market Equilibrium:
11. Fair division and market equilibrium
12. Computing Fisher market equilibrium
13. Fair allocation with indivisible goods
14. Power flows and equilibrium pricing
Part IV. Auctions and Internet Advertising Markets:
15. Internet advertising auctions: position auctions
16. Auctions with budgets and pacing equilibria
17. Pacing algorithms for budget management
18. Demographic fairness
Appendix A. Optimization background
Appendix B. Probability background
References
Index.
Published: May 2026
Format: Hardback
ISBN: 9781009702812
This comprehensive modern look at regression covers a wide range of topics and relevant contemporary applications, going well beyond the topics covered in most introductory books. With concision and clarity, the authors present linear regression, nonparametric regression, classification, logistic and Poisson regression, high-dimensional regression, quantile regression, conformal prediction and causal inference. There are also brief introductions to neural nets, deep learning, random effects, survival analysis, graphical models and time series. Suitable for advanced undergraduate and beginning graduate students, the book will also serve as a useful reference for researchers and practitioners in data science, machine learning, and artificial intelligence who want to understand modern methods for data analysis.
Presents a wide breadth of statistical topics in a concise, big-picture way
Equips readers to investigate causality using causal inference
Provides datasets, code and other resources through a companion website
Preface
Notation
1. Introduction
2. Linear regression
3. Prediction error, cross-validation and model selection
4. High dimensional linear regression
5. Logistic and Poisson regression
6. Univariate nonparametric regression
7. Nonparametric regression with multiple features
8. Quantile regression
9. Classification
10. Prediction sets and conformal inference
11. Causal inference
12. Other topics
Appendix A. Matrix theory
Appendix B. Basic probability and statistics
Data Sources
References
Index.
Series: London Mathematical Society Student Texts
Published: May 2026
Format: Paperback
ISBN: 9781009595322
Starting from ancient astronomy, this text follows the development of celestial mechanics culminating in applications of the most recent results concerning stability of planetary orbits: Kolmogorov's and Nekhoroshev's theorems. Key topics covered include: a historical introduction from ancient astronomy to Kepler and Newton; Lagrange's perturbation theory; the problem of three bodies, with a discussion of Levi-Civita regularization and of Sundman's theorem; methods of algebraic calculation of perturbation series, including a discussion of non-convergence due to the accumulation of small divisors; and a complete application of Kolmogorov's and Nekhoroshev's theorems. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students, and for young researchers. Its approach allows students to learn about perturbation methods leading to advanced results.
Surveys the historical journey from ancient astronomy to our current theory based on Newtonian gravitation
Contains an extended exposition of the problem of three bodies
Provides a complete computational scheme for an explicit application of perturbation methods through computer algebra
Apology
Plan of the book
Part I. From Ancient Astronomy to Newton:
1. Ouverture
2. Kinematics of the Keplerian model
3. The gravitation of Newton
Part II. From Newton to Poincaré:4. Integrability and action-angle variables
5. The perturbing function
6. Classical perturbation methods
7. The problem of three bodies
8. Regularization of collisions
Part III. Modern Celestial Mechanics:
9. A toolbox of perturbation methods
10. Computer-assisted methods for KAM theory
11. Rotational dynamics of celestial bodies
12. Stability of planetary systems
A. Analytical tools
B. Indexing functions
C. Validated numerics in CAP
D. Benchmarking CAP with a simple model
References
Index.
Series: London Mathematical Society Lecture Note Series
Published: June 2026
Format: Paperback
ISBN: 9781009766043
This volume contains eight survey articles by the invited speakers of the 31st British Combinatorial Conference, held at Cardiff University in July 2026. Each article provides an overview of recent developments in a current hot research topic in combinatorics. Topics covered include random planar graphs, temporal graphs, domino tilings, extremal poset theory, asymptotic enumeration, graph homomorphisms, combinatorial rigidity theory, logic and model theory, matroids, and graph bootstrap percolation. The authors are among the world's foremost researchers on their respective topics, but their surveys are accessible to nonspecialist readers: they are written clearly, with little prior knowledge assumed, and with pointers to the wider literature. Taken together, these surveys give a snapshot of the research frontier in contemporary combinatorics, helping researchers and graduate students in mathematics and theoretical computer science to keep abreast of the latest developments in the field.
Includes eight survey articles on current hot topics by leading researchers
Provides an overview of important recent developments in different areas of combinatorics
Broadly accessible to mathematicians and theoretical computer scientists
1. Phase Transitions in Random Planar Graphs Mihyun Kang
2. Extremal Poset Theory Maria Axenovich, Ryan R. Martin and Balázs Patkós
3. Techniques for Taming Temporal Graphs Kitty Meeks
4. Asymptotic Enumeration via Graph Containers and Entropy Jinyoung Park
5. Graph Bootstrap Percolation – A Discovery of Slowness David Fabian, Patrick Morris and Tibor Szabó
6. Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach James Cruickshank, Bill Jackson, Tibor Jordán and Shin-ichi Tanigawa
7. Monadic Second-Order Logic for Hypergraphs and Matroids Dillon Mayhew
8. Domino Tilings Beyond 2D Caroline J. Klivans and Nicolau Saldanha.
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Published: July 2026
Format: Hardback
ISBN: 9781009160438
Based on courses taught at the University of Cambridge, this text presents core contemporary statistical methods and theory in an accessible, self-contained and rigorous fashion, with a focus on finite-sample guarantees as opposed to asymptotic arguments. Many of the topics and results have not appeared in book form previously, and some constitute new research. The prerequisites are relatively light (primarily a good grasp of linear algebra and real analysis) and complete solutions to all 250+ exercises are available online. It is the perfect entry point to the subject for master's and graduate-level students in statistics, data science and machine learning, as well as related disciplines such as artificial intelligence, signal processing, information theory, electrical engineering and econometrics. Researchers in these fields will also find it an invaluable resource. This title is also available as Open Access on Cambridge Core.
Presents material in an accessible, self-contained and concise yet rigorous way, with numerous figures and illustrations complementing the text
Covers methods and ideas that have not previously appeared in book form
Contains more than 250 exercises, with complete solutions to all problems freely available online, along with the R code to generate all the figures
This book is also available as open access
Acknowledgements
1. Introduction
2. Linear models and ordinary least squares
3. High-dimensional linear regression
4. Kernel density estimation
5. Nonparametric regression
6. Reproducing kernel Hilbert spaces and kernel machines
7. Conditional independence, graphical models and causality
8. Minimax lower bounds
9. Shape-constrained estimation
Appendix. Basic tools
References
Index.
Copyright 2026
Hardback
ISBN 9780367702335
1104 Pages 224 Color Illustrations
June 10, 2026 by Chapman & Hall
This handbook presents a thorough introduction to current topics of mathematical research in combinatorial algebraic geometry. The editors’ aim is to introduce researchers to key literature from the past 20-30 years needed to address open questions in the field. The chapters give concrete, computational examples of Lie-theoretic and combinatorial tools applied to the geometry of flag varieties and their subvarieties.
Lie theory provides a common language for the articles in this text, so while chapters are self-contained, it is recommended readers have some prior familiarity with the foundations of the subject. Each chapter benefits multiple sets of readers including:
Graduate students seeking to conduct research in algebraic combinatorics and Lie theory. New researchers will be introduced to relevant techniques used to prove key results and gain insight from leading researchers into the context of these results.
Experts in the field seeking insights and exposure to techniques and the finer expository points of related topics.
Mathematicians looking for a centralized reference on the geometry and combinatorics of flag varieties.
The topics of this handbook break down into four sections. The first section of this book consists of an introduction to the cohomology of flag varieties, Schubert varieties, and Schubert polynomials. The second section explores subvarieties of the flag variety that generalize or complement Schubert varieties in various ways. The third section of the book focuses on Hessenberg varieties. Finally, the last section explores additional topics related to flag varieties.
Last, the editors include a brief word about a few things this book does not do. Although great care is taken to streamline notation, the avid reader will still find variation throughout the chapters. This is reflective of, and prepares the reader for, the state of the field. For example, different notations for Richardson varieties typically appear in work on positivity than in other subfields of combinatorial algebraic geometry.
The editors and contributors hope readers find this book useful and enjoyable.
Part 1: Flag varieties and Schubert varieties
1. Introduction to the Cohomology of the Flag Variety
Sara C. Billey, Yibo Gao, and Brendan Pawlowski
Part 2: Subvarieties of the flag variety
2. Schubert Geometry and Combinatorics
Alexander Woo and Alexander Yong
3. Richardson varieties, projected Richardson varieties and positroid varieties
David E Speyer
4. Torus orbit closures in the flag variety
Eunjeong Lee, Mikiya Masuda, and Seonjeong Park
5. Pattern avoidance and K-orbit closures
William M. McGovern
Part 3: Hessenberg Varieties
6. An Introduction to Hessenberg Varieties
Julianna Tymoczko
7. The cohomology rings of regular nilpotent Hessenberg varieties
Megumi Harada and Tatsuya Horiguchi
8. Hessenberg varieties and algebraic combinatorics of hyperplane arrangements
Satoshi Murai
9. Combinatorics and Hessenberg Varieties
John Shareshian and Michelle L. Wachs
Part 4: Additional topics
10. Generalizations of the flag variety tied to the Macdonald-theoretic delta operators
Brendon Rhoades
11. Nil-Hecke rings and Schubert calculus
Edward Richmond and Kirill Zainoulline
12. Coxeter groups and Billey–Postnikov decompositions
Suho Oh and Edward Richmond
Copyright 2027
Hardback
ISBN 9780367500986
360 Pages 4 Color & 48 B/W Illustrations
August 17, 2026 by Chapman & Hall
Design of experiments is, in essence, a disciplined way to learn about cause and effect. Modern experiments can involve a few to millions of units and hundreds or thousands of covariates. These settings demand tools that are flexible, transparent, and faithful to the underlying design in order reach reliable conclusions about which interventions work and which ones do not. This book provides a modern, accessible, and computationally supported introduction to experimental design grounded firmly in randomization and the formulation of ideas and methods in terms of potential outcomes. Instead of prescribing a model for each design, we begin with the treatment assignment mechanism and link it directly to the observed outcomes through the potential outcomes framework. This formulation illuminates how changing the design changes the analysis, and it naturally distinguishes finite-population inference from super-population modeling. The book also incorporates new developments at the interface of causal inference and experimental design, many stemming from the authors’ recent collaborative research efforts.
Strengthens the link between design and analysis, enabling students to see immediately how the structure of an experiment shapes the exact tools used to analyze it.
Teaches foundational concepts without assuming linear-model assumptions.
Equips readers with the tools needed to analyze non-standard and complex experiments, whose randomization mechanisms fall outside the scope of traditional textbooks.
Support students with limited programming experience by providing algorithms and code throughout the book, enabling them to implement randomization-based methods easily and efficiently.
This book is a textbook for one/two semester course on introductory experimental design.
Preface Symbols 1. Understanding experimental design: fundamental concepts, terminology and examples 2. CRD with one factor, two levels 3. Better comparisons using blocking 4. Beyond blocking: acceptable versus unacceptable randomizations 5. Randomized experiments with J(> 2) treatment arms 6. The 22 factorial experiment 7. 2K factorial designs 8. Design and analysis of factorial experiments with constraints 9. Model-based analysis of designed experiments and superpopulation inference 10. Including covariates in the design, model-based analysis and subsequent inference Appendix Bibliography
Copyright 2027
Hardback
ISBN 9781041152774
292 Pages 21 Color & 18 B/W Illustrations
August 10, 2026 by Chapman & Hall
This book provides a concise account of four components of regression and smoothing methods: linear regression, generalized linear models, spline and kernel methods, and generalized linear mixed models. By bringing together parametric regression and nonparametric smoothing methods, the book emphasizes connections across methods, enabling readers to recognize common structures and to adapt techniques to new problems.
While standard texts often focus on the application of statistical methods from a user's perspective, this book covers the foregoing topics from a developer's perspective, with systematic attention to the mathematical, statistical, and computational ideas and results that underlie the methods. The distinction is analogous to that between a user’s manual and a developer’s manual for software: the goal is not only to demonstrate how to apply the methods, but also how they are derived and implemented.
Assuming a basic knowledge of undergraduate statistics, the book is intended primarily as a graduate textbook for the teaching and studying regression and smoothing methods. It serves as a useful resource for students and researchers in Statistics, Data Science, and related fields who wish to move beyond routine application and study modern regression and smoothing methods at a more advanced level.
Focuses on core and representative topics in regression and smoothing while addressing important methodological issues often omitted at the introductory level.
Presents regression and smoothing methods in a coherent, interconnected manner that highlights their common structures and relationships.
Explains and demonstrates numerical algorithms in a self-contained way, with R code that implements the methods directly rather than solely relying on existing packages.
Reinforces learning through not only end-of-chapter exercises but also questions and exercises integrated into the main text.
Preface 1 Linear regression 2 Generalized linear regression 3 Smoothing methods: Splines and kernels 4 Generalized linear mixed regression Bibliography Index