Electro-Diffusion of Ions

Electro-Diffusion of Ions

This is one of the first texts in which electro-diffusion of ions in its different aspects is considered as a unified subject. As a subject it is relevant to understanding the behavior of apparently different physical objects such as electrolyte solution, ion-exchangers, ion-selective membranes, and semiconductors. This text treats a selection of topics in electro-diffusion of ions in an aqueous medium – a nonlinear transport process whose essence is diffusion of ions combined with their migration in a selfconsistent electric field. Electro-Diffusion of Ions is intended to enhance the understanding of particular electro-diffusional transport phenomena and to spark the interest of the mathematical community in the corresponding area of applications and development of a unified scientific vision. Contains some previously unpublished results for electro-diffusional problems.

Electro-Diffusion of Ions

The Computing Dendrite

The Computing Dendrite

Neuronal dendritic trees are complex structures that endow the cell with powerful computing capabilities and allow for high neural interconnectivity. Studying the function of dendritic structures has a long tradition in theoretical neuroscience, starting with the pioneering work by Wilfrid Rall in the 1950s. Recent advances in experimental techniques allow us to study dendrites with a new perspective and in greater detail. The goal of this volume is to provide a rsum of the state-of-the-art in experimental, computational, and mathematical investigations into the functions of dendrites in a variety of neural systems.

The Computing Dendrite

On Vision and Colors

On Vision and Colors

During the first two decades of the nineteenth century, two of the most significant theoretical works on color since Leonardo da Vinci’s Trattato della Pittura were written and published in Germany: Arthur Schopenhauer’s On Vision and Colors and Philipp Otto Runge’s Color Sphere. For Schopenhauer, vision iswholly subjective in nature and characterized by processes that cross over into the territory of philosophy. Runge’s Color Sphere and essay ‘The Duality of Color’ contained one of the first attempts to depict a comprehensive and harmonious color system in three dimensions. Runge intended his color sphere to be understood not as a product of art, but rather as a ‘mathematical figure of various philosophical reflections.’

On Vision and Colors

Open Quantum Systems I

Open Quantum Systems I

Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. From a mathematical point of view, it involves a large body of knowledge. Significant progress in the understanding of such systems has been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.

Open Quantum Systems I

Quantum Concepts in Physics

Quantum Concepts in Physics

Written for advanced undergraduates, physicists, and historians and philosophers of physics, this book tells the story of the development of our understanding of quantum phenomena through the extraordinary years of the first three decades of the twentieth century. Rather than following the standard axiomatic approach, this book adopts a historical perspective, explaining clearly and authoritatively how pioneers such as Heisenberg, Schrodinger, Pauli and Dirac developed the fundamentals of quantum mechanics and merged them into a coherent theory, and why the mathematical infrastructure of quantum mechanics has to be as complex as it is. The author creates a compelling narrative, providing a remarkable example of how physics and mathematics work in practice. The book encourages an enhanced appreciation of the interaction between mathematics, theory and experiment, helping the reader gain a deeper understanding of the development and content of quantum mechanics than any other text at this level.

Quantum Concepts in Physics

Proportional Representation

Proportional Representation

The book offers a rigorous description of the procedures that proportional representation systems use to translate vote counts into seat numbers. Since the methodological analysis is guided by practical needs, plenty of empirical instances are provided and reviewed to motivate the development, and to illustrate the results. Concrete examples, like the 2009 elections to the European Parliament in each of the 27 Member States and the 2013 election to the German Bundestag, are analyzed in full detail. The level of mathematical exposition, as well as the relation to political sciences and constitutional jurisprudence makes this book suitable for special graduate courses and seminars.

Proportional Representation

The Mathematics of Logic

The Mathematics of Logic

This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with Knig’s Lemma, and progressing via order relations, Zorn’s Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.

The Mathematics of Logic

Recent Advances in Operator Theory, Operator Algebras and Their Applications

Recent Advances in Operator Theory, Operator Algebras and Their Applications

This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.

Recent Advances in Operator Theory, Operator Algebras and Their Applications

Discrete Mathematics Using aComputer

Discrete Mathematics Using aComputer

This volume offers a new, ‘hands-on’ approach to teaching Discrete Mathematics. A simple functional language is used to allow students to experiment with mathematical notations which are traditionally difficult to pick up. This practical approach provides students with instant feedback and also allows lecturers to monitor progress easily. All the material needed to use the book will be available via ftp (the software is freely available and runs on Mac, PC and Unix platforms), including a special module which implements the concepts to be learned. No prior knowledge of Functional Programming is required: apart from List Comprehension (which is comprehensively covered in the text) everything the students need is either provided for them or can be picked up easily as they go along. An Instructors Guide will also be available on the WWW to help lecturers adapt existing courses.

Discrete Mathematics Using aComputer

The Mathematics of the Bose Gas and Its Condensation

The Mathematics of the Bose Gas and Its Condensation

This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.

The Mathematics of the Bose Gas and Its Condensation

Italian Mathematics Between the Two World Wars

Italian Mathematics Between the Two World Wars

This book describes Italian mathematics in the period between the two World Wars. We analyze its development by focusing on both the interior and the external influences. Italian mathematics in that period was shaped by a colorful array of strong personalities who concentrated their efforts on a select number of fields and won international recognition and respect in an incredibly short time. Consequently, Italy was considered a third ‘mathematical power’ after France and Germany, and qualified Italian universities became indispensable stops on the ‘tour’, organized for the improvement of young foreign mathematicians. At that time, Italy was also dominated by a fascist regime. This political situation and the social and academic structure of Italian society are included in the analysis as influences external to mathematics itself. The authors have provided a fascinating study of a most difficult time in the history of the world and of mathematics.

Italian Mathematics Between the Two World Wars

Mathematics

Mathematics

This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed explanations of the important mathematical procedures actually used by famous mathematicians, giving more mathematically talented students a greater opportunity to learn the history and philosophy by way of problem solving. Several important philosophical topics are pursued throughout the text, giving the student an opportunity to come to a full and consistent knowledge of their development. These topics include infinity, the nature of motion, and Platonism. This book offers, in fewer pages, a deep penetration into the key mathematical and philosophical aspects of the history of mathematics.

Mathematics

Games, Puzzles and Computation

Games, Puzzles and Computation

The authors show that there are underlying mathematical reasons for why games and puzzles are challenging (and perhaps why they are so much fun). They also show that games and puzzles can serve as powerful models of computationquite different from the usual models of automata and circuitsoffering a new way of thinking about computation. The appendices provide a substantial survey of all known results in the field of game complexity, serving as a reference guide for readers interested in the computational complexity of particular games, or interested in open problems about such complexities.

Games, Puzzles and Computation

Mathematical Modeling in Continuum Mechanics

Mathematical Modeling in Continuum Mechanics

Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrdinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

Mathematical Modeling in Continuum Mechanics

Early Mathematics Learning

Early Mathematics Learning

This book will gather current research in early childhood mathematics education. A special focus will be the tension between instruction and construction of knowledge. The book includes research on the design of learning opportunities, the development of mathematical thinking, the impact of the social setting and the professionalization of nursery teachers.

Early Mathematics Learning

Computational Prospects of Infinity - Part 2

Computational Prospects of Infinity - Part 2

This volume is a collection of written versions of the talks given at the Workshop on Computational Prospects of Infinity, held at the Institute for Mathematical Sciences from 18 June to 15 August 2005. It consists of contributions from many of the leading experts in recursion theory (computability theory) and set theory. Topics covered include the structure theory of various notions of degrees of unsolvability, algorithmic randomness, reverse mathematics, forcing, large cardinals and inner model theory, and many others. Book jacket.

Computational Prospects of Infinity - Part 2

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms provides a complete analytical approach to the invention of new robot mechanisms and the analysis of existing designs based on a unified mathematical description of the kinematic and geometric constraints of mechanisms.

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms

Lectures on Infinite-Dimensional Lie Algebra

Lectures on Infinite-Dimensional Lie Algebra

The representation theory of affine Lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three excellent books on it, written by Victor G Kac. This book begins with a survey and review of the material treated in Kac’s books. In particular, modular invariance and conformal invariance and are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation theory of affine Lie algebras. Since these topics are important not only in themselves but also in their application to some areas of mathematics and mathematical physics, the book expounds them with examples and detailed calculations.

Lectures on Infinite-Dimensional Lie Algebra

Geometric Algebra And Applications to Physics

Geometric Algebra And Applications to Physics

Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations.

Geometric Algebra And Applications to Physics

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes

The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potential representations, and the solution of the latter in Sobolev spaces.

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes