A Primer for Mathematical Analysis

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.

List of contents

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

Summary

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.

Product details

• Authors: David Borthwick
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Release: 12.06.2025
• EAN: 9783031917127
• ISBN: 978-3-0-3191712-7
• No. of pages: 100
• Illustrations: VIII, 100 p. 18 illus., 16 illus. in color.
• Series: Synthesis Lectures on Mathematics & Statistics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics; Analysis, Mathematische Analysis, allgemein, Funktionalanalysis und Abwandlungen, Integralrechnung und -gleichungen, Komplexe Analysis, komplexe Variablen, Funktionentheorie, Mathematics, Reelle Analysis, Real-Variablen, Functional Analysis, Real Functions, Integral Transforms and Operational Calculus, Several Complex Variables and Analytic Spaces, Metric Spaces, compactness, Metric Topology, Continuous Functions