How to study from a Real Analysis textbook like this

In summary, the speaker is taking a class in real analysis and has studied some chapters over the summer. They wanted to use a more rigorous book, but were advised against it and ended up using Pugh's "Real Mathematical Analysis" instead. They are confused about the book's approach of providing minimal material in each chapter, followed by a large number of theoretical exercises. They are seeking advice on how to effectively study from this type of textbook and where to find routine problems that reinforce the basic definitions and theorems. The speaker mentions their preference for the Schaum's Outline series for self-study and practice exercises.
  • #1
Saph
17
9
Hello,
I am taking a class in RA, where we're using Bartle/Sherbert. Since I have studied few chapters from it in the summer before, I decided to take a look at a more rigorous book, like baby rudin, but since many have advised against that book, I turned to Pugh's real mathematical analysis, but I am confused a little bit about the book.
Unlike every textbook that I have studied, this book presents the material in the chapter to give you the absolute minimum you need to solve the exercises or maybe less ( with very few examples, no problems /section) then at the end of the chapter it gives you a ton of exercises, but the problem is, these exercises are mostly theoretical, and almost non of the usual drill exercises that enforces the theory, and some of the problems in Pugh are sections in bartle/sherbert, like the monotone convergence property.
So my questions are, how to study (effectively) from a textbook like this, and how to know which problems to solve? ( in chapter 2, about topology, there are 152 exercise at the end of the chapter, non of them is a routine calculation, then 15 prelim problems from UCBerkely, thus a total of 167 problems), and where to find routine problems that enforces the basic def/theorems ?
 
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  • #2
For self study and exercises to practice on, I have always been a fan of the Schaum's Outline series. They have one on real analysis. The problem of matching it's content to another book is something I have never attempted, but the content is fairly standard.
 

Related to How to study from a Real Analysis textbook like this

1. How do I approach studying from a Real Analysis textbook?

Studying from a Real Analysis textbook requires a specific approach. First, make sure you have a solid foundation in calculus and basic mathematical concepts. Next, read the material carefully and take notes. Practice solving problems and proofs to solidify your understanding. Lastly, review the material regularly to reinforce your knowledge.

2. How can I understand difficult concepts in Real Analysis?

Real Analysis can be challenging, but with persistence and the right approach, you can understand difficult concepts. Start by breaking down complex ideas into smaller, more manageable parts. Use examples and diagrams to help visualize the concepts. Don't be afraid to ask questions and seek clarification from your professor or peers.

3. How much time should I spend studying from a Real Analysis textbook?

The amount of time you spend studying from a Real Analysis textbook will vary depending on your understanding of the material and your learning style. It is recommended to spend at least 2-3 hours per week studying for this course. However, you may need to adjust your study time based on your individual needs.

4. How do I prepare for exams in Real Analysis?

To prepare for exams in Real Analysis, it's essential to review your notes and practice solving problems and proofs. Make sure you understand all the concepts and theorems covered in the textbook. Utilize practice exams and study with peers to test your knowledge and identify any areas that need improvement.

5. What resources can I use to supplement my studying from a Real Analysis textbook?

There are many resources available to supplement your studying from a Real Analysis textbook. These include online lectures, practice problems, study guides, and additional textbooks. You can also attend study groups or seek help from your professor or teaching assistant if you need further clarification on certain topics.

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