Series: London Mathematical Society Lecture Note Series
Published: April 2026
Format: Paperback
ISBN: 9781009720588
Spanning elementary, algebraic, and analytic approaches, this book provides an introductory overview of essential themes in number theory. Designed for mathematics students, it progresses from undergraduate-accessible material requiring only basic abstract algebra to graduate-level topics demanding familiarity with algebra and complex analysis. The first part covers classical themes: congruences, quadratic reciprocity, partitions, cryptographic applications, and continued fractions with connections to quadratic Diophantine equations. The second part introduces key algebraic tools, including Noetherian and Dedekind rings, then develops the finiteness of class groups in number fields and the analytic class number formula. It also examines quadratic fields and binary quadratic forms, presenting reduction theory for both definite and indefinite cases. The final section focuses on analytic methods: L-series, primes in arithmetic progressions, and the Riemann zeta function. It addresses the Prime Number Theorem and explicit formulas of von Mangoldt and Riemann, equipping students with foundational knowledge across number theory's major branches.
Offers a comprehensive overview of essential number theory themes, helping readers to see how major ideas connect and build upon each other
Includes exercises ranging from routine to challenging for each topic, supporting both mastery of fundamentals and the development of advanced problem-solving skills
Incorporates historical perspectives, highlighting key milestones in number theory's development
Preface
Part I. Elementary Methods:
1. Congruences and primes
2. Continued fractions
3. Euclidean and principal ideal domains
Part II. Algebraic Methods:
4. Some commutative algebra
5. Integrality
6. Ideal class groups and units
7. Quadratic fields and binary quadratic forms
8. Cyclotomic fields
Series: Cambridge Tracts in Mathematics
Published: April 2026
Format: Hardback
ISBN: 9781009741125
Filling a gap in the literature, this book explores the theory of gradient flows of convex functionals in metric measure spaces, with an emphasis on weak solutions. It is largely self-contained and assumes only a basic understanding of functional analysis and partial differential equations. With appendices on convex analysis and the basics of analysis in metric spaces, it provides a clear introduction to the topic for graduate students and non-specialist researchers, and a useful reference for anyone working in analysis and PDEs. The text focuses on several key recent developments and advances in the field, paying careful attention to technical detail. These include how to use a first-order differential structure to construct weak solutions to the p-Laplacian evolution equation and the total variation flow in metric spaces, how to show a Euler–Lagrange characterisation of least gradient functions in this setting, and how to study metric counterparts of Cheeger problems.
Pays a high level of attention to technical detail and highlights any possible traps, complications and simplifications
Features a historical overview section in every chapter, as well as a discussion situating the results discussed within the wider literature
Includes two appendices providing background on convex analysis and on the different equivalent definitions of Sobolev spaces in metric measure spaces
1. Analysis in metric spaces
2. The p-Laplacian evolution equation
3. Gradient flows of functionals with inhomogeneous growth
4. A general Gauss-Green formula
5. Total variation flow on the whole space
6. Total variation flow on bounded domains
7. Applications to related problems
Appendix A. Results from Convex Analysis
Appendix B. Equivalent definitions of Sobolev and BV spaces.
Language: English
Published/Copyright: 2025
The book discusses the stability, observability, and controllability of nonlinear systems of PDEs (such as Wave, Heat, Euler-Bernoulli beam, Petrovsky, Kirchhoff, equations, and more). Methods based on the theory of classical weak functions analysis and movements in Sobolev spaces are used to analyze nonlinear systems of evolutionary partial differential equations. With the unifying theme of evolutionary dynamic equations, both linear and nonlinear, in more complex environments with different approaches, the book presents a multidisciplinary blend of topics, spanning the fields of PDEs applied to various models coming from theoretical physics, biology, engineering, and natural sciences.
This comprehensive book is prepared for a diverse audience interested in applied mathematics. With its broad applicability, this book aims to foster interdisciplinary collaboration and facilitate a deeper understanding of complex phenomenon concepts, practically in electromagnetic waves, the acoustic model for seismic waves, waves in blood vessels, wind drag on space, the linear shallow water equations, sound waves in liquids and gases, non-elastic effects in the string.
The first book devoted on the stability, observability, and controllability
Provides decoupling of all classes of linear damped dynamic equations
Provides some examples illustrating the leading theory
Akram Ben Aissa was born on June 26, 1986, in Eljem, Tunisia. A graduate with high honors from the Faculty of Sciences in Monastir, Akram's academic prowess earned him a Master's degree in Mathematics in 2011. In 2016, Akram earned his Ph.D. in Mathematics from the University of Monastir. His thesis, "Grushin problems and Control theory of PDEs". Akram's research interests span Control theory of Partial Differential Equations, Functional Analysis, and Stability and Control of PDEs. With an impressive publication record, including works on viscoelastic wave equations and second-order evolution equations, he continues to shape the mathematical landscape. In 2022, armed with a Habilitation à diriger des recherches (HdR) from the University of Sousse, he is now an associate Professor at University of Sousse, Tunisia.
Khaled Zennir was born in Algeria 1982. He received his PhD in Mathematics
in 2013 from Sidi Bel Abbès University, Algeria (Assist. professor). He
is now associate Professor at Qassim University, KSA. His research interests
lie in Nonlinear Hyperbolic Partial Differential Equations: Global Existence,
Blow-Up, and Long Time Behavior
1 Introduction
2 Qualitative properties for impulsive wave equation: controllability and observability
3 Viscoelastic wave equation with dynamic boundary conditions
4 Passage from internal exact controllability of beam equation to pointwise exact controllability
5 Second-order evolution equations with/without delay
6 Euler–Bernoulli beam conveying fluid equation with nonconstant velocity and dynamical boundary conditions
7 Stabilization of dissipative nonlinear evolution models
8 Nonlinear Petrovsky-type models
Bibliography
Index
Language: English
Published/Copyright: 2026
November 7, 2025
The book consists of eight chapters, each focusing on different aspects of multiple integrals and related topics in mathematical analysis.
In Chapter 1, multiple integrals are defined and developed. The Jordan measure in n-dimensional unit balls is introduced, along with the definition and criteria for multiple integrals, as well as their properties.
Chapter 2 delves into advanced techniques for computing multiple integrals. It introduces the Taylor formula, discusses linear maps on measurable sets, and explores the metric properties of differentiable maps.
In Chapter 3, we focus on improper multiple integrals and their properties. The chapter deduces criteria for the integrability of functions of several variables and develops concepts such as improper integrals of nonnegative functions, comparison criteria, and absolute convergence.
Chapter 4 investigates the Stieltjes integral and its properties. Topics covered include the differentiation of monotone functions of finite variation and the Helly principle of choice, as well as continuous functions of finite variation.
Chapter 5 addresses curvilinear integrals, defining line integrals of both the first and second kinds. It also discusses the independence of line integrals from the path of integration.
In Chapter 6, surface integrals of the first and second kinds are introduced. The chapter presents the Gauss-Ostrogradsky theorem and Stokes’ formulas, along with advanced practical problems to practice these concepts.
One of the first books on the theory of functions of multiple variables that provides:
A clear, well-organized treatment of the concept behind the development of mathematics as well as solution techniques.
Many examples illustrating the main theory.
Svetlin G. Georgiev works on various aspects of mathematics. His current research focuses on harmonic analysis, ordinary differential equations, partial differential equations, fractional calculus, time scale calculus, integral equations, numerical analysis, differential geometry, and dynamic geometry.
Khaled Zennir: was born in Algeria 1982. He received his PhD in Mathematics in 2013 from Sidi Bel Abbès University, Algeria (Assist. professor). He is now associate Professor at Qassim University, KSA. His research interests lie in Nonlinear Hyperbolic Partial Differential Equations: Global Existence, Blow-Up, and Long Time Behavior.
Mathematics
Analysis
Mathematics
Differential Equations and Dynamical Systems
Mathematics
Applied Mathematics
This book examines Levi-Civita’s lectures on tensor calculus as a lens to illuminate key aspects of his scientific legacy. It highlights the deep interplay between his teaching and research, particularly in tensor calculus, differential geometry, and relativity, as well as his role as a mentor at the University of Rome. More broadly, it traces the history of Riemannian differential geometry from roughly 1870 to 1930.
Key themes emerge: the influence of the Italian mathematical tradition in Levi-Civita’s work on tensor calculus, the intrinsic link between analysis, geometry, and relativity in his work, and his pedagogical approach, which incorporates physics and geometric intuition to extend mathematical results. The book also explores his collaborations with Enrico Fermi and Enrico Persico, shedding light on the Via Panisperna group during a pivotal period in theoretical physics.
Levi-Civita’s treatise became a foundational text in absolute differential calculus, essential for physicists mastering tensor calculus in Einstein’s theories.
Drawing extensively from his archives – preserved at the Archivio Storico
dell’Accademia Nazionale dei Lincei in Rome and within the Ceccherini-Silberstein
family – the book offers fresh insights into his personal, scientific, and
academic life. His correspondence reveals his far-reaching influence, spanning
students in Rome, international scholars, Rockefeller fellows, and colleagues
inspired by his ideas and mentorship
1 Introduction pp. 1–15
2 An Italian tradition: From Beltrami to Ricci Curbastropp. 17–51
3 A change of perspectivepp. 53–85
4 From Padua to Rome pp. 87–117
5 Levi-Civita’s lectures on tensor calculus, 1925–1928 pp. 119–158
6 A teaching tool for tensor calculus pp. 159–198
7 Advances in research pp. 199–249
8 Dissemination of tensor calculus pp. 251–302
9 Against tensor calculus pp. 303–335
10 Epilogue pp. 337–375
A Appendix pp. 377–472
References pp. 473–516
Index of names pp. 517–523
This volume is sold both independently and as part of a volume set.
Proceedings of the International Conference of Basic Science 2024 (two-volume set)
Description
The International Congress of Basic Science (ICBS) is a major event that brought together the world's leading researchers in Mathematics, Theoretical Physics, and Theoretical Computer Science. The second ICBS was held at Beijing China in July 2024.
This is the second of two volumes comprising the Proceedings of the International Congress of Basic Science (2024). This volume focuses on the physics and computer science sections of the ICBS. It features the lectures delivered by Edward Witten, Alexei Kitaev, Andrew Chi-Chih Yao, and Leslie Valiant, who were the recipients of the Basic Science Lifetime Awards, and also includes the summaries of the award-winning papers from the Frontiers of Science Awards.
The ICBS Proceedings serve as a valuable resource for researchers, students, and anyone interested in the latest developments in basic science. They provide a comprehensive overview of the current state of research in Mathematics, Physics, and Computer Science and offer a glimpse into the future direction of these subjects.
Publication Information
Publisher
International Press of Boston, Inc.
Pages
809
ISBN: 978-1-394-29404-6
February 2026
480 pages
A newly updated and authoritative exploration of differential and difference equations used in queueing theory
In the newly revised second edition of Differential and Difference Equations with Applications in Queueing Theory, a team of distinguished researchers delivers an up-to-date discussion of the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. The authors provide a deep exploration of first principles and a wide variety of examples in applied mathematics and engineering and stochastic processes.
This book demonstrates the wide applicability of queuing theory in a range
of fields, including telecommunications, traffic engineering, computing,
and facility design. It contains brand-new information on partial differential
equations as a prerequisite for solving queueing models, as well as sample
MATLAB code for addressing these models
A large collection of new examples and enhanced end-of-chapter problems with included solutions
Comprehensive explorations of single-server, multiple-server, parallel, and series queue models
Practical discussions of splitting, delayed-service, and delayed feedback
Enhanced treatments of concepts queueing theory, accessible across engineering and mathematics
Perfect for junior and up undergraduate, as well as graduate students in electrical and mechanical engineering, Differential and Difference Equations with Applications in Queueing Theory will also benefit students of computer science, mathematics, and applied mathematics.