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A primer for mathematical analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	A primer for mathematical analysisby David Borthwick.
Author:	Borthwick, David.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	viii, 119 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis.
Online resource:	https://doi.org/10.1007/978-3-031-91713-4
ISBN:	9783031917134$q(electronic bk.)

A primer for mathematical analysis
Borthwick, David.

A primer for mathematical analysis[electronic resource] /by David Borthwick. - Cham :Springer Nature Switzerland :2025. - viii, 119 p. :ill. (some col.), digital ;24 cm. - Synthesis lectures on mathematics & statistics,1938-1751. - Synthesis lectures on mathematics & statistics..

Real Numbers -- Complex Numbers and Series -- Metric Topology -- Functions on Metric Spaces. Solutions to Exercises -- Index.

This book presents a concise introduction to real and complex number systems and metric space theory. The goal is to help students bridge the gap between undergraduate courses in advanced calculus and graduate level material in analysis or related subjects such as differential geometry or probability. The unifying feature in all of these subject areas is the predominance of the limit, and metric space theory is the mathematical language in which limits are formulated. To understand analysis at a graduate level, students need to develop fluency in this language. To facilitate this development, exercises are incorporated into the main text, with many key results posed as problems. Solutions are provided to help readers fill in any gaps. This book: Covers the most crucial prerequisites for graduate level analysis, including metric space theory Contains plentiful exercises to help develop proficiency in the key ideas and techniques, with solutions provided Features a self-contained presentation designed for students to review or study on their own.

ISBN: 9783031917134$q(electronic bk.)

Standard No.: 10.1007/978-3-031-91713-4doiSubjects--Topical Terms:

186133
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

A primer for mathematical analysis
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520 $a This book presents a concise introduction to real and complex number systems and metric space theory. The goal is to help students bridge the gap between undergraduate courses in advanced calculus and graduate level material in analysis or related subjects such as differential geometry or probability. The unifying feature in all of these subject areas is the predominance of the limit, and metric space theory is the mathematical language in which limits are formulated. To understand analysis at a graduate level, students need to develop fluency in this language. To facilitate this development, exercises are incorporated into the main text, with many key results posed as problems. Solutions are provided to help readers fill in any gaps. This book: Covers the most crucial prerequisites for graduate level analysis, including metric space theory Contains plentiful exercises to help develop proficiency in the key ideas and techniques, with solutions provided Features a self-contained presentation designed for students to review or study on their own.
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