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Lie Algebras and Lie Groups
The American Mathematical Society, with the financial support of the National Science Foundation, held its First Summer Mathematical Institute from June 20 to July 31, 1953. The topic chosen was Lie theory, twenty-nine mathematicians active in this area attended. The six-week period provided opportunity both for the interchange of ideas and for the subsequent shaping of ideas into theorems. The five papers present some results achieved by the participants.--Foreword.
Euclidean Geometry and its Subgeometries
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embed...
Class Field Theory and L Functions
The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras. While the first three chapters presuppose only basic algebraic and topological knowledge, the rest of the books assumes knowledge of the basic theory of algebraic numbers and algebraic functions, such as those contained in my previous book, An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020). The main features of the book are: A detailed study of Pontrjagin’s dualtiy theorem. A thorough presentation of the cohomology of profinite groups. A i...
Algebraic Number Theory
From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993
Lectures on Algebra
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.
Discovery Science
These are the conference proceedings of the 4th International Conference on Discovery Science (DS 2001). Although discovery is naturally ubiquitous in s- ence, and scientific discovery itself has been subject to scientific investigation for centuries, the term Discovery Science is comparably new. It came up in conn- tion with the Japanese Discovery Science project (cf. Arikawa's invited lecture on The Discovery Science Project in Japan in the present volume) some time during the last few years. Setsuo Arikawa is the father in spirit of the Discovery Science conference series. He led the above mentioned project, and he is currently serving as the chairman of the international steering committ...
Empirical Studies of Environmental Policies in Europe
The visible encroachment of industrial development on the environment, and its unintended consequences, has increased public demand for better environmental management and policy. As policy makers struggle to meet these demands, empirical analysis of the effects of environmental policies is crucial for guiding the development, the implementation, and the evaluation of alternative government interventions and regulatory approaches. Such analysis is scarce, however. The need for empirical studies is particularly large in Europe, where environmental policy debates are still mainly theoretical and tend to reflect different ideological positions more than informed assessments of alternative policies. Empirical Studies of Environmental Policies in Europe presents contributions on empirical environmental policy evaluation. The individual chapters, written by authors from Europe and the US, contain quantitative studies of proposed and implemented environmental policies, at both the micro and macroeconomic levels. The policy issues studied in this volume include the 'double dividend-hypothesis' of carbon taxation, the political economy of en
Advances in Integrated Design and Production
This book reports on innovative concepts and practical solutions at the intersection between engineering design, engineering production and industrial management. It covers cutting-edge design, modeling and control of dynamic and multiphysics systems, knowledge management systems in industry 4.0, cyber-physical production systems, additive and sustainable manufacturing and many other related topics. The original, carefully selected, peer-reviewed chapters highlight collaborative works between different countries and between industry and universities, thus offering a timely snapshot for the research and industrial communities alike, as well as a bridge to facilitate communication and collaboration.
The Absolute Galois Group of a Semi-Local Field
This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory. Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups. The book will be of interest to researchers in field arithmetic, Galois theory and profinite groups.
