Where can I learn real analysis and proving online?

AI Thread Summary
The discussion centers on the challenges faced in a mathematics course, particularly with real analysis and proof-based questions. The individual is considering self-studying these topics online but is advised by their teacher to focus on other subjects. However, there is a strong belief that self-study is essential for mastering proof techniques and real analysis. The individual plans to purchase the Velleman book and seeks recommendations for affordable analysis textbooks, ideally under $50. They also inquire about online resources for learning series and sequences, expressing a preference for specific YouTube lecture series on real analysis. Additionally, they share their experience with a test that includes difficult questions, questioning whether a university textbook is necessary given their current performance and the time available before finals. The conversation emphasizes the importance of self-study and finding the right resources to enhance understanding in mathematics.
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Hello,
I noticed that the most difficult questions in my maths course are usually real analysis and proving questions like http://i.imgur.com/IBols.png and http://i.imgur.com/KETnq.png.
I was going to buy university level textbooks to cover them but my teacher told me not to because I need to concentrate on my other subjects as well and not only maths so I thought the solution is to cover them online.
 
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If you want to learn them well, then you do need to go through textbooks. Resources on the internet can be good, but should never be used as a primary resource.

I disagree with your teacher. It's true that you need to spend time on other subjects as well and that you shouldn't neglect them. But nobody says that you can't study proving in your free time. I think it's an excellent idea to learn how to proof things and to learn real analysis.

How are you ever going to get ahead of others if you never self-study things. It's not a good idea to only rely on your classes. Self-studying is a good and useful skill to have.
 
Ok, I will buy the Velleman book then but does it cover proving for analysis type of questions?
If not what analysis books do you recommend? Hopefully they are no more expensive than about $50 :)
But if I want to cover the basics of series and sequences online do you recommend any websites/YouTube channels?
Can you please have a look at this test: http://www.mediafire.com/view/?cu74f59c395cafv
Most tests are about this difficulty (or easier) and they give us 3 hours to do it. I can do about 3/4 of the test in 1.5-2 hours but the last questions are usually very difficult. I have about 10 months before I do the finals, they are in October. So do you think a uni textbook is necessary or are these questions too easy?
 
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