Algebras, Rings and Modules: Volume 1 (Mathematics and Its Applications)

Publisher: Springer | ISBN: 1402026900 | edition 2004 | PDF | 380 pages | 1,82 mb

The text of the first volume of the book covers the major topics in ring and module theory and includes both fundamental classical results and more recent developments. The basic tools of investigation are methods from the theory of modules, which allow a very simple and clear approach both to classical and new results. An unusual main feature of this book is the use of the technique of quivers for studying the structure of rings. A considerable part of the first volume of the book is devoted to a study of special classes of rings and algebras, such as serial rings, hereditary rings, semidistributive rings and tiled orders. Many results of this text until now have been available in journal articles only. This book is aimed at graduate and post-graduate students and for all mathematicians who use algebraic techniques in their work. This is a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and algebras and is suitable for independent study.

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English : Algebras Rings and Modules: Volume 1 (Mathematics and Its Applications)

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Marc Aerts, “An Invitation to Quantum Cohomology: Kontsevich’s Formula for Rational Plane Curves”

Birkhäuser Boston | 2006-10-24 | ISBN: 0817644563 | 159 pages | PDF | 6,7 MB

This book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint is mostly that of enumerative geometry, and the red thread of the exposition is the problem of counting rational plane curves. Kontsevich’s formula is initially established in the framework of classical enumerative geometry, then as a statement about reconstruction for GromovWitten invariants, and finally, using generating functions, as a special case of the associativity of the quantum product.

Emphasis is given throughout the exposition to examples, heuristic discussions, and simple applications of the basic tools to best convey the intuition behind the subject. The book demystifies these new quantum techniques by showing how they fit into classical algebraic geometry.

Some familiarity with basic algebraic geometry and elementary intersection theory is assumed. Each chapter concludes with some historical comments and an outline of key topics and themes as a guide for further study, followed by a collection of exercises that complement the material covered and reinforce computational skills. As such, the book is ideal for self-study, as a text for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory. The book will prove equally useful to graduate students in the classroom setting as to researchers in geometry and physics who wish to learn about the subject.

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English : An Invitation to Quantum Cohomology: Kontsevich’s Formula for Rational Plane Curves

Chinese : An Invitation to Quantum Cohomology: Kontsevich’s Formula for Rational Plane Curves

Chaos, Scattering and Statistical Mechanics

Publisher:Cambridge University |Pages: 495 | 1998-06-28 | ISBN 0521395119 | DJVU | 17 MB

This book describes recent advances in the application of chaos theory to classical scattering and nonequilibrium statistical mechanics generally, and to transport by deterministic diffusion in particular. The author presents the basic tools of dynamical systems theory, such as dynamical instability, topological analysis, periodic-orbit methods, Liouvillian dynamics, dynamical randomness and large-deviation formalism. These tools are applied to chaotic scattering and to transport in systems near equilibrium and maintained out of equilibrium. This book will be bought by researchers interested in chaos, dynamical systems, chaotic scattering, and statistical mechanics in theoretical, computational and mathematical physics and also in theoretical chemistry.

English : Chaos Scattering and Statistical Mechanics

Chinese : Chaos Scattering and Statistical Mechanics

Improvising Theory: Process and Temporality in Ethnographic Fieldwork By Allaine Cerwonka, Liisa H. Malkki

Publisher:University Of Chicago Press 2007 | 224 Pages | ISBN: 0226100316 | PDF | 1.4 MB

Scholars have long recognized that ethnographic method is bound up with the construction of theory in ways that are difficult to teach. The reason, Allaine Cerwonka and Liisa H. Malkki argue, is that ethnographic theorization is essentially improvisatory in nature, conducted in real time and in necessarily unpredictable social situations. In a unique account of, and critical reflection on, the process of theoretical improvisation in ethnographic research, they demonstrate how both objects of analysis, and our ways of knowing and explaining them, are created and discovered in the give and take of real life, in all its unpredictability and immediacy.

Improvising Theory centers on the year-long correspondence between Cerwonka, then a graduate student in political science conducting research in Australia, and her anthropologist mentor, Malkki. Through regular e-mail exchanges, Malkki attempted to teach Cerwonka, then new to the discipline, the basic tools and subtle intuition needed for anthropological fieldwork. The result is a strikingly original dissection of the processual ethics and politics of method in ethnography.

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