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.

About the author

David Borthwick, Ph.D., is a Professor in the Department of Mathematics at Emory University.  He received his Ph.D. in physics from Harvard University in 1993 and has taught mathematics at Emory for over 25 years. His research focuses on mathematical physics, spectral theory, and geometric analysis. He is the author of several books, including Spectral Theory in the Springer GTM series.

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
• Released: 12.06.2025
• EAN: 9783031917127
• ISBN: 978-3-0-3191712-7
• No. of pages: 119
• Dimensions: 168 mm x 10 mm x 240 mm
• Weight: 341 g
• Illustrations: VIII, 119 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