An Elementary Overview of Mathematical Structures

Since the last century, a large part of Mathematics is concerned with the study of mathematical structures, from groups to fields and vector spaces, from lattices to Boolean algebras, from metric spaces to topological spaces, from topological groups to Banach spaces.More recently, these structured sets and their transformations have been assembled in higher structures, called categories.We want to give a structural overview of these topics, where the basic facts of the different theories are unified through the 'universal properties' that they satisfy, and their particularities stand out, perhaps even more.This book can be used as a textbook for undergraduate studies and for self-study. It can provide students of Mathematics with a unified perspective of subjects which are often kept apart. It is also addressed to students and researchers of disciplines having strong interactions with Mathematics, like Physics and Chemistry, Statistics, Computer Science, Engineering.Contents: PrefaceIntroductionAlgebraic Structures, IAlgebraic Structures, IITopological Structures, ITopological Structures, IICategories and FunctorsCategorical Limits and AdjunctionsSolutions and HintsReferencesIndex
Readership: Undergraduate and graduate students in Mathematics, Physics, Computer Sciences, Chemistry, Statistics, Engineering.Algebra;Topology;Category Theory;Mathematical Structures0Key Features:presents a unified approach to the main mathematical structures, in Algebra, Topology and Category TheoryThe exposition draws on the author's experience, while teaching courses of Algebra, or Topology, or Category Theory, or CalculusNotions are presented in a concrete, 'inductive' way, starting from elementary examples. Whenever possible, the reader is guided to build the theory, through a series of some 600 exercises. Most of them have a solution or sufficient hints, generally deferred to the last chapterMany references for further reading or study are given