Introductory Algebraic Number TheorySuitable for senior undergraduates and beginning graduate students in mathematics, this book is an introduction to algebraic number theory at an elementary level. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested readings and to the biographies of mathematicians who have contributed to the development of algebraic number theory are provided at the end of each chapter.
Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures
This book for the first time introduces neutrosophic groups, neutrosophic semigroups, neutrosophic loops and neutrosophic groupoids and their neutrosophic N-structures. The special feature of this book is that it tries to analyze when the general neutrosophic algebraic structures like loops, semigroups and groupoids satisfy some of the classical theorems for finite groups viz. Lagrange, Sylow, and Cauchy.
Algebraic Geometry and Statistical Learning Theory
Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.
These volumes contain survey papers given at the 1991 international symposium on geometric group theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. Volume I contains reviews of such subjects as isoperimetric and isodiametric functions, geometric invariants of a groups, Brick's quasi-simple filtrations for groups and 3-manifolds, string rewriting, and algebraic proof of the torus theorem, the classification of groups acting freely on R-trees, and much more.
The main aim of this book is to present a completely algebraic approach to the Enriques' classification of smooth projective surfaces defined over an algebraically closed field of arbitrary characteristic. This algebraic approach is one of the novelties of this book among the other modern textbooks devoted to this subject. Two chapters on surface singularities are also included. The book can be useful as a textbook for a graduate course on surfaces, for researchers or graduate students in algebraic geometry, as well as those mathematicians working in algebraic geometry or related fields.
