[English]

Essays in Group Theory, by Gersten
Contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol’shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallings contains gems. For example, the reader will delight in Stallings’ explicit construction of free actions of orientable surface groups on R-trees. Gersten’s paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups. Shalen’s article reviews the rapidly expanding theory of group actions on R-trees and the Baumslag-Shalen article uses modular representation theory to establish properties of presentations whose relators are pth-powers.

Ergodic Theory, by Karl Petersen
A classic. The author presents the fundamentals of the ergodic theory of point transformations and several advanced topics of intense research. Each of the basic aspects of ergodic theory–examples, convergence theorems, recurrence properties, and entropy–receives a basic and a specialized treatment. The author’s accessible style and the profusion of exercises, references, summaries, and historical remarks make this a useful book for graduate students or self study.

Begriffsschrift, a Formula Language, Modeled Upon that of Arithmetic, for Pure Thought, by Gottlob Frege
This is the first work that Frege work in the field of logic, and, although a mere booklet of 88 pages, it is perhaps the most important single work ever written in logic. Its fundamental contributions, among lesser points, are the truth-functional propositional calculus, the analysis of the propositon into function and arguments instead of subject and predicate, the theory of quantification, a system of logic in which derivations are carried out exclusively according to the form of the expressions, and a logical definition of the notion of mathematical sequence.

Sur la puissance des ensembles measurables B, by Paul S. Alexandroff (Alexandrov)
The birth of the operation (A), called also “Suslin (Souslin) schemes”.

And in Physics:

Fundamentals of photonic crystal guiding, by Maksim Skorobogatiy and Jianke Yang.
For anyone looking to understand photonic crystals, this systematic, rigorous, and pedagogical introduction is a must. Here you’ll find intuitive analytical and semi-analytical models applied to complex and practically relevant photonic crystal structures. You will also be shown how to use various analytical methods borrowed from quantum mechanics, such as perturbation theory, asymptotic analysis, and group theory, to investigate many of the limiting properties of photonic crystals which are otherwise difficult to rationalize using only numerical simulations. An introductory review of nonlinear guiding in photonic lattices is also presented, as are the fabrication and application of photonic crystals.

Principles of radiation interaction in matter and detection, by Claude Leroy and Pier-Giorgio Rancoita.
Data analysis and instrumentation applications require an excellent knowledge of the interactions between radiation and matter, radiation and particle detectors, the principles and conditions of detector operation, as well as the limitations and advantages. This book provides abundant information about the energy deposition in detecting systems, the performance and optimization of detectors. It also addresses the situation where detectors (scanners of various types, etc.) have to be modified and improved to full optimization by the users. Furthermore, the book offers a description of detectors and techniques used in medical physics and covers physics principles and instrumentation knowledge needed in radioprotection and nuclear engineering.

Theory of elasticity (second edition), by Timoshenko and Goodier

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[Español]

Essays in Group Theory, de Gersten
Contiene cinco artículos de interés actual que fueron presentados en un seminario en el MSRI, Berkeley, en Junio de 1985. Mención especial merece el artículo de Gromov, uno de los más significativos de las últimas décadas. Desarrolla la teoría de los grupos hiperbólicos para incluir una versión de la teoría de cancelación pequeña lo suficientemente potente como para recuperar resultados profundos de Ol’shanskii y Rips.

Ergodic Theory, de Karl Petersen

Un clásico. El autor presenta los fundamentos de la teoría ergódica de trasnformaciones punto a punto y diversos tópicos de investigación avanzada.

Begriffsschrift, a Formula Language, Modeled Upon that of Arithmetic, for Pure Thought, de Gottlob Frege
El primer trabajo de Frege en el campo de la lógica y, probablemente, el artículo más importante de la historia en este campo.

Sur la puissance des ensembles measurables B, de Paul S. Alexandroff (Alexandrov)
El nacimiento de la operación (A), también llamada “esquemas de Suslin (Souslin)”.

Y en Física:

Fundamentals of photonic crystal guiding, de Maksim Skorobogatiy y Jianke Yang.
Introducción sistemática y rigurosa a los cristales fotónicos.

Principles of radiation interaction in matter and detection, de Claude Leroy y Pier-Giorgio Rancoita.
El análisis de datos y las aplicaciones instrumentales requieren un conocimiento excelente de las interaciones entre radiación y materia, radiación y detectores de partículas y los principios y condiciones de operación de los detectores.

Theory of elasticity (segunda edición), de Timoshenko y Goodier