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(Mostly) Commutative Algebra
This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.
Fuzzy Semigroups
Lotfi Zadeh introduced the notion of a fuzzy subset of a set in 1965. Ris seminal paper has opened up new insights and applications in a wide range of scientific fields. Azriel Rosenfeld used the notion of a fuzzy subset to put forth cornerstone papers in several areas of mathematics, among other discplines. Rosenfeld is the father of fuzzy abstract algebra. Kuroki is re sponsible for much of fuzzy ideal theory of semigroups. Others who worked on fuzzy semigroup theory, such as Xie, are mentioned in the bibliogra phy. The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. We concentrate mainly on theoretical aspects, but we do inc...
Fuzzy Information and Engineering Volume 2
This book is the proceedings of the Third International Conference on Fuzzy Information and Engineering (ICFIE 2009) held in the famous mountain city Chongqing in Southwestern China, from September 26-29, 2009. Only high-quality papers are included. The ICFIE 2009, built on the success of previous conferences, the ICFIE 2007 (Guangzhou, China), is a major symposium for scientists, engineers and practitioners in the world to present their updated results, ideas, developments and applications in all areas of fuzzy information and engineering. It aims to strengthen relations between industry research laboratories and universities, and to create a primary symposium for world scientists in fuzzy fields as follows: Fuzzy Information; Fuzzy Sets and Systems; Soft Computing; Fuzzy Engineering; Fuzzy Operation Research and Management; Artificial Intelligence; Fuzzy Mathematics and Systems in Applications, etc.
Data Analysis and Pattern Recognition in Multiple Databases
Pattern recognition in data is a well known classical problem that falls under the ambit of data analysis. As we need to handle different data, the nature of patterns, their recognition and the types of data analyses are bound to change. Since the number of data collection channels increases in the recent time and becomes more diversified, many real-world data mining tasks can easily acquire multiple databases from various sources. In these cases, data mining becomes more challenging for several essential reasons. We may encounter sensitive data originating from different sources - those cannot be amalgamated. Even if we are allowed to place different data together, we are certainly not able...
Basic Language Of Mathematics
This book originates as an essential underlying component of a modern, imaginative three-semester honors program (six undergraduate courses) in Mathematical Studies. In its entirety, it covers Algebra, Geometry and Analysis in One Variable.The book is intended to provide a comprehensive and rigorous account of the concepts of set, mapping, family, order, number (both natural and real), as well as such distinct procedures as proof by induction and recursive definition, and the interaction between these ideas; with attempts at including insightful notes on historic and cultural settings and information on alternative presentations. The work ends with an excursion on infinite sets, principally a discussion of the mathematics of Axiom of Choice and often very useful equivalent statements.
Symbolic and Quantitative Approaches to Reasoning with Uncertainty
This book constitutes the refereed proceedings of the 14th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2017, held in Lugano, Switzerland, in July 2017. The 44 revised full papers presented together with 5 abstracts of invited talks were carefully reviewed and selected from 63 submissions and cover topics on analogical reasoning; argumentation; Bayesian networks; belief functions; conditionals; credal sets, credal networks; decision theory, decision making and reasoning under uncertainty; fuzzy sets, fuzzy logic; logics; orthopairs; possibilistic networks; and probabilistic logics, probabilistic reasoning.
Advances in Knowledge Discovery in Databases
This book presents recent advances in Knowledge discovery in databases (KDD) with a focus on the areas of market basket database, time-stamped databases and multiple related databases. Various interesting and intelligent algorithms are reported on data mining tasks. A large number of association measures are presented, which play significant roles in decision support applications. This book presents, discusses and contrasts new developments in mining time-stamped data, time-based data analyses, the identification of temporal patterns, the mining of multiple related databases, as well as local patterns analysis.
Representations of Finite Groups: Local Cohomology and Support
The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algeb...
