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222 results in Algorithmics, Complexity, Computer Algebra, Computational Geometry

Page 1 of 12

Global Governance by Data
  • Infrastructures of Algorithmic Rule
  • Edited by Fleur Johns, Gavin Sullivan, Dimitri Van Den Meerssche
  • Coming soon
  • Expected online publication date:
    September 2026
    Print publication:
    31 August 2026
  • We are living through an era of unprecedented data-driven regulatory transformation. AI and algorithmic governance are rapidly altering how global problems are known and governed, and reconfiguring how people, places, and things are drawn into legal relation across diverse areas - from labour, media and communications, and global mobilities to environmental governance, security, and war. These changes are fostering new forms of power, inequality, and violence, and posing urgent conceptual and methodological challenges for law and technology research. Global Governance by Data: Infrastructures of Algorithmic Rule brings together leading interdisciplinary scholars working at the forefront of creative thinking and research practice in this area. The book offers fresh takes on the prospects for working collectively to critique and renew those legal and technological infrastructures that order, divide, empower and immiserate across our data-driven world. This title is also available as open access on Cambridge Core.

Extremal Graph and Hypergraph Theory
  • With Ramsey Theory
  • Dhruv Mubayi, Jacques A. Verstraete
  • Coming soon
  • Expected online publication date:
    June 2026
    Print publication:
    30 April 2026
  • Providing a cohesive reference for advanced undergraduates, graduate students and even experienced researchers, this text contains both introductory and advanced material in extremal graph theory, hypergraph theory and Ramsey theory. Along the way, the book includes many modern proof techniques in the field such as the probabilistic method and algebraic methods. Several recent breakthroughs are presented with complete proofs, for example, recent results on the sunflower problem, and off-diagonal and geometric Ramsey theory. It is perhaps unique in containing material on both hypergraph regularity and containers. Featuring an extensive list of exercises, the text is suitable as a teaching text for a variety of courses in extremal combinatorics. Each of the two parts can form the basis of separate courses, and the majority of sections are designed to match the length of a single lecture.

Basic Graph Theory
  • Béla Bollobás, Robert Morris
  • Published online:
    15 March 2026
    Print publication:
    26 March 2026
  • Over the past few decades, graph theory has developed into one of the central areas of modern mathematics, with close (and growing) connections to areas of pure mathematics such as number theory, probability theory, algebra and geometry, as well as to applied areas such as the theory of networks, machine learning, statistical physics, and biology. It is a young and vibrant area, with several major breakthroughs having occurred in just the past few years. This book offers the reader a gentle introduction to the fundamental concepts and techniques of graph theory, covering classical topics such as matchings, colourings and connectivity, alongside the modern and vibrant areas of extremal graph theory, Ramsey theory, and random graphs. The focus throughout is on beautiful questions, ideas and proofs, and on illustrating simple but powerful techniques, such as the probabilistic method, that should be part of every young mathematician's toolkit.

Quantum Computing Unveiled
  • A Concise Course with Topological Extensions
  • Yidun Wan
  • Published online:
    27 February 2026
    Print publication:
    19 March 2026
  • Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.

Quantum Computing for Programmers
  • 2nd edition
  • Robert Hundt
  • Published online:
    24 December 2025
    Print publication:
    20 November 2025
  • This introduction to quantum computing from a classical programmer's perspective is meant for students and practitioners alike. More than 50 quantum techniques and algorithms are explained with mathematical derivations and code for simulation, using an open-source code base in Python and C++. New material throughout this fully revised and expanded second edition includes new chapters on Quantum Machine Learning, State Preparation, and Similarity Tests. Coverage includes algorithms exploiting entanglement, black-box algorithms, the quantum Fourier transform, phase estimation, quantum walks, and foundational QML algorithms. Readers will find detailed, easy-to-follow derivations and implementations of Shor's algorithm, Grover's algorithm, SAT3, graph coloring, the Solovay-Kitaev algorithm, Moettoenen's algorithm, quantum mean, median, and minimum finding, Deutsch's algorithm, Bernstein-Vazirani, quantum teleportation and superdense coding, the CHSH game, and, from QML, the HHL algorithm, Euclidean distance, and PCA. The book also discusses productivity issues like quantum noise, error correction, quantum programming languages, compilers, and techniques for transpilation.

The Mathematics of Origami
  • Joseph O'Rourke
  • Published online:
    28 November 2025
    Print publication:
    18 December 2025
  • When you see a paper crane, what do you think of? A symbol of hope, a delicate craft, The Karate Kid? What you might not see, but is ever present, is the fascinating mathematics underlying it. Origami is increasingly applied to engineering problems, including origami-based stents, deployment of solar arrays in space, architecture, and even furniture design. The topic is actively developing, with recent discoveries at the frontier (e.g., in rigid origami and in curved-crease origami) and an infusion of techniques and algorithms from theoretical computer science. The mathematics is often advanced, but this book instead relies on geometric intuition, making it accessible to readers with only a high school geometry and trigonometry background. Through careful exposition, more than 160 color figures, and 49 exercises all completely solved in an Appendix, the beautiful mathematics leading to stunning origami designs can be appreciated by students, teachers, engineers, and artists alike.

Syntax and Semantics of Petri Nets
  • Roberto Gorrieri
  • Published online:
    09 September 2025
    Print publication:
    25 September 2025
  • Petri nets are one of the most popular tools for modeling distributed systems. This book provides a modern look at the theory behind them, by studying three classes of nets that model (i) sequential systems, (ii) non-communicating parallel systems, and (iii) communicating parallel systems. A decidable and causality respecting behavioral equivalence is presented for each class, followed by a modal logic characterization for each equivalence. The author then introduces a suitable process algebra for the corresponding class of nets and proves that the behavioral equivalence proposed for each class is a congruence for the operator of the corresponding process algebra. Finally, an axiomatization of the behavioral congruence is proposed. The theory is introduced step by step, with ordinary-language explanations and examples provided throughout, to remain accessible to readers without specialized training in concurrency theory or formal logic. Exercises with solutions solidify understanding, and the final chapter hints at extensions of the theory.

Combinatorial and Computational Geometry
  • Edited by Jacob E. Goodman, Janos Pach, Emo Welzl
  • Mathematical Sciences Research Institute
  • Published online:
    27 June 2025
    Print publication:
    08 August 2005
  • During the past few decades, the gradual merger of Discrete Geometry and the newer discipline of Computational Geometry has provided enormous impetus to mathematicians and computer scientists interested in geometric problems. This 2005 volume, which contains 32 papers on a broad range of topics of interest in the field, is an outgrowth of that synergism. It includes surveys and research articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension. There are points of contact with many applied areas such as mathematical programming, visibility problems, kinetic data structures, and biochemistry, as well as with algebraic topology, geometric probability, real algebraic geometry, and combinatorics.

Oriented Matroids
  • Laura Anderson
  • Published online:
    04 June 2025
    Print publication:
    10 April 2025
  • Oriented matroids appear throughout discrete geometry, with applications in algebra, topology, physics, and data analysis. This introduction to oriented matroids is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure mathematics. The presentation is geometrically motivated and largely self-contained, and no knowledge of matroid theory is assumed. Beginning with geometric motivation grounded in linear algebra, the first chapters prove the major cryptomorphisms and the Topological Representation Theorem. From there the book uses basic topology to go directly from geometric intuition to rigorous discussion, avoiding the need for wider background knowledge. Topics include strong and weak maps, localizations and extensions, the Euclidean property and non-Euclidean properties, the Universality Theorem, convex polytopes, and triangulations. Themes that run throughout include the interplay between combinatorics, geometry, and topology, and the idea of oriented matroids as analogs to vector spaces over the real numbers and how this analogy plays out topologically.

Games of No Chance 4
  • Edited by Richard J. Nowakowski
  • Mathematical Sciences Research Institute
  • Published online:
    30 May 2025
    Print publication:
    16 April 2015
  • Combinatorial games are the strategy games that people like to play, for example chess, Hex, and Go. They differ from economic games in that there are two players who play alternately with no hidden cards and no dice. These games have a mathematical structure that allows players to analyse them in the abstract. Games of No Chance 4 contains the first comprehensive explorations of misère (last player to move loses) games, extends the theory for some classes of normal-play (last player to move wins) games and extends the analysis for some specific games. It includes a tutorial for the very successful approach to analysing misère impartial games and the first attempt at using it for misère partisan games. Hex and Go are featured, as well as new games: Toppling Dominoes and Maze. Updated versions of Unsolved Problems in Combinatorial Game Theory and the Combinatorial Games Bibliography complete the volume.

Algorithmic Number Theory
  • Lattices, Number Fields, Curves and Cryptography
  • Edited by J. P. Buhler, P. Stevenhagen
  • Mathematical Sciences Research Institute
  • Published online:
    30 May 2025
    Print publication:
    20 October 2008
  • Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and because of the discovery of surprising and powerful algorithms. As a consequence, algorithmic number theory has gradually emerged as an important and distinct field with connections to computer science and cryptography as well as other areas of mathematics. This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area, and in addition, there are contributions pointing in broader directions, including cryptography, computational class field theory, zeta functions and L-series, discrete logarithm algorithms, and quantum computing.

More Games of No Chance
  • Edited by Richard Nowakowski
  • Mathematical Sciences Research Institute
  • Published online:
    29 May 2025
    Print publication:
    25 November 2002
  • This 2003 book provides an analysis of combinatorial games - games not involving chance or hidden information. It contains a fascinating collection of articles by some well-known names in the field, such as Elwyn Berlekamp and John Conway, plus other researchers in mathematics and computer science, together with some top game players. The articles run the gamut from theoretical approaches (infinite games, generalizations of game values, 2-player cellular automata, Alpha-Beta pruning under partial orders) to other games (Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex). Many of these advances reflect the interplay of the computer science and the mathematics. The book ends with a bibliography by A. Fraenkel and a list of combinatorial game theory problems by R. K. Guy. Like its predecessor, Games of No Chance, this should be on the shelf of all serious combinatorial games enthusiasts.

Proof Complexity Generators
  • Jan Krajíček
  • Published online:
    29 May 2025
    Print publication:
    26 June 2025
  • The P vs. NP problem is one of the fundamental problems of mathematics. It asks whether propositional tautologies can be recognized by a polynomial-time algorithm. The problem would be solved in the negative if one could show that there are propositional tautologies that are very hard to prove, no matter how powerful the proof system you use. This is the foundational problem (the NP vs. coNP problem) of proof complexity, an area linking mathematical logic and computational complexity theory. Written by a leading expert in the field, this book presents a theory for constructing such hard tautologies. It introduces the theory step by step, starting with the historic background and a motivational problem in bounded arithmetic, before taking the reader on a tour of various vistas of the field. Finally, it formulates several research problems to highlight new avenues of research.

Quantum Algorithms
  • A Survey of Applications and End-to-end Complexities
  • Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, Fernando G. S. L. Brandão
  • Published online:
    03 May 2025
    Print publication:
    24 April 2025
  • The 1994 discovery of Shor's quantum algorithm for integer factorization—an important practical problem in the area of cryptography—demonstrated quantum computing's potential for real-world impact. Since then, researchers have worked intensively to expand the list of practical problems that quantum algorithms can solve effectively. This book surveys the fruits of this effort, covering proposed quantum algorithms for concrete problems in many application areas, including quantum chemistry, optimization, finance, and machine learning. For each quantum algorithm considered, the book clearly states the problem being solved and the full computational complexity of the procedure, making sure to account for the contribution from all the underlying primitive ingredients. Separately, the book provides a detailed, independent summary of the most common algorithmic primitives. It has a modular, encyclopedic format to facilitate navigation of the material and to provide a quick reference for designers of quantum algorithms and quantum computing researchers.

Data Structures and Algorithms Using Python
  • Subrata Saha
  • Published online:
    30 April 2025
    Print publication:
    15 June 2023
  • Efficiently using data structures to collect, organise and retrieve information is one of the core abilities modern computer engineers are expected to have. This student-friendly textbook provides a complete view of data structures and algorithms using the Python programming language, striking a balance between theory and practical application. All major algorithms have been discussed and analysed in detail, and the corresponding codes in Python have been provided. Diagrams and examples have been extensively used for better understanding. Running time complexities are also discussed for each algorithm, allowing the student to better understand how to select the appropriate one. Written with both undergraduate and graduate students in mind, the book will also be helpful with competitive examinations for engineering in India such as GATE and NET. As such, it will be a vital resource for students as well as professionals who are looking for a handbook on data structures in Python.

Initial Algebras and Terminal Coalgebras
  • The Theory of Fixed Points of Functors
  • Jiří Adámek, Stefan Milius, Lawrence S. Moss
  • Published online:
    30 January 2025
    Print publication:
    06 February 2025
  • 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 those enriched over 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 of endofunctors on other categories. Representing more than fifteen years of work, this will be the leading text on the subject for years to come.

Data Structures and Algorithms in Java
  • A Project-Based Approach
  • Dan S. Myers
  • Published online:
    19 December 2024
    Print publication:
    31 October 2024
  • Learn with confidence with this hands-on undergraduate textbook for CS2 courses. Active-learning and real-world projects underpin each chapter, briefly reviewing programming fundamentals then progressing to core data structures and algorithms topics including recursion, lists, stacks, trees, graphs, sorting, and complexity analysis. Creative projects and applications put theoretical concepts into practice, helping students master the fundamentals. Dedicated project chapters supply further programming practice using real-world, interdisciplinary problems which students can showcase in their own online portfolios. Example Interview Questions sections prepare students for job applications. The pedagogy supports self-directed and skills-based learning with over 250 'Try It Yourself' boxes, many with solutions provided, and over 500 progressively challenging end-of-chapter questions. Written in a clear and engaging style, this textbook is a complete resource for teaching the fundamental skills that today's students need. Instructor resources are available online, including a test bank, solutions manual, and sample code.

Approximation Algorithms for Traveling Salesman Problems
  • Vera Traub, Jens Vygen
  • Published online:
    14 November 2024
    Print publication:
    05 December 2024
  • The Traveling Salesman Problem (TSP) is a central topic in discrete mathematics and theoretical computer science. It has been one of the driving forces in combinatorial optimization. The design and analysis of better and better approximation algorithms for the TSP has proved challenging but very fruitful. This is the first book on approximation algorithms for the TSP, featuring a comprehensive collection of all major results and an overview of the most intriguing open problems. Many of the presented results have been discovered only recently, and some are published here for the first time, including better approximation algorithms for the asymmetric TSP and its path version. This book constitutes and advances the state of the art and makes it accessible to a wider audience. Featuring detailed proofs, over 170 exercises, and 100 color figures, this book is an excellent resource for teaching, self-study, and further research.

How to Think about Algorithms
  • 2nd edition
  • Jeff Edmonds
  • Published online:
    10 October 2024
    Print publication:
    07 March 2024
  • Understand algorithms and their design with this revised student-friendly textbook. Unlike other algorithms books, this one is approachable, the methods it explains are straightforward, and the insights it provides are numerous and valuable. Without grinding through lots of formal proof, students will benefit from step-by-step methods for developing algorithms, expert guidance on common pitfalls, and an appreciation of the bigger picture. Revised and updated, this second edition includes a new chapter on machine learning algorithms, and concise key concept summaries at the end of each part for quick reference. Also new to this edition are more than 150 new exercises: selected solutions are included to let students check their progress, while a full solutions manual is available online for instructors. No other text explains complex topics such as loop invariants as clearly, helping students to think abstractly and preparing them for creating their own innovative ways to solve problems.

Online Algorithms
  • Rahul Vaze
  • Published online:
    07 May 2024
    Print publication:
    16 November 2023
  • Online algorithms are a rich area of research with widespread applications in scheduling, combinatorial optimization, and resource allocation problems. This lucid textbook provides an easy but rigorous introduction to online algorithms for graduate and senior undergraduate students. In-depth coverage of most of the important topics is presented with special emphasis on elegant analysis. The book starts with classical online paradigms like the ski-rental, paging, list-accessing, bin packing, where performance of online algorithms is studied under the worst-case input and moves on to newer paradigms like 'beyond worst case', where online algorithms are augmented with predictions using machine learning algorithms. The book goes on to cover multiple applied problems such as routing in communication networks, server provisioning in cloud systems, communication with energy harvested from renewable sources, and sub-modular partitioning. Finally, a wide range of solved examples and practice exercises are included, allowing hands-on exposure to the concepts.

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