Real Analysis 101: Tips for Writing Good Proofs

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SUMMARY

The forum discussion centers on tips for writing proofs in real analysis, specifically for beginners. The participant is using "Introduction to Real Analysis" by Bartle, which they find too formal. A recommendation is made to follow examples alongside proofs to better understand the abstract nature of real analysis. Additionally, a link to a standard book on analysis is provided for further study.

PREREQUISITES
  • Understanding of basic mathematical concepts and terminology.
  • Familiarity with proof techniques such as direct proof, contradiction, and induction.
  • Basic knowledge of real numbers and functions.
  • Experience with mathematical notation and formal writing.
NEXT STEPS
  • Explore "Understanding Analysis" by Stephen Abbott for a beginner-friendly approach.
  • Practice writing proofs using examples from "Introduction to Real Analysis" by Bartle.
  • Study proof techniques in detail, focusing on direct proofs and proofs by contradiction.
  • Engage with online resources or forums dedicated to real analysis for additional support.
USEFUL FOR

Students new to real analysis, mathematics educators, and anyone looking to improve their proof-writing skills in abstract mathematics.

Rakiztah
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hello everyone!
I just started a course in real analysis and i must say that it is quite different from all the "engineering math" that i have taken before.I was wondering if anyone could give me tips or advice on how to get better at writing good proofs. Right now,we are using a book called Introduction to real analysis by Bartle,but its too formal for my taste. Also,if anyone could suggest a book that is made for a total beginner,that would be much appreciated.
Thanks in advance.
 
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Proofs are by nature more abstract and different than engineering problems. Best you can do is choose some examples and follow the proof along such examples in parallel. A standard book about analysis is
https://www.amazon.com/dp/0914098918/?tag=pfamazon01-20
(older editions are cheaper)
 

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