Overview
- 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
Part of the book series: Synthesis Lectures on Mathematics & Statistics (SLMS)
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About this book
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.
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Table of contents (5 chapters)
Authors and Affiliations
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.
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Bibliographic Information
Book Title: A Primer for Mathematical Analysis
Authors: David Borthwick
Series Title: Synthesis Lectures on Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-031-91713-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2025
Hardcover ISBN: 978-3-031-91712-7Published: 01 August 2025
Softcover ISBN: 978-3-031-91715-8Due: 15 August 2026
eBook ISBN: 978-3-031-91713-4Published: 31 July 2025
Series ISSN: 1938-1743
Series E-ISSN: 1938-1751
Edition Number: 1
Number of Pages: VIII, 119
Number of Illustrations: 2 b/w illustrations, 16 illustrations in colour
Topics: Mathematics, general, Analysis, Real Functions, Several Complex Variables and Analytic Spaces, Integral Transforms, Operational Calculus, Functional Analysis