A Primer for Mathematical Analysis

Erscheinungsjahr 2025
ISBN: 978-3-031-91712-7
Verlag: Springer

Buch, Englisch, 119 Seiten, Format (B × H): 173 mm x 246 mm, Gewicht: 402 g

Reihe: Synthesis Lectures on Mathematics & Statistics

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 , 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Borthwick, David

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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

Über Autor(innen)

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 in the Springer GTM series.