Part of Cambridge Studies in Advanced Mathematics
DATE PUBLISHED: August 2023
Paperback ISBN: 9781009262484
Part of Cambridge Studies in Advanced Mathematics
FORMAT: HardbackISBN: 9781009262491
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson?Schensted?Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood?Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.
New edition includes over 150 new exercises on symmetric functions, most with solutions
Shows the broad applicability of the material to many other areas of mathematics
Features a section with 66 combinatorial interpretations of Catalan numbers that will appeal to amateur as well as professional mathematicians
'This is one of the great books; readable, deep and full of gems. It brings algebraic combinatorics to life. I teach out of it and feel that if I can get my students to 'touch Stanley' I have given them a gift for life.' Persi Diaconis, Stanford University
'It is wonderful to celebrate the completion of the second edition of Richard Stanley's Enumerative Combinatorics, one of the finest mathematical works of all time. He has added nearly 200 exercises, together with their answers, to what was already a uniquely masterful summary of a vast and beautiful theory. When paired with the second edition of Volume 1, his two classic volumes will surely be a timeless treasure for generations to come.' Donald E. Knuth, Stanford University
'An updated classic with a mesmerizing array of interconnected examples. Through Stanley's masterful exposition, the current and future generations of mathematicians will learn the inherent beauty and pleasures of enumeration.' June Huh, Princeton University
'I have used Richard Stanley's books on Enumerative Combinatorics numerous times for the combinatorics classes I have taught. This new edition contains many new exercises, which will no doubt be extremely useful for the next generation of combinatorialists.' Anne Schilling, University of California, Davis
'Richard Stanley's Enumerative Combinatorics, in two volumes, is an essential reference for researchers and graduate students in the field of enumeration. Volume 2, newly revised, includes comprehensive coverage of composition and inversion of generating functions, exponential and algebraic generating functions, and symmetric functions. The treatment of symmetric functions is especially noteworthy for its thoroughness and accessibility. Engaging problems and solutions, and detailed historical notes, add to the value of this book. It provides an excellent introduction to the subject for beginners while also offering advanced researchers new insights and perspectives.' Ira Gessel, Brandeis University
Preface to Second Edition
Preface
5. Trees and the Composition of Generating Functions
6. Algebraic Generating Functions
7. Symmetric Functions
Appendices: References
Index.
Copyright 2024
Hardback
ISBN 9781032561714
492 Pages 4 B/W Illustrations
October 6, 2023 by Chapman & Hall
This book describes in detail the basic context of the Banach setting and the most important Lie structures found in finite dimension. The authors expose these concepts in the convenient framework which is a common context for projective and direct limits of Banach structures. The book presents sufficient conditions under which these structures exist by passing to such limits. In fact, such limits appear naturally in many mathematical and physical domains. Many examples in various fields illustrate the different concepts introduced.
Many geometric structures, existing in the Banach setting, are "stable" by passing to projective and direct limits with adequate conditions. The convenient framework is used as a common context for such types of limits. The contents of this book can be considered as an introduction to differential geometry in infinite dimension but also a way for new research topics.
This book allows the intended audience to understand the extension to the Banach framework of various topics in finite dimensional differential geometry and, moreover, the properties preserved by passing to projective and direct limits of such structures as a tool in different fields of research.
Copyright 2024
Hardback
ISBN 9781032133409
Paperback
ISBN 9781032606989
376 Pages 191 B/W Illustrations
January 23, 2024 by Chapman & Hall
Graphs & Digraphs, Seventh Edition masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory.
This classic text, widely popular among students and instructor alike for decades, is thoroughly streamlined in this new, seventh edition, to present a text consistent with contemporary expectations.
Changes and updates to this edition include:
A rewrite of four chapters from the ground up.
Streamlining by over a third for efficient, comprehensive coverage of graph theory.
Flexible structure with foundational Chapters 1-6 and customizable topics in Chapters 7-11.
Incorporation of the latest developments in fundamental graph theory.
Statements of recent groundbreaking discoveries, even if proofs are beyond scope.
Completely reorganized chapters on traversability, connectivity, coloring, and extremal graph theory to reflect recent developments.
The text remains the consummate choice for an advanced undergraduate level or introductory graduat-level course exploring the subjectfs fascinating history while covering a host of interesting problems and diverse applications.
Our major objective remains to introduce and treat graph theory as the beautiful area of mathematics we have always found it to be. We have striven to produce a reader-friendly, carefully written book that emphasizes the mathematical theory of graphs, in all their forms. While a certain amount of mathematical maturity, including a solid understanding of proof, is required to appreciate the material, with a small number of exceptions this is the only pre-requisite.
In addition, owing to the exhilarating pace of progress in the field, there have been countless developments in fundamental graph theory even since the previous edition and many of these discoveries have been incorporated into the book. Of course, some of the proofs of these results are beyond the scope of the book, in which cases we have only included their statements. In other cases, however, these new results have led us to completely reorganize our presentation. Two examples are the chapters on coloring and extremal graph theory.
At the end of the book are indices and lists of mathematiciansf names, terms, symbols, and useful references. There is also a section giving hints and solutions to all odd-numberedselected exercises. A complete solutions manual is available with qualifying course adoption.
Copyright 2024
Hardback
ISBN 9781032584041
370 Pages
December 6, 2023 by Chapman & Hall
The Grothendieck construction provides an explicit link between indexed categories and opfibrations. It is a fundamental concept in category theory and related fields with far reaching applications. Bipermutative categories are categorifications of rings. They play a central role in algebraic K-theory and infinite loop space theory.
This monograph is a detailed study of the Grothendieck construction over a bipermutative category in the context of categorically enriched multicategories, with new and important applications to inverse K-theory and pseudo symmetric E-algebras. After carefully recalling preliminaries in enriched categories, bipermutative categories, and enriched multicategories, we show that the Grothendieck construction over a small tight bipermutative category is a pseudo symmetric Cat-multifunctor and generally not a Cat-multifunctor in the symmetric sense. Pseudo symmetry of Cat-multifunctors is a new concept we introduce in this work.
The following features make it accessible as a graduate text or reference for experts:
Complete definitions and proofs.
Self-contained background. Parts of Chapters 1?3, 7, 9, and 10 contain background material from the research literature.
Extensive cross-references.
Connections between chapters. Each chapter has its own introduction discussing not only the topics of that chapter but also its connection with other chapters.
Open questions. Appendix A contains open questions that arise from the material in the text and are suitable for graduate students.
This book is suitable for graduate students and researchers with an interest in category theory, algebraic K-theory, homotopy theory, and related fields. The presentation is thorough and self-contained, with complete details and background material for non-expert readers.
Part I: Bipermutative Categories, Enriched Multicategories, and Pseudo Symmetry
Chapter 1: Preliminaries on Enriched Categories and 2-Categories
Chapter 2: Symmetric Bimonoidal and Bipermutative Categories
Chapter 3: Enriched Multicategories and Multiequivalences
Chapter 4: Pseudo Symmetry
Part II: Grothendieck Multiequivalence from Bipermutative-Indexed Categories to Permutative Opfibrations
Chapter 5: Enriched Multicategories of Indexed Categories
Chapter 6: The Grothendieck Construction is a Pseudo Symmetric Cat-Multifunctor
Chapter 7: Permutative Opfibrations from Bipermutative-Indexed Categories
Chapter 8: The Grothendieck Construction is a Cat-Multiequivalence
Part III: Pseudo Symmetric Enriched Multifunctorial Inverse K-Theory
Chapter 9: The Cat-Multifunctor A
Chapter 10: Inverse K-Theory is a Pseudo Symmetric Cat-Multifunctor
Appendix A: Open Questions
Appendix B: List of Main Facts
Bibliography
Index
Not yet published - available from October 2023
FORMAT: Paperback ISBN: 9781108435543
This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.
Multidisciplinary, with contributions from leading philosophers, logicians and linguists
Includes both criticism and defense of the semantic tradition and its applications
Demonstrates the breadth and depth of the semantic conception and traces its influence in a number of different areas
Introduction: The Semantic Conception of Logic: Problems and Prospects Gil Sagi and Jack Woods
Part I. Invariance Criteria for Logicality:
1. Invariance and Logicality in Perspective Gila Sher
2. The Problem of Logical Constants and the Semantic Tradition: From Invariantist Views to a Pragmatic Account Mario Gomez-Torrente
3. The Ways of Logicality: Invariance and Categoricity Denis Bonnay and Sebastian G. W. Speitel
4. Invariance without Extensionality Beau Madison Mount
5. There Might Be a Paradox of Logical Validity After All Roy Cook
Part II. Critiques and Applications of the Semantic Approach:
6. Semantic Perspectives in Logic Johan van Benthem
7. Overgeneration in the Higher Infinite Luca Incurvarti and Salvatore Florio
8. Propositional Logics of Logical Truth A.C. Paseau and Owen Griffiths
9. Reinterpreting Logic Alexandra Zinke
Part III. Logic and Natural Language:
10. Models, Model Theory, and Modeling Michael Glanzberg
11. On Being Trivial: Grammar vs. Logic Gennaro Chierchia
12. Grammaticality and Meaning Shift Marta Abrusan, Nicholas Asher and Tim Van de Cruys
Bibliography
Index.
Not yet published - available from September 2023
FORMAT: Hardback ISBN: 9781009437189
How should we treat the liar and kindred paradoxes? A Theory of Truth argues that we should diverge from classical logic, and presents a new formal theory of truth. The theory does not incorporate contradictions and is not substructural, but deviates from classical logic significantly, and endorses principles like 'No sentence is both true and false' and 'No sentence is neither true nor false'. The book starts with an introduction to the paradoxes, suitable for newcomers to the subject, before presenting its approach. Four versions of the theory are covered, extending the theory to a determinacy operator and to a full first-order language with quantifiers. Each includes all Tarskian biconditionals that can be formulated in its language. The author uses original methods to prove the consistency of each version and compares the theory to alternative non-classical theories, including Field's paracomplete approach, Ripley's nontransitive system and Zardini's contraction-free calculus.
Presents theories of truth using non-classical logic, from both formal and philosophical viewpoints
Contains a new and original framework for the theory of truth, as well as original ways of proving key theorems
Assumes no previous familiarity with the semantic paradoxes and begins with an introduction to the subject
1. Aspects of paradox
2. Against classical logic
3. Ambiguity and indexicality
4. A propositional theory of truth
5. Proving central theorem 1
6. Truth and determinacy
7. A first-order logic and theory of truth
8. Proving central theorem 4
9. Another first-order theory of truth
10. Truth in different non-classical logics
Afterword
References
Index.
Not yet published - available from December 2023
FORMAT: Hardback ISBN: 9781009278904
A large international conference celebrated the 50-year career of Anatole Katok and the body of research across smooth dynamics and ergodic theory that he touched. In this book many leading experts provide an account of the latest developments at the research frontier and together set an agenda for future work, including an explicit problem list. This includes elliptic, parabolic, and hyperbolic smooth dynamics, ergodic theory, smooth ergodic theory, and actions of higher-rank groups. The chapters are written in a readable style and give a broad view of each topic; they blend the most current results with the developments leading up to them, and give a perspective on future work. This book is ideal for graduate students, instructors and researchers across all research areas in dynamical systems and related subjects.
Written by a broad range of leading experts, providing a wide and specialized perspective on the discipline
Presents results from the current forefront of dynamical systems, setting an agenda for future research
Inspired by the Legacy of Professor Anatole Katok, presenting his pivotal research and celebrating his contribution to the field
Contents
Editors note
1. Rigidity of topological entropy of boundary maps associated to Fuchsian groups
2. Open problems from 2020 vision for dynamics conference in Bedlewo
3. Flexibility of entropies for piecewise expanding unimodalm maps
4. Recent results and open questions on pseudo-rotations
5. SRB and equilibrium measures via dimension theory
6. Abelian Livshits theorems and geometric applications
7. A dynamical approach to validated numerics
8. Non-stationary normal forms for contracting extensions
9. Survey on entropy-type invariants of sub-exponential growth in dynamical systems
10. On the smooth realization problem and the AbC method
11. On some spectral problems in ergodic theory
12. Area preserving surface diffeomorphisms with polynomial decay of Correlation's are ubiquitous 13. Linear cocycles over hyperbolic system