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Galois.The study of algebraic equations has served as a motivating terrain for a large part of abstract algebra, and according to this, algebraic equations are visible as a guiding thread throughout the book.

The history of mechanics, and more particularly, the history of mechanics applied to constructions, constitutes a field of research that is relatively recent. This volume, together with the recent publication "Towards a History of Construction", is intended as an homage to the two eminent scholars who made a determinant contribution to the history of mechanics: Edoardo Benvenuto and Clifford Truesdell.

The book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.First published in the series Science Networks Historical Studies, Vol. 17 (1996).In the second rev. edition the author has eliminated misprints, revised the chapter on Richard Dedekind, and updated the bibliographical index.

This text is a self-contained introduction to the three main families that we encounter in analysis – metric spaces, normed spaces, and inner product spaces – and to the operators that transform objects in one into objects in another.  With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.”Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of ℓp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle.  The text is constructed in such a way that instructors have the option whether to include more advanced topics.Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course.  Instructors have several options for building a course around the text depending on the level and interests of their students.Key features:Aimed at students who have a basic knowledge of undergraduate real analysis.  All of the required background material is reviewed in the first chapter.Suitable for undergraduate-level courses; no familiarity with measure theory is required.Extensive exercises complement the text and provide opportunities for learning by doing.A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1).     Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.

Ihr Fell gleicht dem der Mäuse, doch sie fliegen wie Vögel – und das vornehmlich nachts. Verhalten und Aussehen der Fledermäuse erregten bereits im Mittelalter Misstrauen, so dass sie seither mit einem schlechten Ruf zu kämpfen haben. Wenn man sich jedoch näher mit ihnen beschäftigt, erkennt man schnell, dass es sich um außergewöhnliche Tiere mit verblüffenden Eigenschaften handelt.So sind sie nicht nur virtuose Flieger, für die Saltos, Sturz- und Steigflüge kein Problem sind, sondern auch vorbildhafte Energiesparer, wenn sie in ihren Höhlen als dicker Cluster zusammenhängen – kopfunter, versteht sich. Ja, warum eigentlich kopfunter? Ein Geheimnis, auf das die Wissenschaftler bis jetzt noch keine befriedigende Antwort gefunden haben. Jürgen Gebhards Buch besticht durch seine außergewöhnlichen Fotos, von denen die meisten noch nie veröffentlicht wurden. Darüber hinaus ist es ihm gelungen, nicht nur eine Vielzahl neuer Informationen zusammenzustellen, insbesondere zum Thema Fortpflanzung, sondern auch seiner Bewunderung und Leidenschaft für diese fliegenden Säugetiere Ausdruck zu verleihen.

This volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resultingapplications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.

This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics.

In studying mathematics, one can encounter surprises, whether in results that seem astonishing or in proofs that lead down unexpected paths.  Over his career, the author came across many such gems.  This book includes his favorites and invites readers to experience the same sense of wonder they inspired in him.Here are results about number theory, Euclidean geometry, trigonometry, algebra, and infinite series, with stories from the history of mathematics added to the mix.  There are theorems from such masters as Euler, Newton, and Ramanujan, while some lesser known mathematicians get their moments in the spotlight.  Although the author does not avoid technical details, his narrative style makes the book accessible to anyone with an interest in mathematics. “[This book] is irresistibly fun. It has everything you’d expect from Dunham: delightful math and charming stories, all delivered with his trademark clarity, wit, and enthusiasm.” -    Steven Strogatz, Cornell University, and author of Infinite Powers“This is a great read, tremendously entertaining (and informative).  Dunham is truly the master of us all with regards to writing about fascinating mathematics.”-    Clifford Taubes, Harvard University“As always, Dunham’s unique gift for mathematical storytelling shines through. [His] enthusiasm for mathematics jumps off the page and sweeps his reader along on a joyous intellectual ride.”  -    Linda McGuire, Muhlenberg College“As the book’s title promises, unexpected results abound.  I encourage you to let Dunham be your guide to some of the wonders of mathematics – you are in for an intellectual treat.-    Howard Stone, Princeton University

Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Many applied problems center around metric questions, such as optimization with respect to distances. After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers.

These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May-June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians.

This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis:Sparse Representations, Compressed Sensing and Multifractal Analysis".

The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students.Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory.  Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques.Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these.  Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups.Reviews of the First Edition“[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them… From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view…[W]ith compelling forceand clarity, he provides many carefully worked-out examples and well-chosen specific problems… Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student.  [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.”—Physics Today"Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning.  The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.”—MAA Reviews

This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools.

Magic squares are among the more popular mathematical recreations. Over the last 50 years, many generalizations of “magic” ideas have been applied to graphs. Recently there has been a resurgence of interest in “magic labelings” due to a number of results that have applications to the problem of decomposing graphs into trees. Key features of this second edition include:·         a new chapter on magic labeling of directed graphs·         applications of theorems from graph theory and interesting counting arguments·         new research problems and exercises covering a range of difficulties·         a fully updated bibliography and indexThis concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings. It may serve as a graduate or advanced undergraduate text for courses in mathematics or computer science, and as reference for the researcher.

This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.

This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.

Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades.Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development.A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades.Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development.A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations.  If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods.A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques.This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.

The classes of bounded operators that are investigated include trace class and Hilbert-Schmidt operators, finite rank perturbations of Volterra operators, infinite Leslie operators, discrete semi-separable operators, integral operators with semi-separable kernels, and period maps corresponding to delay differential equations.

The classes of bounded operators that are investigated include trace class and Hilbert-Schmidt operators, finite rank perturbations of Volterra operators, infinite Leslie operators, discrete semi-separable operators, integral operators with semi-separable kernels, and period maps corresponding to delay differential equations.

This book gathers twenty-two papers presented at the second NLAGA-BIRS Symposium, which was held at Cap Skirring and at the Assane Seck University in Ziguinchor, Senegal, on January 25–30, 2022.The five-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems.The book addresses a range of topics related to partial differential equations, geometric analysis, geometric structures, dynamics, optimization, inverse problems, complex analysis, algebra, algebraic geometry, control theory, stochastic approximations, and modelling.

This book gathers twenty-two papers presented at the second NLAGA-BIRS Symposium, which was held at Cap Skirring and at the Assane Seck University in Ziguinchor, Senegal, on January 25–30, 2022.The five-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems.The book addresses a range of topics related to partial differential equations, geometric analysis, geometric structures, dynamics, optimization, inverse problems, complex analysis, algebra, algebraic geometry, control theory, stochastic approximations, and modelling.