A Primer for Mathematical Analysis (Synthesis Lectures on Mathematics & Statistics) - Hardcover

Borthwick, David

Hardcover

ISBN 10: 303191712X ISBN 13: 9783031917127

Verlag: Springer, 2025

Inhaltsangabe

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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Über die Autorin bzw. den Autor

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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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

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2025
• Sprache: Englisch
• ISBN 10: 303191712X
• ISBN 13: 9783031917127
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 127
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland