Theory of Sets, Groups, Rings, Fields,Integral Domains, Vector Spaces, Metric Spaces and Topoloical Spaces - Misra, Ram B.
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By now Algebra (based on set theoretic notions) and Topology have established their dominance over almost all the disciplines in pure mathematics. Both of these subjects have become so vast that they need their detailed discussion separately. However, an attempt has been made here to present the basic and core topics of these subjects together. The book comprises of three main parts:(i) Algebraic systems: Sets and Functions, Groups, Rings, Fields, Integral domains and Linear (or Vector) spaces; (ii) Metric spaces, and (iii) Topological spaces. The first chapter starts with Sets and Functions.…mehr

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Produktbeschreibung
By now Algebra (based on set theoretic notions) and Topology have established their dominance over almost all the disciplines in pure mathematics. Both of these subjects have become so vast that they need their detailed discussion separately. However, an attempt has been made here to present the basic and core topics of these subjects together. The book comprises of three main parts:(i) Algebraic systems: Sets and Functions, Groups, Rings, Fields, Integral domains and Linear (or Vector) spaces; (ii) Metric spaces, and (iii) Topological spaces. The first chapter starts with Sets and Functions. It includes the main features of the Set Theory needed in our subsequent discussions. The next three chapters dwell upon different kinds of algebraic structures as detailed above and cover almost all the necessary information needed by a beginner. Metric spaces have been dealt in detail in Chapter 5 including topics on Sequences and their convergence'. Bounded and unbounded sets in the metric spaces are also given. The last chapter deals with the Topological spaces. It gives a detailed account of various types of these spaces and covers almost all important topics in the subject needed for a first course.
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Autorenporträt
El profesor Dr. RB Misra ha estado enseñando matemáticas en los niveles UG / PG desde 1962. Comenzando en la Uni de Allahabad (la cuarta universidad más antigua del subcontinente indio) enseñó en varias universidades dentro y fuera de la India. Publicó más de 150 Res. Artículos en Maths en las principales revistas de renombre internacional y ha sido revisor habitual en MR y Zbl.