Real Analysis Theorems & Definitions: Notes for Applying the Moore Method

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SUMMARY

The discussion centers on the need for a structured collection of theorems and definitions in real analysis that aligns with the Moore Method, which emphasizes student-led proof construction. A suggested resource is the link to the University of Texas at Austin's reference page, although it does not fully meet the request for a logical sequence starting from the Peano postulates through to derivatives. The user seeks a comprehensive guide that facilitates independent learning through theorem proofing.

PREREQUISITES
  • Understanding of the Peano postulates
  • Familiarity with real number construction
  • Knowledge of sequences and limits in real analysis
  • Basic concepts of derivatives
NEXT STEPS
  • Research resources on the Moore Method in mathematics education
  • Explore comprehensive texts on real analysis, focusing on theorem and definition organization
  • Study the construction of real numbers in detail
  • Investigate proof techniques for sequences and limits in real analysis
USEFUL FOR

Students of mathematics, educators implementing the Moore Method, and anyone seeking a structured approach to learning real analysis through theorem proofing.

CMoore
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Can anyone recommend notes or a book that contains only the theorems and definitions of real analysis in a logical sequence to which the Moore Method could be applied?

Thank You.
 
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Thanks, but that's really not what I'm looking for. What I'm looking for is a logical sequence of definitions and theorems that begins with, say, the Peano postulates, works its way through the construction of real numbers and lists theorems on sequences, limits, derivatives, etc. The idea of this would be for the student (me) to supply the proofs (insofar as that is possible).
 

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