Published: April 2025
Availability: Available
Format: Hardback
ISBN: 9781009560917
In this original and modern book, the complexities of quantum phenomena and quantum resource theories are meticulously unravelled, from foundational entanglement and thermodynamics to the nuanced realms of asymmetry and beyond. Ideal for those aspiring to grasp the full scope of quantum resources, the text integrates advanced mathematical methods and physical principles within a comprehensive, accessible framework. Including over 760 exercises throughout, to develop and expand key concepts, readers will gain an unrivalled understanding of the topic. With its unique blend of pedagogical depth and cutting-edge research, it not only paves the way for a deep understanding of quantum resource theories but also illuminates the path toward innovative research directions. Providing the latest developments in the field as well as established knowledge within a unified framework, this book will be indispensable to students, educators, and researchers interested in quantum science's profound mysteries and applications.
Includes a thorough introduction to quantum mechanics, avoiding assumptions of prior knowledge to ensure the book is approachable for those new to the subject
Applies a resource theory perspective across various quantum information topics, offering a novel and structured approach to understanding core concepts like entropy, divergence, and entanglement
Equips readers with the mathematical tools necessary for active research in quantum resource theories, enhancing their analytical capabilities
Product details
Published: April 2025
Format: Hardback
ISBN: 9781009560917
Length: 833 pages
Dimensions: 254 ~ 178 mm
Weight: 1.856kg
Availability: Available
1. Introductory material
Part I. Preliminaries:
2. Elements of quantum mechanics I: closed systems
3. Elements of quantum mechanics II: open systems
Part II. Tools and Methods:
4. Majorization
5. Divergences and distance measures
6. Entropies and relative entropies
7. Conditional entropy
8. The asymptotic regime
Part III. The General Framework:
9. Static quantum resource theories
10. Quantification of quantum resources
11. Manipulation of resources
Part IV. Entanglement Theory:
12. Pure0state entanglement
13. Mixed-state entanglement
14. Multipartite entanglement
Part V. Additional Examples of Static Resource Theories:
15. The resource theory of asymmetry
16. The resource theory of nonuniformity
17. Quantum thermodynamics
Appendices.
Series: Elements in Applied Category Theory
Published: May 2025
Availability: Not yet published - available from May 2025
Format: Hardback
ISBN: 9781009625708
Paperback
String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.
1. The Case for String Diagrams
2. String Diagrams as Syntax
3. String Diagrams as Graphs
4. Categories of String Diagrams
5. Semantics
6. Other Trends in String Diagram Theory
7. String Diagrams in Science: Some Applications
References
Published: June 2025
Availability: Not yet published - available from May 2025
Format: Paperback
ISBN: 9781009589840
The second edition of this engaging textbook for advanced undergraduate students and beginning graduates covers all the core subjects in linear algebra. It has a unique emphasis on integrating ideas from analysis, in addition to pure algebra, and features a balance of abstraction, practicality, and contemporary applications. Four chapters examine some of the most important of these applications, including quantum mechanics, machine learning, data science, and quantum information. The material is supplemented by a rich collection of exercises designed for students from diverse backgrounds, including a wealth of newly added ones in this edition. Selected solutions are provided at the back of the book for use in self-study, and full solutions are available online to instructors.
Covers all the core topics of linear algebra, approaching many from the viewpoint of analysis
Contains a rich collection of exercises, with a full solution manual available to instructors at www.cambridge.org/Yang2e
Features chapters tackling important contemporary applications, including quantum mechanics, machine learning, data science, and quantum information
Well-motivated presentation avoids unnecessary abstraction, giving readers a clear grasp of the concepts, supplemented with concrete examples where necessary
Demonstrates connections between linear algebra and other important areas
Notation and convention
1. Vector spaces
2. Linear mappings
3. Determinants
4. Scalar products
5. Real quadratic forms and self-adjoint mappings
6. Complex quadratic forms and self-adjoint mappings
7. Jordan decomposition
8. Selected topics
9. Excursion: Quantum mechanics in a nutshell
10. Excursion: Problems in machine learning
11. Excursion: Problems in data analysis
12. Excursion: Multilinear algebra
13. Excursion: Essentials of quantum information and quantum entanglement
Solutions to selected problems
Bibliographic notes
Bibliography
Index.
Published: June 2025
Availability: Not yet published - available from June 2025
Format: Paperback
ISBN: 9781009546539
Hardback
One of life's most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.
Combines mathematics and philosophy to explore the relationship between pattern and change
Uses examples from the world around us to illustrate how thinking has developed over time and in different parts of the world
Includes chapters on information, dynamics, symmetry, chance, order, the brain, and quantum mechanics, all introduced gently and building progressively toward deeper insights
Accompanied online by additional chapters and endnotes to explore topics of further interest
1. Introduction
2. The patterns of heaven
3. The pendulum
4. Difference, change, and information
5. Chance
6. Pattern systems defined
7. Exploring the definition of pattern
8. Entropy and synthesis
9. Symmetry and invariance
10. Pattern systems and the brain
11. Waves
12. Return
13. Quantum
14. Quantum patterns
15. Afterword
Appendix
Bibliography
Index.
Published: August 2025
Availability: Not yet published - available from August 2025
Format: Paperback
ISBN: 9781009556507
This textbook is meant for first-year undergraduates majoring in mathematics or disciplines where formal mathematics is important. It will help students to make a smooth transition from high school to undergraduate differential calculus. Beginning with limits and continuity, the book proceeds to discuss derivatives, tangents and normals, maxima and minima, and mean value theorems. It also discusses indeterminate forms, functions of several variables, and partial differentiation. The book ends with a coverage of curvature, asymptotes, singular points, and curve tracing. Concepts are first presented and explained in an informal, intuitive, and conceptual style. They are then covered in the form of a conventional definition, theorem, or proof. Each concept concludes with at least one solved example. Additional solved examples are also provided under the section "More Solved Examples". Practice numerical exercises are included in the chapters so that students can apply the concepts learnt and sharpen their problem-solving skills.
Explanation of concepts and equations using figures, graphs, and tables
'Focus on Concepts' questions for fostering a deeper engagement with the subject
'Remark' section focusing on common doubts related to understanding of concepts
'Chapter Extras' section focusing on proofs of theorems
Real-world applications provided at the end of chapters for ease of relation to practical situations
Marginal annotations offering explanations, words of cautions, and important comments
1. Before Calculus
2. Limit of a Function
3. Continuity
4. The Derivative
5. Successive Differentiation
6. Tangents and Normals
7. Maxima and Minima
8. Mean Value Theorems
9. Taylor's Theorem
10. Indeterminate Forms
11. Functions of several variables and Partial Differentiation
12. Curvature
13. Asymptotes
14. Singular Points
15. Tracing of Curves
References
Index.
Published: August 2025
Availability: Not yet published - available from August 2025
Series: Cambridge Studies in Advanced Mathematics
Format: Hardback
ISBN: 9781108844161
This up-to-date introduction to type theory and homotopy type theory will be essential reading for advanced undergraduate and graduate students interested in the foundations and formalization of mathematics. The book begins with a thorough and self-contained introduction to dependent type theory. No prior knowledge of type theory is required. The second part gradually introduces the key concepts of homotopy type theory: equivalences, the fundamental theorem of identity types, truncation levels, and the univalence axiom. This prepares the reader to study a variety of subjects from a univalent point of view, including sets, groups, combinatorics, and well-founded trees. The final part introduces the idea of higher inductive type by discussing the circle and its universal cover. Each part is structured into bite-size chapters, each the length of a lecture, and over 200 exercises provide ample practice material.
The first introduction to dependent type theory at the advanced undergraduate level, with minimal prerequisites
Contains over 200 exercises that expand the main theory and cover essential examples, to help students to build working knowledge of the area
Structured into bite-size chapters that each introduce one new concept or idea, and match the length of a lecture to offer regular stopping points for readers
Preface
Introduction
Part I. Martin-Lof's Dependent Type Theory:
1. Dependent type theory
2. Dependent function types
3. The natural numbers
4. More inductive types
5. Identity types
6. Universes
7. Modular arithmetic via the Curry-Howard interpretation
8. Decidability in elementary number theory
Part II. The Univalent Foundations of Mathematics:
9. Equivalences
10. Contractible types and contractible maps
11. The fundamental theorem of identity types
12. Propositions, sets, and the higher truncation levels
13. Function extensionality
14. Propositional truncations
15. Image factorizations
16. Finite types
17. The univalence axiom
18. Set quotients
19. Groups in univalent mathematics
20. General inductive types
Part III. The Circle:
21. The circle
22. The universal cover of the circle
Index
Bibliography.