Part of London Mathematical Society Lecture Note Series
Not yet published - available from May 2024
FORMAT: Paperback
ISBN: 9781009490535
This volume contains nine survey articles by the invited speakers of the 30th British Combinatorial Conference, held at Queen Mary University of London in July 2024. Each article provides an overview of recent developments in a current hot research topic in combinatorics. Topics covered include: Latin squares, Erd?s covering systems, finite field models, sublinear expanders, cluster expansion, the slice rank polynomial method, and oriented trees and paths in digraphs. 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 nine 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. Intersection theory of matroids: variations on a theme Federico Ardila-Mantilla
2. Erd?s covering systems Paul Balister
3. The cluster expansion in combinatorics Matthew Jenssen
4. Sublinear expanders and their applications Shoham Letzter
5. Transversals in Latin squares Richard Montgomery
6. Finite field models in arithmetic combinatorics -twenty years on Sarah Peluse
7. The slice rank polynomial method - a survey a few years later Lisa Sauermann
8. An introduction to transshipments over time Martin Skutella
9. Oriented trees and paths in digraphs Maya Stein.
Not yet published - available from July 2024
FORMAT: Paperback
ISBN: 9781009430890
Description
'Functional Analysis Revisited' is not a first course in functional analysis -although it covers the basic notions of functional analysis, it assumes the reader is somewhat acquainted with them. It is by no means a second course either: there are too many deep subjects that are not within scope here. Instead, having the basics under his belt, the author takes the time to carefully think through their fundamental consequences. In particular, the focus is on the notion of completeness and its implications, yet without venturing too far from areas where the description 'elementary' is still valid. The author also looks at some applications, perhaps just outside the core of functional analysis, that are not completely trivial. The aim is to show how functional analysis influences and is influenced by other branches of contemporary mathematics. This is what we mean by 'Functional Analysis Revisited.'
Helps the reader gain a deeper understanding of functional analysis and its applications with accessible step-by-step explanations and examples
Demonstrates how the fundamental notion of completeness permeates contemporary mathematics
Reinforces learning with short chapter summaries and a variety of thoughtfully designed standard and nonstandard exercises
Table of contents
Introduction
1. Complete metric spaces
2. Banach's principle
3. Picard's theorem
4. Banach spaces
5. Renewal equation in the McKendrick-Von Foerster model
6. Riemann integral for vector-valued functions
7. The Stone-Weierstrass theorem
8. Norms do differ
9. Hilbert spaces
10. Complete orthonormal sequences
11. Heat equation
12. Completeness of the space of operators
13. Working in L(X)
14. The Banach-Steinhaus theorem and strong convergence
15. We go deeper, deeper we go (into the structure of complete spaces)
16. Semigroups of operators
Appendix. Two consequences of the Hahn-Banach theorem
References
Index.
Not yet published - available from July 2024
FORMAT: PaperbackI
SBN: 9781009434096
Supersymmetry, strings and branes are believed to be the essential ingredients in a single unified consistent theory of physics. This book gives a detailed, step-by-step introduction to the theoretical foundations required for research in strings and branes. After a study of the different formulations of the bosonic and supersymmetric point particles, the classical and quantum bosonic and supersymmetric string theories are presented. This book includes accounts of brane dynamics and D-branes and the T, S and U duality symmetries of string theory. The historical derivation of string theory is given as well as the sum over the world-sheet approach to the interacting string. More advanced topics include string field theory and Kac?Moody symmetries. The book contains pedagogical accounts of conformal quantum field theory, supergravity theories, Clifford algebras and spinors, and Lie algebras. It is essential reading for graduate students and researchers wanting to learn strings and branes.
Introduces the theoretical foundations required for research in strings and branes
Gives a pedagogical account of supergravity theories, Lie algebras and Clifford algebras
Covers advanced topics such as string field theory and Kac-Moody symmetries
Preface
1. The point particle
2. The classical bosonic string
3. The quantum bosonic string
4. The light-cone approach
5. Clifford algebras and spinors
6. The classical superstring
7. The quantum superstring
8. Conformal symmetry and two-dimensional field theory
9. Conformal symmetry and string theory
10. String compactification and the heterotic string
11. The physical states and the no ghost theorem
12. Gauge covariant string theory
13. Supergravity theories in 4, 10 and 11 dimensions
14. Brane dynamics
15. D-branes
16. String theory and Lie algebras
17. Symmetries of string theory
18. String interactions
Appendices
Index.
Part of Cambridge Introductions to Philosophy
Not yet published - available from August 2024
FORMAT: HardbackISBN: 9781009450690
FORMAT: PaperbackISBN: 9781009450676
Classical logic - which studies the structural features of purported claims of fact - and modal logic - which studies relations of necessity and possibility -are different but complementary areas of logical thought. In this lively and accessible textbook, Adam Bjorndahl provides a comprehensive and unified introduction to the two subjects, treating them with the same level of rigour and detail and showing how they fit together. The core material appears in the main text, with hundreds of supplemental examples, comments, clarifications, and connections presented throughout in easy-to-read sidenotes, giving the book a distinct conversational feel. A detailed, multi-part appendix covers important background mathematical material that some students may lack, such as induction or the concept of countable infinity. A fully self-contained learning resource, this book will be ideal for a semester-long upper-level university course on either or both of the topics.
Includes a detailed, multi-section appendix covering all the relevant background material, with appropriate pointers to the appendix throughout the text
Strikes a balance between being too philosophical, skirting technical details, or too technical, and gives the reader all the formal tools and knowledge they need to fully understand the mathematical details and import of the topic
Designed to be accessible without skipping any of the core mathematical details
Introduction: what is logic?
1. Classical propositional logic
2. Classical predicate logic
3. Modal logic
4. Group knowledge
5. Topological semantics
A Mathematical tools & techniques
B Selected solutions.
Part of Cambridge Tracts in Theoretical Computer Science
Not yet published - available from September 2024
FORMAT: Hardback
ISBN: 9781108835466
Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgebras obtained by limits of canonical chains, and initial algebras obtained by colimits. These constructions are also developed in enriched settings, especially complete partial orders and complete metric spaces, connecting the book to topics like domain theory. Also included are an extensive treatment of set functors, and the first book-length presentation of the rational fixed point of a functor, and of lifting results which connect fixed points of set functors with fixed points on other categories. Representing more than fifteen years of work, this will be the leading text on the subject for years to come.
Represents more than 15 years of work by this team of authors and will be the leading text on its topics for years to come
Covers topics including the iterative method of constructing initial algebras and terminal coalgebras, transfinite constructions, the limit-colimit coincidence in enriched settings, corecursive algebras and well-founded coalgebras, on the rational fixed point and on liftings
Includes appendices on the most common fixed point theorems and on properties of set functors
Contains nearly all of the needed definitions and pointers to the literature on basic material to remain accessible to a wide readership
1. Introduction
2. Algebras and coalgebras
3. Finitary iteration
4. Finitary set functors
5. Finitary iteration in enriched settings
6. Transfinite iteration
7. Terminal coalgebras as algebras, initial algebras as coalgebras
8. Well-founded coalgebras
9. State minimality and well-pointed coalgebras
10. Fixed points determined by finite behaviour
11. Sufficient conditions for initial algebras and terminal coalgebras
12. Liftings and extensions from Set
13. Interaction between initial algebras and terminal coalgebras
14. Derived functors
15. Special topics
A. Functors with initial algebras or terminal coalgebras
B. A primer on fixed points in ordered and metric structures
C. Set functors
References
Index of categories
Subject index.