Algebraic Methods in Physics

This volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelm

This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily at logisticians in mathematics, philosophy, computer science and

This book pays tribute to two pioneers in the field of Mathematical physics, Jiri Patera and Pavel Winternitz of the CRM. Each has contributed more than forty years to the subject of mathematical phys

Distributions Hilbert Space Operators Variational Methods and Applications in Quantum Physics.

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discre

The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.

This up-to-date account of algebraic statistics and information geometry explores the emerging connections between the two disciplines, demonstrating how they can be used in design of experiments and how they benefit our understanding of statistical models, in particular, exponential models. This book presents a new way of approaching classical statistical problems and raises scientific questions that would never have been considered without the interaction of these two disciplines. Beginning with a brief introduction to each area, using simple illustrative examples, the book then proceeds with a collection of reviews and some new results written by leading researchers in their respective fields. Part III dwells in both classical and quantum information geometry, containing surveys of key results and new material. Finally, Part IV provides examples of the interplay between algebraic statistics and information geometry. Computer code and proofs are also available online, where key examp

This work provides a lucid and rigorous account of the foundations of algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasised throughout. Here in this volume, the authors have again confined their attention to varieties defined on a ground field without characteristic. In order to familiarize the reader with the different techniques available to algebraic geometers, they have not confined themselves to one method and on occasion have deliberately used more advanced methods where elementary ones would serve, when by so doing it has been possible to illustrate the power of the more advanced techniques, such as valuation theory. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

This work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasised throughout. Volume 2 gives an account of the principal methods used in developing a theory of algebraic varieties in spaces of n dimensions. Applications of these methods are also given to some of the more important varieties which occur in projective geometry. The ground field is without characteristic. Since geometry over any field without characteristic conforms to the general pattern of geometry over the field of complex numbers, a sound algebraic basis for classical geometry is provided. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

This work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties, but geometrical meaning has been emphasised throughout. This first volume is divided into two parts. The first is devoted to pure algebra; the basic notions, the theory of matrices over a non-commutative ground field and a study of algebraic equations. The second part is concerned with the definitions and basic properties of projective space in n dimensions. It concludes with a purely algebraic account of collineations and correlations. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. Accompanying the mathematical derivations are full implementations of dozens of numerical methods in Python, as well as more than 250 end-of-chapter problems. Numerical methods and physics examples are clearly separated, allowing this introductory book to be later used as a reference; the penultimate section in each chapter is an in depth project, tackling physics problems which cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. Accompanying the mathematical derivations are full implementations of dozens of numerical methods in Python, as well as more than 250 end-of-chapter problems. Numerical methods and physics examples are clearly separated, allowing this introductory book to be later used as a reference; the penultimate section in each chapter is an in depth project, tackling physics problems which cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the

This text is intended for the undergraduate course in math methods, with an audience of physics and engineering majors. As a required course in most departments, the text relies heavily on explained e

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new

"Algebraic Identification and Estimation Methods in Feedback Control Systems presents the model-based algebraic approach to on-line parameter and state estimation in uncertain dynamic feedback control

Proceedings of a NATO ASI held in Bad Windsheim, Germany, July 22-August 2, 1991

Intended as a textbook for students and a guide for health physicists and nuclear professionals, this book focuses on radiation protection and dosimetry. Topics include an introduction to deterministi

Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined

All there is to know about functional analysis, integral equations and calculus of variations in one handy volume, written for the specific needs of physicists and applied mathematicians.The new editi

This systematic algebraic approach covers statistical mechanics, quantum field theory, and mathematical physics. In addition to a careful formulation of the problems' physical motivations, it features

A reference for physicists desiring to master the finer points of statistical data analysis. It contains material, especially in areas concerning the theory and practice of confidence intervals, inclu

Studying the dynamics of a large number of particles interacting through long-range forces, commonly referred to as the 'N-body problem', is a central aspect of many different branches of physics. In recent years, significant advances have been made in the development of fast N-body algorithms to deal efficiently with such complex problems. This book is the first to give a thorough introduction to these so-called 'tree methods', setting out the basic principles and giving many practical examples of their use. No prior specialist knowledge is assumed, and the techniques are illustrated throughout with reference to a broad range of applications. The book will be of great interest to graduate students and researchers working on the modelling of systems in astrophysics, plasma physics, nuclear and particle physics, condensed matter physics and materials science.

Selected Mathematical Methods in Theoretical Physics shows how a scientist, knowing the answer to a problem intuitively or through experiment, can develop a mathematical method to prove that answer. T

This book provides an introduction to Monte Carlo simulations in classical statistical physics and is aimed both at students beginning work in the field and at more experienced researchers who wish to

This monograph presents the various methods of computational physics, in particular the methods of band theory. It begins with an introduction to the field and the theoretical foundations of band theo

In Monte Carlo Methods in Chemical Physics: An Introduction to the Monte Carlo Method for Particle Simulations J. Ilja Siepmann Random Number Generators for Parallel Applications Ashok Srinivasan, Dav