Hardcover ISBN: 978-1-4704-6947-4
Expected availability date: February 22, 2026
2026; 359 pp
MSC: Primary 11
An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history.
Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers.
Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition.
Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.
In this updated edition, you will find a new chapter which brings the reader from undergraduate calculus into analytic number theory. A new section adds a second proof of quadratic reciprocity due to Gauss and Eisenstein. Hundreds of minor edits correct and improve the original edition.
Undergraduate and graduate students interested in number theory.
Seeing arithmetic
Foundations
The Euclidean algorithm
Prime factorization
Rational and constructible numbers
Gaussian and Eisenstein integers
Analytic methods
Modular arithmetic
The modular worlds
Modular dynamics
Assembling the modular worlds
Quadratic residues
Quadratic forms
The topograph
Definite forms
Indefinite forms
Index of theorems
Index of terms
Index of names
Bibliography
Softcover ISBN: 978-1-4704-7685-4
Expected availability date: March 14, 2026
Contemporary Mathematics Volume: 832;
2026; Estimated: 211 pp
MSC: Primary 11; 14; 20
This volume contains the proceedings of the 19th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T), held from June 5 to June 9, 2023, at the Centre International de Rencontres Mathématiques in Luminy (Marseille, France).
The conference brought together researchers at the interface of arithmetic and algebraic geometry with computer science and information theory including, in particular, applications to cryptography and error correcting codes. The articles in this volume are based on talks given at the conference. They represent a broad spectrum of research ranging from abstract theory to explicit algorithms, with the majority of articles devoted to curves and abelian varieties over finite fields, their isogenies, and their endomorphisms.
Graduate students and research mathematicians interested in curves and abelian varieties over finite fields.
Yves Aubry, Fabien Herbaut, and Julien Monaldi — Closed points on curves over finite fields
Stéphane Ballet, Alexis Bonnecaze, and Bastien Pacifico — Multiplication in finite fields with Chudnovsky-type algorithms over the projective line
Jean-Marc Couveignes and Jean Gasnier — Explicit Riemann-Roch spaces in the Hilbert class field
Kiran S. Kedlaya — The relative class number one problem for function fields, II
Harun Kir — The refined Humbert invariant for an automorphism group of a genus 2 curve
M. Koutchoukali — On the coefficients of the zeta-function’s
-polynomial for algebraic function fields over finite fields
Dimitri Koshelev — Generation of two “independent” points on an elliptic curve of
-invariant
Sergey Rybakov — Principal polarization on products of abelian varieties over finite fields
Yuri G. Zarhin — Superelliptic Jacobians and central simple representations
Softcover ISBN: 978-1-4704-7768-4
Expected availability date: March 26, 2026
Contemporary Mathematics Volume: 833;
2026; Estimated: 292 pp
MSC: Primary 15; 05; 16; 46; 62; 03
Articles in this volume are based on talks given at the International Conference on Linear Algebra and its Applications (ICLAA 2023), which took place in Manipal, India. It contains fifteen articles by mathematicians working in linear algebra and related areas. The topics include, among others, recent developments in matrix theory and its applications to linear algebra, linear operators in Banach algebras, game theory, and optimal designs. In addition to research articles, the volume contains expository papers describing new avenues of research and open problems. The volume can also serve as a reference for researchers working in linear algebra and related topics.
Graduate students and research mathematicians interested in linear algebra and applications.
Rafikul Alam and Jibrail Ali — Canonical forms of holomorphic and meromorphic matrices
S. Arumugam, K. Arathi Bhat, Manjunatha Prasad Karantha, and Raksha Poojary — Stress centrality measure of a vertex
Pallavi Basavaraju, Shrinath Hadimani, and Sachindranath Jayaraman — Stability of quaternion matrix polynomials
Aniekan A. Ebiefung — Vertical block- and-matrices
Stephen J. Haslett, Jarkko Isotalo, Augustyn Markiewicz, and Simo Putanen — Some remarks on the reparametrization of linear models
S. K. Jain, André Leroy, and Ajit Iqbal Singh — Products of idempotents in Banach algebras of operators
J. Maria Jeyaseeli, Jay S. Bagga, and S. Arumugam — Edge sudoku number of a graph-I
Sainik Karak, Tanmoy Paul, and T. S. S. R. K. Rao — On subspaces of Banach spaces which admit unique norm preserving extensions under various embeddings
Umashankara Kelathaya, Savitha Varkady, and Manjunatha Prasad Karantha — Some new characterizations of core-EP inverse
Wanli Ma and Yimin Wei — Discrete multilinear time-invariant systems based on t-product
Shubham Niphadkar and Siuli Mukhopadhyay — Studying optimal designs for multivariate crossover trials
S. Pratihar and K. C. Sivakumar — Inverse
-matrices with the bi-diagonal south-west structure
T. E. S. Raghavan — Totally positive matrices
Punit Kamar Yadav, Sajal Ghosh, and S. K. Neogy — Vertical block matrices and vertical linear complementarity problem
Xiaozhou Ye, Predrag S. Stanimirović, and Yimin Wei — Solving fuzzy linear systems using weighted Moore-Penrose and Drazin inverse of extended matrix
'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-the-art surveys in important topics of contemporary interest
Covers a broad range of fields from data-driven science, to engineering, to computational physics
Published: October 2025
Format: Hardback
ISBN: 9781009708043
Length: 1018 pages
Dimensions: 244 × 170 × 52 mm
Weight: 2.058kg
Availability: Not yet published - available from December 2025
1. Cut finite element methods Erik Burman, Peter Hansbo, Mats G. Larson and Sara Zahedi
2. Ensemble Kalman methods: a mean-field perspective Edoardo Calvello, Sebastian Reich and Andrew M. Stuart
3. The discontinuous Petrov–Galerkin method Leszek Demkowicz and Jay Gopalakrishnan
4. Time parallelization for hyperbolic and parabolic problems Martin J. Gander, Shu-Lin Wu and Tao Zhou
5. Optimization problems governed by systems of PDEs with uncertainties Matthias Heinkenschloss and Drew P. Kouri
6. Distributionally robust optimization Daniel Kuhn, Soroosh Shafiee and Wolfram Wiesemann
7. Acceleration methods for fixed-point iterations Yousef Saad
8. Sparse linear least-squares problems Jennifer Scott and Miroslav Tůma.
The mathematical essence of contextuality lies in the similarity of random variables answering the same question in different contexts: contextuality means they are less similar when considered within their respective contexts than when isolated from them. This book presents a principled way of measuring this similarity and distinguishing two forms of context-dependence: contextuality and disturbance. While applicable across a broad range of disciplines, the concept of contextuality in this book is closest to that in quantum physics, where its special forms –in the absence of disturbance – are known as Bell nonlocality and Kochen–Specker contextuality. This systematic introduction requires no prior familiarity with the subject and a very modest mathematical background. Structured as a textbook, complete with exercises and solutions, it is accessible to a broad readership and suitable for teaching. It will be useful to researchers and students in quantum mechanics, philosophy of science, psychology, computer science, linguistics, and probability theory.
Introduces the theory of contextuality step by step, with rigorous proofs, extensive explanations, and exercises with solutions
Presents the theory in abstract mathematical terms, mentioning but not confining the presentation to its applications in specific domains, thus making the book accessible to readers from a broad range of disciplines
The first systematic presentation of the mathematical foundations of contextuality
Published: February 2026
Format: Hardback
ISBN: 9781009671927
Length: 485 pages
Dimensions: 244 × 170 mm
Weight: 0.5kg
Availability: Not yet published - available from February 2026
1. Preliminaries
2. Context-dependence and contextuality
3. Random variables
4. Systems and their couplings
5. Contextuality I: basic properties
6. Contextuality II: dichotomizations and criteria of contextuality
7. Cyclic systems
8. Consistently connected and consistified systems
9. Hidden variable models
10. Measures of the degree of contextuality
11. Noncontextuality polytopes for cyclic systems
Index.
Series: Cambridge Series in Statistical and Probabilistic Mathematics
From social networks to biological systems, networks are a fundamental part of modern life. Network analysis is increasingly popular across the mathematical, physical, life and social sciences, offering insights into a range of phenomena, from developing new drugs based on intracellular interactions, to understanding the influence of social interactions on behaviour patterns. This book provides a toolkit for analyzing random networks, together with theoretical justification of the methods proposed. It combines methods from both probability and statistics, teaching how to build and analyze plausible models for random networks, and how to validate such models, to detect unusual features in the data, and to make predictions. Theoretical results are motivated by applications across a range of fields, and classical data sets are used for illustration throughout the book. This book offers a comprehensive introduction to the field for graduate students and researchers.
Provides a comprehensive look at both probabilistic and statistical methods for network analysis
Motivates the theoretical results with a large range of examples, from a wide range of disciplines including linguistics, engineering and biology
Includes detailed exercises suitable for course use or self-study
Published: March 2026
Format: Hardback
ISBN: 9781009651721
Length: 964 pages
Dimensions: 254 × 178 mm
Weight: 0.5kg
Availability: Not yet published - available from March 2026
1. Introduction
Part I. Basic Setting:
2. Network data sets
3. Network summaries
4. Models for networks
Part II. Probability Preliminaries:
5. Branching processes
6. Some birth and death processes
7. Poisson approximation
8. Ramifications of Poisson approximation
9. Normal approximation
10. Multivariate normal approximation
Part III. Network Models:
11. The Bernoulli random graph
12. Models related to the Bernoulli random graph
13. The Chung–Lu model
14. The configuration and GPDS models
15. Random geometric graphs
16. Small world graphs
17. Preferential attachment models
18. Dense graph limits and graphon models
19. Random processes on networks
20. Summary of Chapters 5–19
Part IV. Network Inference:
21. Sampling from networks
22. Estimation: fitting a network model
23. Assessing model fit
24. Community detection
25. Using networks for inference
26. Some further topics
Appendix
References
Index.
This textbook chart out an easy-to-comprehend account of the methods of random vibrations, aided by modern yet basic concepts in probability theory and random processes. It starts with a quick review of certain elements of structural dynamics, thus setting the stage for their seamless continuation in developing techniques for response analyses of structures under random environmental loads, such as winds and earthquakes. The book also offers a few glimpses of the powerful tools of stochastic processes to kindle the spirit of scientific inquiry. By way of applications, it contains numerous illustrative examples and exercises, many of which relate to practical design problems of interest to the industry. A companion website provides solutions to all the problems in the exercises. For the benefit of the prospective instructors, a semester-long schedule for offering a course on Random Vibrations is also suggested.
Provides a simple yet modern introduction to basic concepts in probability theory that bear upon the methods of random vibrations
Illustrates numerous examples and exercises, some of which are on practical design problems of interest to the industry
Dedicated online companion, providing MATLAB codes for all relevant problems
Preface
Chapter 1. Mechanical Vibrations – An Overview
Chapter 2. Basic Probability Theory
Chapter 3. An Introduction to Stochastic Processes
Chapter 4. Random Vibrations of Linear Time-Invariant Systems
Chapter 5. Random Vibrations – Some Practical Applications
Chapter 6. Nonlinear Random Vibrations
Index.
Series: London Mathematical Society Student Texts
This two-part book offers a rigorous yet accessible exploration of set theory and transfinite algebra, with a particular emphasis on the axiom of choice and its applications. Part I presents an informal axiomatic introduction to the foundations of set theory, including a detailed treatment of the axiom of choice and its equivalents, suitable for advanced undergraduates. Part II, aimed at graduate students and professional mathematicians, treats selected topics in transfinite algebra where the axiom of choice, in one form or another, is useful or even indispensable. The text features self-contained chapters for flexible use, and includes material rarely found in the literature, such as Tarski's work on complete lattices, Hamel's solution to Cauchy's functional equation, and Artin's resolution of Hilbert's 17th problem. Over 140 exercises, with full solutions provided in the Appendix, support active engagement and deeper understanding, making this a valuable resource for both independent study and course preparation.
Features the first English-language exposition of Artin's solution to Hilbert's 17th problem, originally published in German
Over 140 exercises with complete solutions invite readers to actively engage with the material and test their understanding
Covers seldom-treated topics such as Novotny's morphism construction and Tarski's generalization of Weierstrass' theorem
Published: April 2026
Format: Hardback
ISBN: 9781009737845
Format: Paperback
ISBN: 9781009737876
Length: 217 pages
Dimensions: 229 × 152 mm
Weight: 0.5kg
Availability: Not yet published - available from April 2026
Introduction
Part I. Set Theory:
1. The axioms of set theory
2. Correspondences, mappings, and quotient sets
3. Ordered sets
4. Around the axiom of choice
5. Cardinals and ordinals
6. First-order logic and the axioms of set theory revisited
7. Some excursions
Part II. Topics in Transfinite Algebra:
8. Group and ring structures on non-empty sets
9. Orderable abelian groups and fields
10. Subdirect decomposition of algebras
11. Dependence relations, rank functions, and closure operators
12. Semisimple and injective modules
13. The Jacobson radical of a ring
14. Artin's solution of Hilbert's 17th problem
Appendix. Solutions to exercises
References
Index.
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Series: London Mathematical Society Student Texts
Published: May 2026
Format: Hardback
ISBN: 9781009595339
Format: Paperback
ISBN: 9781009595322
Starting from ancient astronomy, this text follows the development of celestial mechanics culminating in applications of the most recent results concerning stability of planetary orbits: Kolmogorov's and Nekhoroshev's theorems. Key topics covered include: a historical introduction from ancient astronomy to Kepler and Newton; Lagrange's perturbation theory; the problem of three bodies, with a discussion of Levi-Civita regularization and of Sundman's theorem; methods of algebraic calculation of perturbation series, including a discussion of non-convergence due to the accumulation of small divisors; and a complete application of Kolmogorov's and Nekhoroshev's theorems. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students, and for young researchers. Its approach allows students to learn about perturbation methods leading to advanced results.
Surveys the historical journey from ancient astronomy to our current theory based on Newtonian gravitation
Contains an extended exposition of the problem of three bodies
Provides a complete computational scheme for an explicit application of perturbation methods through computer algebra
Apology
Plan of the book
Part I. From Ancient Astronomy to Newton:
1. Ouverture
2. Kinematics of the Keplerian model
3. The gravitation of Newton
Part II. From Newton to Poincaré:4. Integrability and action-angle variables
5. The perturbing function
6. Classical perturbation methods
7. The problem of three bodies
8. Regularization of collisions
Part III. Modern Celestial Mechanics:
9. A toolbox of perturbation methods
10. Computer-assisted methods for KAM theory
11. Rotational dynamics of celestial bodies
12. Stability of planetary systems
A. Analytical tools
B. Indexing functions
C. Validated numerics in CAP
D. Benchmarking CAP with a simple model
References
Index.