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243520 results in Mathematics

Page 1 of 12176

An Introduction to Computational Physics
  • 3rd edition
  • Tao Pang
  • Coming soon
  • Expected online publication date:
    January 2027
    Print publication:
    31 December 2026
  • This classic textbook, thoroughly revised and updated for its third edition, introduces the basic methods of computational physics. Clear, concise and practical, the new edition includes an additional chapter on machine learning and is supported with sample programs in Python. First, readers are presented with the numerical techniques that every computational scientist should have in their toolbox, including approximation of functions, numerical calculus, differential and partial differential equations, spectral analysis, linear algebra and matrix operations. The author then provides self-contained introductions to the research areas of molecular dynamics, fluid dynamics, Monte Carlo simulations, genetic algorithms and machine learning. Important concepts are illustrated with relevant examples, and each chapter concludes with a selection of exercises. Suitable for upper-division undergraduate to graduate courses on computational physics and scientific computing, this book is also a useful resource for anyone interested in using computation to solve scientific problems.

Kernel-Based Methods
  • Milestones and New Trends
  • Stefano De Marchi, Francesco Marchetti, Emma Perracchione
  • Coming soon
  • Expected online publication date:
    November 2026
    Print publication:
    30 November 2026
  • Kernel methods, with origins in the pioneering work of Mercer (1909), Bochner (1933), and Aronszajn (1950), have become central tools in modern mathematics and machine learning. This book explores their deep connections with approximation theory, highlighting both classical results and cutting-edge developments. Through clear explanations and illustrative examples, it guides readers from foundational concepts to contemporary applications, including computational methods and real-world problem solving. By bridging theory and practice, the text not only provides a rigorous understanding of kernels but also inspires further exploration and research. Suitable for students, researchers, and practitioners, it invites readers to engage with ongoing advances in this dynamic field and to contribute to its future growth.

Matrix and Its Applications in Physics

Differential Topology
  • Gereon Quick
  • Coming soon
  • Expected online publication date:
    September 2026
    Print publication:
    30 September 2026
  • Differential topology uncovers the hidden structure of smooth spaces –the foundation of modern geometry and topology. This book offers a clear, rigorous introduction to the subject, blending theory with concrete examples and applications. Beginning with the basics of manifolds and smooth maps, it develops essential tools and concepts such as tangent spaces, transversality, cobordism, and tubular neighbourhoods, before progressing to powerful invariants like the Brouwer degree, intersection numbers, and the Hopf invariant. Along the way, readers encounter landmark results including Whitney's embedding theorem, Brouwer's fixed point theorem, the Pontryagin construction, Hopf's degree theorem, and the Poincaré–Hopf index theorem. Each chapter combines intuitive explanations with precise and detailed proofs, supported by exercises and detailed solutions that deepen understanding. Ideal for advanced undergraduates, graduate students, and researchers, this text provides a gateway to one of mathematics' most elegant and influential fields – where analysis, geometry, and topology meet.

Periodic Elliptic Partial Differential Operators
  • The Main Structures
  • Volume 1
  • Peter Kuchment
  • Coming soon
  • Expected online publication date:
    September 2026
    Print publication:
    30 September 2026
  • The study of periodic partial differential equations has experienced significant growth in recent decades, driven by emerging applications in fields such as photonic crystals, metamaterials, fluid dynamics, carbon nanostructures, and topological insulators. This book provides a uniquely comprehensive overview for mathematicians, physicists, and material scientists engaged in the analysis and construction of periodic media. It describes all the mathematical objects, tools, problems, and techniques involved. Topics covered are central for areas such as spectral theory of PDEs, homogenization, condensed matter physics and optics. Although it is not a textbook, some basic proofs, background material, and references to an extensive bibliography providing pointers to the wider literature are included to allow graduate students to access the content.

The Physics of Gas and Vapor Bubbles
  • Andrea Prosperetti
  • Coming soon
  • Expected online publication date:
    August 2026
    Print publication:
    31 August 2026
  • Bubbles have unique properties that make them of great importance in disparate fields such as energy production, acoustics, chemical engineering, material processing, biomedicine, food science and a host of others which, on the surface, appear to have little in common. Bringing together information scattered in many hundreds of sources, this book provides a unified treatment of the subject, illustrating the roots of this surprising versatility with a wealth of examples. The emphasis is on physics, explained with words and images before introducing a limited mathematical apparatus. Building on the foundation of the compressible and incompressible Rayleigh-Plesset equation, the treatment continues with the volume oscillations of gas bubbles and associated scattering and emission of sound, the diffusion of dissolved gases and of heat, boiling, nucleation and the behavior of bubbles in elastic and visco-elastic media. The book concludes with chapters on biomedical applications, sonochemistry, acoustic and flow cavitation and bubbly liquids.

Geometric Quantum Field Theories
  • Piljin Yi
  • Coming soon
  • Expected online publication date:
    August 2026
    Print publication:
    31 August 2026
  • This graduate-level volume is a coherent and self-contained introduction to Quantum Field Theory, uniquely focused on geometric and non-perturbative aspects. The first part covers quantum fields and Euclidean path integral, Yang-Mills field theories, and Wilsonian renormalization. Wilson's notion of the effective field theory and its heavy implication for the QFT framework itself are given particular attention. Next, geometrical and topological aspects are thoroughly treated, accompanied by a healthy dose of underlying mathematics. Anomalies, or quantum failures of classical symmetries, follow as crucial litmus tests for self-consistency, which are delineated in unprecedented detail, spanning decades of development. In the final part, the book asks how relativistic gravity, known to resist standard quantization schemes, may reconcile with the quantum world. This question is approached by invoking d=2 Weyl anomaly, Hawking effects, black hole partition functions, and the renormalization of fundamental strings, with a view toward quantum gravity and superstring theory.

Infinite-Dimensional Spectral Computations
  • Foundations, Algorithms, and Modern Applications
  • Matthew J. Colbrook
  • Coming soon
  • Expected online publication date:
    August 2026
    Print publication:
    31 August 2026
  • Mathematicians, physicists, engineers, and data scientists will welcome this comprehensive, practical guide to computing spectral properties of operators in infinite-dimensional settings with rigorous guarantees. It explains why standard discretisation can fail and shows how to overcome these pitfalls. It develops resolvent-based algorithms with provable convergence and certified error bounds, organised by a precise computability classification that clarifies what is achievable, what is impossible, and what extra information makes problems tractable. Topics include spectra and pseudospectra, spectral measures and functional calculus, spectral types, fractal and Cantor-type spectra, essential versus discrete spectra and multiplicities, spectral radii, abscissas and gaps, nonlinear operator pencils, and verified computation. A distinctive feature is the integration of modern applications, including a fully rigorous treatment of data-driven Koopman spectral analysis. Hundreds of worked examples, exercises with solutions, notes, and usable code make the book both a reference and a practical toolkit for researchers and students.

Random Vibrations
  • A Primer
  • Debasish Roy, G. Visweswara Rao
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • 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.

Differential Calculus and its Applications
  • Idrees Qasim
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • 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.

Birational Geometry and Manin's Conjecture
  • Sho Tanimoto
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • This book provides the first comprehensive study of the geometric aspects of Manin's conjecture. It equips the reader with a working knowledge of higher dimensional algebraic geometry, including the minimal model program and its applications to arithmetic and Diophantine geometry. The text also develops the foundations of the moduli theory of rational curves on Fano varieties and explores its role in the geometric formulation of Manin's conjecture, supported by worked examples. The book is suitable for graduates and researchers in arithmetic geometry seeking a modern introduction to birational geometry and the moduli theory of rational curves. It will also interest experts in higher‑dimensional algebraic geometry who wish to understand recent applications of these techniques to arithmetic geometry.

Classical Algebraic Geometry
  • A Modern View
  • Volume 1, 2nd edition
  • Igor V. Dolgachev
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • The 20th century saw the development of many of the key concepts and theories in algebraic geometry. However, the evolution of style and approach over time has rendered the original texts challenging for modern readers to decipher. Bridging the gap between classical and modern algebraic geometry, this book explains classical results using modern tools and language. The second edition has undergone significant expansion. This first volume includes an extensive look at the enumerative geometry of quadrics and a more in-depth exploration of Cremona transformations, featuring more examples of different types. Furthermore, the expanded bibliography now encompasses over 800 references, including references to results obtained in the twelve years since the publication of the first edition. This carefully crafted reference will continue to keep classical algebraic geometry results alive and accessible to new generations of graduate students and researchers today.

Classical Algebraic Geometry
  • A Modern View
  • Volume 2, 2nd edition
  • Igor V. Dolgachev
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • The 20th century saw the development of many of the key concepts and theories in algebraic geometry. However, the evolution of style and approach over time has rendered the original texts challenging for modern readers to decipher. Bridging the gap between classical and modern algebraic geometry, this book explains classical results using modern tools and language. The second edition has undergone significant expansion. This second volume includes new chapters on quartic surfaces, and on the theory of congruences of lines, the first known modern treatment of the work of E. Kummer and R. Sturm. Furthermore, the expanded bibliography now encompasses over 800 references, including references to results obtained in the 12 years since the publication of the first edition. This carefully crafted reference will continue to keep classical algebraic geometry results alive and accessible to new generations of graduate students and researchers today.

Dilation and Model Theory for Pairs of Commuting Contraction Operators
  • Joseph A. Ball, Haripada Sau
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • Exactly a decade after the publication of the Sz.-Nagy Dilation Theorem, Tsuyoshi Andô proved that, just like for a single contractive operator, every commuting pair of Hilbert-space contractions can be lifted to a commuting isometric pair. Although the inspiration for Andô's proof comes from the elegant construction of Schäffer for the single-variable case, his proof did not shed much light on the explicit nature of the dilation operators and the dilation space as did the original Schäffer and Douglas constructions for a single contraction. Consequently, there has been little follow-up in the direction of a more systematic extension of the Sz.-Nagy–Foias dilation and model theory to the bi-variate setting. Sixty years since the appearance of Andô's first step comes this thorough systematic treatment of a dilation and model theory for pairs of commuting contractions.

Equivariant Principal ∞-Bundles
  • Hisham Sati, Urs Schreiber
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • Principal bundles and their associated fiber bundles famously play a foundational role in both algebraic and differential topology, as well as in fundamental and solid-state physics. More recently, their equivariant and higher homotopy enhancements (gerbes) have been crucial in generalized cohomology theory and for the physics of extended solitons and topological phases. This text is the first to offer a unified perspective of, and introduction to, these topics, providing an insight into material previously scattered across the literature. After a self-contained account of the classical theory of equivariant principal bundles in modern topological groupoid language, the book develops, on the novel backdrop of cohesive higher topos theory, a powerful theory of equivariant principal higher bundles. It establishes new methods like the 'smooth Oka principle' and 'twisted Elmendorf theorem' to elegantly prove classification results and clarify the relation to proper equivariant generalized cohomology theories.

Relevant Logics
  • Implication, Modality, Quantification
  • Shawn Standefer
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • Relevant logics are forms of non-classical logic that require the antecedent and consequent of implications to be relevantly related. They are paraconsistent logics, i.e. they are able to robustly handle contradictory information. The field of non-classical logics is rapidly expanding, particularly with the addition of modalities and quantifiers. This is the first book to develop systematically a basic frame theory of relevant logics that includes both modal and quantified extensions. It includes sections comparing features of relevant logics with other, more common logics used in philosophy, examples and exercises to make the material more accessible, and an extensive bibliography. It also includes philosophical discussion of many aspects of relevant logics, and highlights several directions for future research, both philosophical and formal.

Control Systems Theory
  • N Sukavanam
  • Coming soon
  • Expected online publication date:
    June 2026
    Print publication:
    01 September 2027

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.

Optimization
  • A Bootcamp for Machine Learning, Inverse Problems, and Control
  • Steven L. Brunton
  • Coming soon
  • Expected online publication date:
    June 2026
    Print publication:
    30 June 2026
  • Optimization is a foundational topic in mathematics, underpinning nearly all of our modern industrial and technological world. Assuming only basic knowledge of linear algebra and calculus, this book provides a rapid, yet thorough, overview of applied mathematical optimization for advanced undergraduates, beginning graduate students, or practitioners in engineering and science. The text opens with an 'Optimization Bootcamp', introducing methods at a beginning level, before progressing to deep-dives into advanced topics and research-ready methods. The focus throughout is on modern applications of machine learning, inverse problems, and control. Rich pedagogy includes Python code with simple working examples and advanced case studies. Every section is accompanied by YouTube lectures to encourage interaction with the material. Using intuitive explanations, this book makes the material as simple and interesting as possible, while still having the depth, breadth and precision required to empower use in research and real-world applications.

Spectra of Signed Graphs
  • Zoran Stanić
  • Coming soon
  • Expected online publication date:
    June 2026
    Print publication:
    31 July 2026
  • This monograph extends the classical spectral theory of ordinary graphs to the broader framework of signed graphs. It integrates foundational results with recent advances, explores applications, and clarifies connections with related mathematical structures while indicating promising directions for future research. The exposition remains rigorous throughout, presenting core concepts, major developments, and emerging ideas in a coherent and accessible manner. Complementing the theoretical material, the monograph includes illustrative examples and problem sections to support understanding and encourage continued study. This monograph will serve as a reference for mathematicians working in the spectral theory of signed graphs as well as a tutorial for graduate students entering the subject area and computer scientists, chemists, physicists, biologists, electrical engineers and others whose work involves graph-based modelling.

Page 1 of 12176