Part of Mathematical Sciences Research Institute Publications
available from June 2019
FORMAT: Hardback ISBN: 9781108485807
This book surveys the state-of-the-art in the theory of combinatorial games, that is games not involving chance or hidden information. Enthusiasts will find a wide variety of exciting topics, from a trailblazing presentation of scoring to solutions of three piece ending positions of bidding chess. Theories and techniques in many subfields are covered, such as universality, Wythoff Nim variations, misere play, partizan bidding (a.k.a. Richman games), loopy games, and the algebra of placement games. Also included are an updated list of unsolved problems, extremely efficient algorithms for taking and breaking games, a historical exposition of binary numbers and games by David Singmaster, chromatic Nim variations, renormalization for combinatorial games, and a survey of temperature theory by Elwyn Berlekamp, one of the founders of the field. The volume was initiated at the Combinatorial Game Theory Workshop, January 2011, held at the Banff International Research Station.
Features a survey by Elwyn Berlekamp on temperature theory
Presents seminal research on the notion of universality of a ruleset of combinatorial games
Includes the first comprehensive survey of games and sequences related to Wythoff Nim and complementary Beatty sequences
1. About this book Urban Larsson
2. Temperatures of games and coupons Elwyn Berlekamp
3. Wythoff visions Eric Duchene, Aviezri Fraenkel, Vladimir Gurvich, Nhan Ho, Clark Kimberling and Urban Larsson
4. Scoring games: the state of play Urban Larsson, Richard Nowakowski and Carlos Pereira dos Santos
5. Restricted developments in partizan misere game theory Rebecca Milley and Gabriel Renault
6. Unsolved problems in combinatorial games Richard Nowakowski
7. Misere games and misere quotients Aaron Siegel
8. An historical tour of binary and tours David Singmaster
9. A note on polynomial profiles of placement games J. I. Brown, D. Cox, A. Hoefel, Neil McKay, Rebecca Milley, Richard Nowakowski and Angela A. Siegel
10. A PSPACE-complete Graph Nim Kyle Burke and Olivia George
11. A nontrivial surjective map onto the short Conway group Alda Carvalho and Carlos Pereira dos Santos
12. Games and complexes I: transformation via ideals Sara Faridi, Svenja Huntemann and Richard Nowakowski
13. Games and complexes II: weight games and Kruskal-Katona type bounds Sara Faridi, Svenja Huntemann and Richard Nowakowski
14. Chromatic Nim finds a game for your solution Mike Fisher and Urban Larsson
15. Take-away games on Beatty's theorem and the notion of k-invariance Aviezri Fraenkel and Urban Larsson
16. Geometric analysis of a generalized Wythoff game Eric Friedman, Scott M. Garrabrant, Ilona Phipps-Morgan, Adam S. Landsberg and Urban Larsson
17. Searching for periodicity in officers J. P. Grossman
18. Good pass moves in no-draw HyperHex: two proverbs Ryan Hayward
19. Conjoined games: Go-Cut and Sno-Go Melissa Huggan and Richard Nowakowski
20. Impartial games whose rulesets produce continued fractions Urban Larsson and Mike Weimerskirch
21. Endgames in bidding chess Urban Larsson and Johan Wastlund
22. Phutball draws Sucharit Sarkar
23. Scoring play combinatorial games Fraser Stewart
24. Generalized misere play Mike Weimerskirch.
Part of Institute of Mathematical Statistics Textbooks
available from September 2019
FORMAT: Hardback ISBN: 9781108476591
FORMAT: Paperback ISBN: 9781108701112
This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Lof in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters.
Expands and extends the theory and application of exponential families within one concise volume
Uses recurrent themes in examples and exercises to build familiarity with the models
Gives a concise account of the philosophy of Per Martin-Lof, connecting statistical modelling with ideas in statistical physics
Preface
1. Random walks on graphs
2. Uniform spanning tree
3. Percolation and self-avoiding walk
4. Association and influence
5. Further percolation
6. Contact process
7. Gibbs states
8. Random-cluster model
9. Quantum Ising model
10. Interacting particle systems
11. Random graphs
12. Lorentz gas
References
Index.
available from October 2019
FORMAT: Hardback ISBN: 9781108424189
FORMAT: Paperback ISBN: 9781108439534
Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed 'scratch work' sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians.
Perfect for self-study, an introduction to proofs course, or as a supplementary text for a discrete mathematics course or foundations of computing course
Systematic and thorough, showing how several techniques can be combined to construct a complex proof
Covers logic, set theory, relations, functions, and cardinality
1. Sentential logic
2. Quantificational logic
3. Proofs
4. Relations
5. Functions
6. Mathematical induction
7. Number theory
8. Infinite sets.
Part of London Mathematical Society Lecture Note Series
available from September 2019
FORMAT: Paperback ISBN: 9781108740722
This volume contains eight survey articles based on the invited lectures given at the 27th British Combinatorial Conference, held at the University of Birmingham in July 2019. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, cryptography, matroids, incidence geometries and graph limits. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.
Includes eight survey articles by world-leading researchers in combinatorics
Summarises the current state of the field
Accessible to non-experts, assuming little prior knowledge
1. Clique-width for hereditary graph classes Konrad K. Dabrowski, Matthew Johnson and Dani„vl Paulusma
2. Analytic representations of large graphs Andrzej Grzesik and Daniel Kral
3. Topological connectedness and independent sets in graphs Penny Haxell
4. Expanders ? how to find them, and what to find in them Michael Krivelevich
5. Supersingular isogeny graphs in cryptography Kristin E. Lauter and Christophe Petit
6. Delta-matroids for graph theorists Iain Moffatt
7. Extremal theory of vertex or edge ordered graphs Gabor Tardos
8. Some combinatorial and geometric constructions of spherical buildings Hendrik Van Maldeghem and Magali Victoor.
Part of Cambridge Studies in Advanced Mathematics
available from December 2019 FORMAT:
HardbackISBN: 9781108476355
Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several areas of pure and applied mathematics, with applications to many areas such as quantum control, Hamiltonian dynamics, robotics and Lie theory. This comprehensive introduction proceeds from classical topics to cutting-edge theory and applications, assuming only standard knowledge of calculus, linear algebra and differential equations. The book may serve as a basis for an introductory course in Riemannian geometry or an advanced course in sub-Riemannian geometry, covering elements of Hamiltonian dynamics, integrable systems and Lie theory. It will also be a valuable reference source for researchers in various disciplines.
Provides a comprehensive and systematic presentation of sub-Riemannian geometry
Accessible to graduate students with no prior knowledge of the subject
Contains useful models and tools for researchers working in various areas of application, including robotics, quantum control and image processing
Introduction
1. Geometry of surfaces in R^3
2. Vector fields
3. Sub-Riemannian structures
4. Pontryagin extremals: characterization and local minimality
5. First integrals and integrable systems
6. Chronological calculus
7. Lie groups and left-invariant sub-Riemannian structures
8. End-point map and exponential map
9. 2D almost-Riemannian structures
10. Nonholonomic tangent space
11. Regularity of the sub-Riemannian distance
12. Abnormal extremals and second variation
13. Some model spaces
14. Curves in the Lagrange Grassmannian
15. Jacobi curves
16. Riemannian curvature
17. Curvature in 3D contact sub-Riemannian geometry
18. Integrability of the sub-Riemannian geodesic flow on 3D Lie groups
19. Asymptotic expansion of the 3D contact exponential map
20. The volume in sub-Riemannian geometry
21. The sub-Riemannian heat equation
Appendix. Geometry of parametrized curves in Lagrangian Grassmannians with Igor Zelenko
References
Index.