Exercises in Classical Ring Theory

Exercises in Classical Ring Theory

‘ This useful book, which grew out of the author’s lectures at Berkeley, presents some 400 exercises of varying degrees of difficulty in classical ring theory, together with complete solutions, background information, historical commentary, bibliographic details, and indications of possible improvements or generalizations. The book should be especially helpful to graduate students as a model of the problem-solving process and an illustration of the applications of different theorems in ring theory. The author also discusses ‘the folklore of the subject: the ‘tricks of the trade’ in ring theory, which are well known to the experts in the field but may not be familiar to others, and for which there is usually no good reference’. The problems are from the following areas: the Wedderburn-Artin theory of semisimple rings, the Jacobson radical, representation theory of groups and algebras, (semi)prime rings, (semi)primitive rings, division rings, ordered rings, (semi)local rings, the theory of idempotents, and (semi)perfect rings. Problems in the areas of module theory, category theory, and rings of quotients are not included, since they will appear in a later book. ‘

Exercises in Classical Ring Theory

Lectures on Numerical Mathematics

Lectures on Numerical Mathematics

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Lectures on Numerical Mathematics

Clusters in Nuclei, Volume 3

Clusters in Nuclei, Volume 3

Following the pioneering discovery of alpha clustering and of molecular resonances, the field of nuclear clustering is today one of those domains of heavy-ion nuclear physics that faces the greatest challenges, yet also contains the greatest opportunities. After many summer schools and workshops, in particular over the last decade, the community of nuclear molecular physicists has decided to collaborate in producing a comprehensive collection of lectures and tutorial reviews covering the field. This third volume follows the successful Lect. Notes Phys. 818 (Vol. 1) and 848 (Vol. 2), and comprises six extensive lectures covering the following topics:

Clusters in Nuclei, Volume 3

Axions

Axions

Axions are peculiar hypothetical particles that could both solve the CP problem of quantum chromodynamics and at the same time account for the dark matter of the universe. Based on a series of lectures by world experts in this field held at CERN (Geneva), this volume provides a pedagogical introduction to the theory, cosmology and astrophysics of these fascinating particles and gives an up-to-date account of the status and prospect of ongoing and planned experimental searches. Learners and practitioners of astroparticle physics will find in this book both a concise introduction and a current reference work to a showcase topic that connects the ‘inner space’ of the elementary particle world with the ‘outer space’ of the universe at large.

Axions

Analysis, Geometry and Topology of Elliptic Operators

Analysis, Geometry and Topology of Elliptic Operators

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah?Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski’s work in the theory of elliptic operators.

Analysis, Geometry and Topology of Elliptic Operators

Silence

Silence

Silence, John Cage’s first book and epic masterpiece, was published in October 1961. In these lectures, scores, and writings, Cage tries, as he says, to find a way of writing that comes from ideas, is not about them, but that produces them. Often these writings include mesostics and essays created by subjecting the work of other writers to chance procedures using the I Ching. Fifty years later comes a beautiful new edition with a foreword by eminent music critic Kyle Gann. A landmark book in American arts and culture, Silence has been translated into more than forty languages and has sold over half a million copies worldwide. Wesleyan University Press is proud to celebrate the fiftieth anniversary of the book’s publication with this special hardcover edition.

Silence

Generic and Indexed Programming

Generic and Indexed Programming

Generic programming is about making programs more widely applicable via exotic kinds of parametrization—not just along the dimensions of values or of types, but also of things such as the shape of data, algebraic structures, strategies, computational paradigms, and so on. Indexed programming is a lightweight form of dependently typed programming, constraining flexibility by allowing one to state and check relationships between parameters: that the shapes of two arguments agree, that an encoded value matches some type, that values transmitted along a channel conform to the stated protocol, and so on. The two forces of genericity and indexing balance each other nicely, simultaneously promoting and controlling generality. The 5 lectures included in this book stem from the Spring School on Generic and Indexed Programming, held in Oxford, UK, in March 2010 as a closing activity of the generic and indexed programming project at Oxford which took place in the years 2006-2010.

Generic and Indexed Programming

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

Lectures on Algebra, Volume 1

Lectures on Algebra, Volume 1

This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author’s fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author’s lectures at Purdue University over the last few years.

Lectures on Algebra, Volume 1

Lectures in Functional Analysis and Operator Theory

Lectures in Functional Analysis and Operator Theory

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Lectures in Functional Analysis and Operator Theory

13 Lectures on Fermats Last Theorem

13 Lectures on Fermats Last Theorem

In the first two lectures, there is a very brief description of the early history, as well as a selection of a few of the more representative recent results. In the lectures which follow, I examine in succession the main theories connected with the problem. The last two lectures are about analogues to Fermat’s theorem.

13 Lectures on Fermats Last Theorem

Lectures on Chern-Weil Theory and Witten Deformations

Lectures on Chern-Weil Theory and Witten Deformations

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Lectures on Chern-Weil Theory and Witten Deformations

String Theory

String Theory

String Theory is our current best candidate for the unification of all fundamental forces, including gravity, in a consistent quantum framework. In this collection of lectures delivered at the Carghse Summer School String Theory: from Gauge Interactions to Cosmology”, world leading experts provide an up-to-date survey of the latest developments in this topic, including the gauge/gravity correspondence, superstring cosmology and cosmic strings, topological string theory and matrix models, physics beyond the standard model and the landscape of vacua of string theory, conformal field theory and critical phenomena in statistical mechanics. Many more topics are also discussed in shorter contributions by School participants. Written with an emphasis on pedagogy, this volume will be a invaluable resource to students and experts alike.

String Theory

The Attractor Mechanism

The Attractor Mechanism

This book is based upon lectures presented in June 2007 at the INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci. The symposium included such prestigious lecturers as S. Ferrara, M. Gnaydin, P. Levay, and T. Mohaupt. All lectures were given at a pedagogical, introductory level, which is reflected in the specific ‘flavor’ of this volume. The book also benefits from extensive discussions about, and related reworking of, the various contributions. In addition, this volume contains contributions originating from short presentations of recent original results and an essay on the relation between complexity science and high-energy physics by A. Zichichi. It is the fourth volume in a series of books on the general topics of supersymmetry, supergravity, black holes and the attractor mechanism.

The Attractor Mechanism

Lectures on Quantum Mechanics

Lectures on Quantum Mechanics

Beautifully illustrated and engagingly written, Twelve Lectures in Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevants style is clear and stimulating, in the manner of a brisk lecture that can be followed with ease and enjoyment. Here is a sample of the books style, from the opening of Chapter 1: ‘If one were to ask a passer-by to quote a great formula of physics, chances are that the answer would be E = mc2. There is no way around it: all physics is quantum, from elementary particles, to stellar physics and the Big Bang, not to mention semiconductors and solar cells.’

Lectures on Quantum Mechanics

Schaums Outline of Advanced Mathematics for Engineers and Scientists

Schaums Outline of Advanced Mathematics for Engineers and Scientists

Tough Test Questions? Missed Lectures? Not Enough Time?

Schaums Outline of Advanced Mathematics for Engineers and Scientists