Writing Proofs in Analysis

• Main Author: Kane, Jonathan M. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Subjects: Mathematics.; Fourier analysis.; Functional analysis.; Mathematical logic.; Functional Analysis.; Fourier Analysis.; Mathematical Logic and Foundations.

This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, whe...

Table of Contents:

• What Are Proofs, And Why Do We Write Them?
• The Basics of Proofs
• Limits
• Continuity
• Derivatives
• Riemann Integrals
• Infinite Series
• Sequences of Functions
• Topology of the Real Line
• Metric Spaces .