Part of Acta Numerica
DATE PUBLISHED: December 2021
AVAILABILITY: In stock
FORMAT: Hardback
ISBN: 9781009098977
Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.
The latest issue of the leading review in mathematics as measured by Impact factor
Outstanding contributors provide state-of-art surveys in important topics of contemporary interest
Covers a broad range of fields from data-driven science, to engineering, to computational physics
LENGTH: 864 pages DIMENSIONS: 254 x 181 x 37 mm
WEIGHT: 1.67kg
1. Numerical homogenization beyond scale separation Robert Altmann, Patrick Henning and Daniel Peterseim
2. Deep learning: a statistical viewpoint Peter L. Bartlett, Andrea Montanari and Alexander Rakhlin
3. Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation Mikhail Belkin
4. Optimal transportation, modelling and numerical simulation Jean-David Benamou
5. Neural network approximation Ronald DeVore, Boris Hanin and Guergana Petrova
6. Learning physics-based models from data: perspectives from inverse problems and model reduction Omar Ghattas and Karen Willcox
7. Tensors in computations Lek-Heng Lim
8. Modelling and computation of liquid crystals Wei Wang, Lei Zhang and Pingwen Zhang.
PUBLICATION PLANNED FOR: February 2022
AVAILABILITY: Not yet published - available from February 2022
FORMAT: Hardback ISBN: 9781108834315
In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical ? as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.
Concisely reviews and compares different versions of Potentialist set theory
Sheds new light on the relationship between mathematics and logic by taking a potentialist approach to set theory
Connects the philosophy of set theory to philosophy of language, metaontology and philosophy of science
LENGTH: 288 pages DIMENSIONS: 244 x 170 mm
AVAILABILITY: Not yet published - available from February 2022
PUBLICATION PLANNED FOR: May 2022 AVAILABILITY: Not yet published - available from May 2022
FORMAT: Hardback ISBN: 9781316518618
Written for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincare invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.
A comprehensive introduction to uses of groups, algebras, and topology in modern physics, written at a level suitable for both advanced undergraduate and graduate students
Provides a broader and more integrated view of current applications in modern physics of groups, algebras, and topology, reflective of the authors' own research and teaching experience
Supports both instructors and students in teaching and learning through the inclusion of 344 worked problems with full solutions
LENGTH: 600 pages DIMENSIONS: 246 x 189 mm
AVAILABILITY: Not yet published - available from May 2022
Part of London Mathematical Society Student Texts
PUBLICATION PLANNED FOR: June 2022AVAILABILITY: Not yet published - available from June 202
2FORMAT: Hardback ISBN: 9781316516331
Stochastic games are have an element of chance: the state of the next round is determined probabilistically depending upon players' actions and the current state. Successful players need to balance the need for short-term payoffs while ensuring future opportunities remain high. The various techniques needed to analyze these often highly non-trivial games are a showcase of attractive mathematics, including methods from probability, differential equations, algebra, and combinatorics. This book presents a course on the theory of stochastic games going from the basics through to topics of modern research, focusing on conceptual clarity over complete generality. Each of its chapters introduces a new mathematical tool ? including contracting mappings, semi-algebraic sets, infinite orbits, and Ramsey's theorem, among others ? before discussing the game-theoretic results they can be used to obtain. The author assumes no more than a basic undergraduate curriculum and illustrates the theory with numerous examples and exercises, with solutions available online.
Suitable for beginning graduate students and other newcomers to stochastic games
Emphasizes core mathematical techniques over best-possible results
Contains numerous worked examples and 150 exercises, with solutions online
PUBLICATION PLANNED FOR: June 2022
FORMAT: Hardback ISBN: 9781316516331
FORMAT: Paperback ISBN: 9781009014793
LENGTH: 275 pages DIMENSIONS: 229 x 152 mm
AVAILABILITY: Not yet published - available from June 2022
Introduction
1. Markov decision problems
2. A Tauberian theorem and uniform ƒÃ-optimality in hidden Markov decision problems
3. Strategic-form games ? a review
4. Stochastic games ? the model
5. Two-player zero-sum discounted games
6. Semi-algebraic sets and the limit of the discounted value
7. B-Graphs and the continuity of the limit $\lim_{\lambda \to 0} v_\lambda(s
q,r)$
8. Kakutani's fixed-point theorem and multi-player discounted stochastic games
9. Uniform equilibrium
10. The vanishing discount factor approach and uniform equilibrium in absorbing games
11. Ramsey's theorem and two-player deterministic stopping games
12. Infinite orbits and quitting games
13. Linear complementarity problems and quitting games
References
Index.
**
Part of Cambridge Tracts in Mathematics
PUBLICATION PLANNED FOR: July 2022
AVAILABILITY: Not yet published - available from July 2022
FORMAT: HardbackI SBN: 9781316511893
This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.
The first book to study large deviations for Markov chains in depth in the framework of the theory of irreducible kernels on a general state space. The relevant aspects of this theory are presented in several appendices
An essential role is played by irreducibility, its consequences, and its derivative notions, such as the convergence parameter of an irreducible kernel
Many results in the book have not previously appeared in the literature ? this includes new results on uniformity sets and the role of invariant distributions
PUBLICATION PLANNED FOR: July 2022
FORMAT: HardbackI SBN: 9781316511893
LENGTH: 230 pagesDIMENSIONS: 229 x 152 mm
AVAILABILITY: Not yet published - available from July 2022
Preface
1. Introduction
2. Lower bounds and a property of lambda
3. Upper bounds I
4. Identification and reconciliation of rate functions
5. Necessary conditions ? bounds on the rate function, invariant measures, irreducibility and recurrence
6. Upper bounds II ? equivalent analytic conditions
7. Upper bounds III ? sufficient conditions
8. The large deviations principle for empirical measures
9. The case when S is countable and P is matrix irreducible
10. Examples
11. Large deviations for vector-valued additive functionals
Appendix A - K
Appendix B
References
Author index
Subject index.