Foundations of analysis
type: Item
instance of: scholarly article
zbMATH Open document ID: 1258.26001
author: Joseph L. Taylor
publication date: 2012-08-10T00:00:00Z
Mathematics Subject Classification ID: 26-01
Mathematics Subject Classification ID: 26Axx
Mathematics Subject Classification ID: 26Bxx
Mathematics Subject Classification ID: 26Dxx
Mathematics Subject Classification ID: 03E10
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 97I10
zbMATH DE Number: 6064534
zbMATH Keywords: textbooks (real function)
zbMATH Keywords: one-variable calculus
zbMATH Keywords: functions of several variables
zbMATH Keywords: differential forms
zbMATH Keywords: integral formulas
zbMATH Keywords: metric spaces
zbMATH Keywords: normed linear spaces
MaRDI profile type: Publication
title: Foundations of analysis
published in: Pure and Applied Undergraduate Texts
review text: About one year ago, the author published his excellent textbook ``Complex variables'' [Providence, RI: American Mathematical Society (AMS) (2011; Zbl 1234.30002)]. Like that profound introduction to the classical theory of functions of one complex variable, the book under review evolved from the author's notes for a basic undergraduate course at the University of Utah. As it is pointed out in the preface, this course on foundations of real analysis is geared toward students who have completed three semesters of calculus and one semester of linear algebra, by which the prerequisites for the present book are already outlined. Also, as the author particularly emphasizes, the book reflects the two main goals of this specific course, namely to help students develop the necessary mathematical maturity and sophistication needed for senior or graduate level mathematics courses, on the one hand, and to present a first rigorous treatment of calculus from scratch on the other. Although the topics covered in the current analysis primer are quite standard, their treatment is certainly rather special and didactically refined. In fact, the rich material is presented in a fashion that combines lucidity, rigor, conciseness, straightforward explanations, and instructive examples in a masterly manner, thereby displaying an exceptionally high degree of didactical effectivity and user-friendliness. Actually, this text has been used by the author and his colleagues for several years at the University of Utah. It has undergone many improvements, additions, and corrections in the course of these years, and appears now in a well-tested, highly polished design.NEWLINENEWLINE As for the precise contents, the book comprises eleven chapters, each of which is subdivided in several sections.NEWLINENEWLINE Chapter 1 gives an outline of the construction of the field of real numbers. Starting with some basics on sets and functions, the natural numbers (via Peano's axioms), integers and rational numb…
reviewed by: Werner Kleinert
description: scientific article; zbMATH DE number 6064534