From Numbers To Analysis

by Inder K Rana

Overview

Starting with the Zermelo-Fraenhel axiomatic set theory, this book gives a self-contained, step-by-step construction of real and complex numbers. The basic properties of real and complex numbers are developed, including a proof of the Fundamental Theorem of Algebra. Historical notes outline the evolution of the number systems and alert readers to the fact that polished mathematical concepts, as presented in lectures and books, are the culmination of the efforts of great minds over the years. The text also includes short life sketches of some of the contributing mathematicians. The book provides the logical foundation of Analysis and gives a basis to Abstract Algebra. It complements those books on real analysis which begin with axiomatic definitions of real numbers.The book can be used in various ways: as a textbook for a one semester course on the foundations of analysis for post-calculus students; for a seminar course; or self-study by school and college teachers.

Product Details

ISBN-13:	9789810233044
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	10/12/1998
Pages:	388
Product dimensions:	6.30(w) x 8.60(h) x 1.00(d)

Editorial Reviews

Presents an enlarged version of notes for participants at a November 1994 workshop in mathematics held at the Indian Institute of Technology Bombay. Offers a self-contained and detailed account of the construction of real and complex numbers based on the axiomatic theory of sets and discusses their basic properties needed in higher analysis and various other branches of mathematics. Each chapter contains historical background on the number system described, and discussion of abstract concepts evolving out of the construction of the number system. For advanced undergraduates and graduates with previous knowledge of set theory and numbers. Annotation c. by Book News, Inc., Portland, Or.

Booknews