Format: Paperback / softback, 217 pages, height x width: 235x155 mm, 1 Illustrations, color; 4 Illustrations, black and white
Series: Birkhäuser Advanced Texts Basler Lehrbücher
Pub. Date: 09-Nov-2025
ISBN-13: 9783031677861
Description
This book presents four topics related to undergraduate courses, typically not covered in standard lectures.
Written in a clear and careful style, these four pearls aim at complementing and deepening the knowledge of students and instructors by presenting a variety of techniques and useful methods. The first chapter provides a detailed discussion of real numbers, the foundation of any mathematical construction. Chapter two of the book is dedicated to the study of sequences defined by recurrence relations. The third chapter explores certain problems in asymptotic analysis, and the final chapter of the book discusses mathematical results related to Integration in Finite Terms. Each chapter of the book is accompanied by its respective bibliography.
The book is intended for readers with a level of maturity typically attained after completing a bachelors degree in mathematics.
Real Number System.- Recurrences.- Elements of Asymptotic
Analysis.- Integration in Finite Terms.
Format: Hardback, 407 pages, height x width: 235x155 mm, 26 Illustrations, color; 88 Illustrations, black and white
Pub. Date: 14-May-2026
ISBN-13: 9783032124654
This volume is the first English edition, with commentaries and introductory material, of the writings on spherical geometry by Leonhard Euler, Joseph-Louis Lagrange and Johann Heinrich Lambert. The book is divided into two parts. The first part contains essays related the works by Euler, Lagrange and Lambert on spherical geometry. The goal of these essays is to include these works in the appropriate mathematical, historical and philosophical contexts. The second part of the volume is devoted to the English translations of the original memoirs, originally written in Latin, French and German. These translations are new and they are done by mathematicians who are involved in the subjects of the memoirs. Footnotes by the editors and the translators are appended to the translations. The book is addressed to students and researchers in geometry. It constitutes an invaluable reference in mathematics, and also in the history and philosophy of mathematics.
1 Introduction by Renzo Caddeo and Athanase Papadopoulos.- Part
I: Essays.- 2 Eulers work on spherical geometry: An overview with comments
by Athanase Papadopoulos and Vladimir Turaev.- 3 An introduction to spherical
geometry based on fundamental works of Euler and Lagrange by Charalampos
Charitos.- 4 On Eulers memoir A construction relative to a problem of Pappus
of Alexandria by Guillaume Théret.- 5 Notes on angles and solid angles, in
relation with Eulers memoir De mensura angulorum solidorum by Stelios
Negrepontis and Athanase Papadopoulos.- 6 On the life and work of Johann
Heinrich Lambert by Athanase Papadopoulos.- 7 A review of Johann Heinrich
Lamberts memoir Theorie der Parallellinien by Athanase Papadopoulos and
Guillaume Théret.- 8 The pentagramma mirificum from Napier to Lambert: Notes
on Lamberts memoir on spherical trigonometry by Annette ACampo-Neuen.-
9 Spherical trigonometry before the modern era: The treatise of Nar al-Dn
al-s by Athanase Papadopoulos.- 10 The polar triangle, from Ibn Irq to
Euler and Lagrange by Athanase Papadopoulos.- Part II: Sources.-
11 Principles of spherical trigonometry deduced from the method of maxima and
minima by Leonhard Euler. Translated from the French by Athanase Papadopoulos
and Alena Zhukova.- 12 General spherical trigonometry, deduced from
fundamental principles in a brief and clear
manner by Leonhard Euler. Translated from the Latin by Renzo
Caddeo.- 13 Various speculations on the area of spherical triangles by
Leonhard Euler. Translated from the Latin by Renzo Caddeo.- 14 On the measure
of solid angles by Leonhard Euler. Translated from the Latin by Renzo
Caddeo.- 16 A construction relative to a problem of Pappus of Alexandria by
Leonhard Euler. Translated from the Latin by Renzo Caddeo.- 17 Algebraic
solution of a problem in geometry
by Joseph-Louis Lagrange. Translated from the French by Athanase
Papadopoulos.- 18 Solution of some problems relative to spherical triangles
with a complete analysis of these triangles by Joseph-Louis Lagrange.
Translated from the French by Vincent Alberge and Athanase Papadopoulos.-
19 Notes and Comments on Trigonometry by Johann-Heinrich Lambert. Translated
from the German by Annette ACampo Neuen.- 15 Some questions of the geometry
of the plane and of the sphere by Leonhard Euler. Translated from the Latin
by Renzo Caddeo.
Format: Hardback, 1034 pages, height x width: 235x155 mm, 51 Illustrations, black and white
Series: Grundlehren der mathematischen Wissenschaften
Pub. Date: 09-Apr-2026
ISBN-13: 9783662724446
This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum mechanics is not required.
As with its earlier editions, the book is addressed to a diverse group of readers: younger researchers, newcomers to the area, looking for a broad overview of the field; specialists in the analysis of hyperbolic conservation laws aspiring to fathom its genetic relation to mathematical physics; experts in continuum mechanics, as a vehicle for acquiring the necessary analytical tools; and numerical analysts as a reference source to the general theory. This new edition contains an account of recent results on the Euler equations, pertaining to the breakdown of classical solutions and the construction of very weak, measure-valued, solutions as well as of milder, continuous but wildly oscillating turbulent solutions. Furthermore, the presentation of a number of topics in the previous editions has been revised, expanded and brought up to date. The bibliography has also been expanded, now comprising twenty-five hundred titles.
From the reviews of earlier editions:
Written from a unique and unifying perspective, this treatise provides the mathematical community with a wonderfully entire and exhaustive portrait of the field. Heinrich Freistühler, Jahresber Dtsch Math-Ver.
A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the 'Bible' on the subject. Phillippe G. LeFloch, Math. Reviews.
I Balance Laws.- II Introduction to Continuum Physics.- III Hyperbolic
Systems of Balance Laws.- IV The Cauchy Problem.- V Entropy and the Stability
of Classical Solutions.- VI The General Theory for Scalar Conservation Laws.-
VII Hyperbolic Systems of Balance Laws in One-Space Dimension.- VIII
Admissible Shocks.- IX Admissible Wave Fans and the Riemann Problem.- X
Generalized Characteristics.- XI Scalar Conservation Laws in One Space
Dimension.- XII Genuinely Nonlinear Systems of Two Conservation Laws.- XIII
The Random Choice Method.- XIV The Front Tracking Method and Standard Riemann
Semigroups.- XV Construction of BV Solutions by the Vanishing Viscosity
Method.- XVI BV Solutions for Systems of Balance Laws.- XVII Compensated
Compactness.- XVIII Steady and Self-similar Solutions in Multi-Space
Dimensions.- XIX Euler Equations.- Bibliography.- Author Index.- Subject
Index.
Format: Hardback, 597 pages, height x width: 279x210 mm, 44 Illustrations, color; 17 Illustrations, black and white
Series: Springer Texts in Statistics
Pub. Date: 01-May-2026
ISBN-13: 9781071651810
This book is a unique compendium of core topics in the Statistics Ph.D. program, as well as covering the latest statistical theory, graduate probability and simulation techniques. The Complete Guide to Statistical Theory, Simulation and Probability: A Bridge to the Future gives an elaborate treatment of standard statistics topics such as parametric inference, basic theory of linear models, large sample theory, as well as more advanced topics such as robust estimation, density estimation, bootstrap, multiple testing, and the latest breakthrough developments such as the LASSO and thresholding and regularization. It also gives self-contained treatments of standard graduate probability and major Monte Carlo techniques, including MCMC. As such, this book can be used as an all-purpose text in the statistics Ph.D. programs, as well as a unique research reference.
The book provides 918 exercises, and an additional 98 exercises at the end of the book. The book also has a complete and comprehensive synopsis of real analysis, calculus, linear algebra and matrix theory as an invaluable source of consultation for students, instructors, and researchers.
Preface.
Chapter 1 Graduate Probability.
Chapter 2 Writing Models for Data.
Chapter 3 Exponential Families as a Unifier in Inference.
Chapter 4 The Problems of Inference: A Nontechnical First Glimpse.
Chapter 5 Decision Theory: Basic Concepts.
Chapter 6 Decision Theory: Basic Concepts.-
Chapter 7 Bayes, Empirical Bayes and Shrinkage Estimates.
Chapter 8 Testing of Hypotheses and Confidence Regions.
Chapter 9 Asymptotic Approximations and Practical Asymptotic Tools.
Chapter 10 Least Squares Theory and Linear Models.
Chapter 11 Chi-square Tests.
Chapter 12 Empirical Processes and the Kolmogorov-Smirnov Tests.
Chapter 13 Density Estimation.
Chapter 14 Robust Estimates.
Chapter 15 Bootstrap, Jackknife and Permutation Tests.
Chapter 16 Simulation and the EM Algorithm.
Chapter 17 Markov Chain Monte Carlo.-
Chapter 18 Epilogue: Metamorphosis of Statistics?.
Chapter 19 Sample Midterms.
Chapter 20 Appendix.- Index.
Format: Paperback / softback, 169 pages, height x width: 235x155 mm, 1 Illustrations, color
Series: Compact Textbooks in Mathematics
Pub. Date: 29-Mar-2026
ISBN-13: 9783032074058
This textbook offers a self-contained introduction to the theory of connections on vector bundles that is accessible to both advanced undergraduate students and graduate students. Constructions and proofs of key results are presented in detail in order to be easily understandable and instructive, and each chapter concludes with a set of interesting exercises.
Standard material about vector bundles is covered in the first chapter, with many examples illustrating the main concepts. Chapter 2 is concerned with the theory of connections on vector bundles, with special attention to the curvature of a connection. The third chapter explores several useful topics not always included in similar texts, such as the computation of the holomorphic tangent and canonical bundles of a Grassmann manifold and the curvature of the tautological and tautological quotient bundles. Finally, Chapter 4 discusses Chern, Pontryagin and Euler classes as an important application of the theory of connections on vector bundles to the theory of characteristic classes.
This book can serve as a text for a one-semester course in differential geometry focused on vector bundles and connections, or as a resource for students pursuing studies in algebraic geometry and mathematical physics. Readers should have a basic understanding of manifolds, differential forms, and cohomology.
Vector Bundles.- Connections on Vector Bundles.- Tautological
(Universal) Bundles.- Chern, Pontryagin, and Euler Classes.
Format: Hardback, 430 pages, height x width: 235x155 mm, XXXIX, 430 p.
Series: MATRIX Book Series
Pub. Date: 26-Mar-2026
ISBN-13: 9783032162052
MATRIX is Australias residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 14 weeks in duration.
This book is a scientific record of the six research programs held at MATRIX in the second half of 2024, including a tandem workshop with the Mathematisches Forschungsinstitut Oberwolfach (MFO).
Part II.- 1 MATRIX Program: Mathematics and Physics of Integrability.- 2
MATRIX Program: Multivariate Dependence Modelling: Theory and Applications.-
3 MATRIX Program: Mathematical Models for Lipids and Cells in Atherosclerotic
Plaques.- 4 MATRIX Program: The Geometry of Moduli Spaces in String Theory.-
5 MATRIX Program: Tensor Categories, Quantum Symmetries, and Mathematical
Physics.- 6 MATRIX Program: The Geometry of Moduli Spaces in String Theory.
Format: Hardback, 439 pages, height x width: 235x155 mm, 85 Illustrations, color; 5 Illustrations, black and white
Pub. Date: 03-Jan-2026
ISBN-13: 9789819525133
In this book, a novel high-dimensional linear and nonlinear regression model is introduced to address, in part, the challenges of evaluating the stability and confidence of large-scale models' interpretability. The book begins by reviewing foundational concepts in regression analysis, and discussing the current state and challenges of AI interpretability. Through an in-depth exploration of regression models, the core principles of data-driven linear regression are explained. To enhance the explanatory power of regression models, variable-parameter regression models are further investigated and extended to variable-parameter nonlinear regression models. To handle complex relationships, the Gauss-Newton iterative method is incorporated, ensuring the stability of high-dimensional nonlinear regression. The Confidence Interval-based Credibility Evaluation (CICE) framework combines statistical indicators—such as interval width, center deviation, and accuracy—into a single score to assess the stability and reliability of explanations, validated through case studies in engineering, finance, and time series prediction. Overall, the book presents a coherent framework for interpretable AI, integrating regression modeling, confidence region construction, and credibility evaluation to enhance interpretability and statistical accountability, fostering more trustworthy AI systems. Chapter 1 introduces the fundamental concepts and theoretical developments of both regression analysis and AI explainability, highlighting their interconnections. Chapter 2 reviews essential probability theory and mathematical statistics, covering random variables, measure spaces, probability distributions, parameter estimation (including least squares and maximum likelihood methods), and asymptotic theory, which serve as the foundation for analyzing model consistency and convergence. Chapter 3 focuses on the effects of correlated errors in linear regression, establishing parameter convergence conditions to ensure the consistency and asymptotic normality of covariance estimators. Chapter 4 introduces variable-parameter regression models and systematically studies M-estimators and generalized regression models within the framework of robust statistics. By addressing non-normal errors and outliers, these methods improve model adaptability. The chapter also establishes the robustness of the generalized regression model through theoretical analysis of covariance estimation. Chapter 5 introduces the Confidence Interval-based Credibility Evaluation (CICE) framework, which integrates multiple statistical indicators into a unified score to assess the stability and reliability of model explanations. Through real-world case studies in engineering, finance, and time series prediction, the effectiveness of CICE in detecting unstable interpretations and enhancing model transparency is demonstrated.
Introduction.- Elements.- Fixed-Parameter Prototype Regression Models.-
Variable-Parameter Regression Models.- Locally Interpretable Models
Confidence Evaluation Framework.- Appendix.
Format: Paperback / softback, 439 pages, height x width: 235x155 mm, 1 Illustrations, black and white
Series: UNITEXT
Pub. Date: 03-Feb-2026
ISBN-13: 9783032124937
This book is intended as a first course in the theory of functions of a single complex variable for students (of Engineering, Physics or Mathematics) who have already acquired the fundamental notions of real Mathematical Analysis. It is the English version of an older book, published by Springer in Italian, based on the lectures given by the author to the students of the University of Rome La Sapienza and of the Scuola Superiore di Catania. The claim of mathematical rigor is accompanied by the idea that students should also develop know-how skills: half of the book is devoted to the detailed solution of 288 exercises illustrating, also with figures, the theory. Also, the choice of the topics reflects the above point of view.
Chapter 1. Complex numbers.
Chapter 2. Metric spaces.
Chapter 3. Limits and continuity.
Chapter 4. Sequences and series of functions.-
Chapter 5. Derivatives and analytic functions.
Chapter 6. Elementary functions.
Chapter 7. Integrals.
Chapter 8. Taylor and Laurent series.-
Chapter 9. Residues.
Chapter 10. Applications of residues.
Chapter 11. Further properties of analytic functions.
Format: Paperback / softback, 155 pages, height x width: 235x155 mm, XII, 155 p.
Series: Lecture Notes in Mathematics
Pub. Date: 18-Mar-2026
ISBN-13: 9783032156709
This is a new, updated edition of a foundational text on the representation theory of p-adic groups. The book develops the theory of spherical functions for reductive groups defined over nonarchimedean local fields. It provides explicit formulas, studies their properties (positivity, normalization, etc.), and describes a pioneering construction of the spherical transform and the Plancherel formula. This theory underlies the modern theory of affine Hecke algebras, unramified representations of p-adic groups, and the local Langlands program. This augmented and annotated edition makes a standard reference widely available to contemporary researchers in the representation theory of p-adic groups, automorphic forms, and harmonic analysis on locally compact groups.
Introduction. I Basic properties of spherical functions.- II Groups of
p-adic type.- III Spherical functions on a group of p-adic type.- IV
Calculation of the spherical functions.- V Plancherel measure.