# Real Analysis 101: Tips for Writing Good Proofs

• Rakiztah
In summary, the speaker is asking for tips and advice on how to improve their proof writing skills in a real analysis course. They mention that the material is different from their previous experience with engineering math and that they find the current textbook too formal. They also request recommendations for a beginner-friendly book on the subject. Another person responds by suggesting to use examples to better understand proofs and recommends a standard book on analysis.
Rakiztah
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.

Last edited by a moderator:
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)

## 1. What is Real Analysis?

Real Analysis is a branch of mathematics that deals with the study of real numbers and their properties. It involves rigorous proofs and logical reasoning to analyze mathematical concepts and structures.

## 2. Why is writing good proofs important in Real Analysis?

Writing good proofs is crucial in Real Analysis because it allows for clear and precise communication of mathematical ideas and concepts. It also helps in developing logical thinking and problem-solving skills.

## 3. What are some tips for writing good proofs in Real Analysis?

Some tips for writing good proofs in Real Analysis include clearly stating the hypothesis and conclusion, using precise and concise language, providing logical and step-by-step reasoning, and using mathematical notation correctly.

## 4. How can I improve my proof-writing skills in Real Analysis?

You can improve your proof-writing skills in Real Analysis by practicing regularly, seeking feedback from peers and professors, studying and analyzing well-written proofs, and understanding the underlying concepts and definitions.

## 5. What are some common mistakes to avoid when writing proofs in Real Analysis?

Some common mistakes to avoid when writing proofs in Real Analysis include using ambiguous language, making assumptions without justification, skipping steps, and using incorrect mathematical notation. It is also important to avoid circular reasoning and to always check your work for errors.

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