Where can I learn real analysis and proving online?

Click For Summary

Discussion Overview

The discussion centers around finding resources for learning real analysis and proof techniques online, particularly in the context of balancing study with other subjects. Participants explore the effectiveness of online resources versus traditional textbooks and seek recommendations for specific materials.

Discussion Character

  • Exploratory
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses difficulty with real analysis and proof questions and seeks online resources as an alternative to textbooks.
  • Another participant argues that while online resources can be helpful, textbooks should be the primary resource for a thorough understanding of real analysis and proving.
  • A participant plans to purchase the Velleman book and inquires about its coverage of proof techniques relevant to analysis questions.
  • There is a request for recommendations on affordable analysis books and online resources for learning about series and sequences.
  • One participant shares a link to a YouTube series on introductory real analysis lectures, indicating they found it helpful.
  • A follow-up request for recommendations on resources specifically focused on proving techniques is made, indicating a continued search for suitable materials.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether online resources can adequately replace textbooks for learning real analysis and proof techniques. There are differing opinions on the necessity of university-level textbooks versus online learning.

Contextual Notes

Participants express varying levels of confidence in their ability to tackle real analysis questions, with some indicating they can handle most test questions while finding others particularly challenging. The discussion reflects a range of experiences and expectations regarding the difficulty of the material.

Who May Find This Useful

Students seeking to enhance their understanding of real analysis and proof techniques, particularly those balancing multiple subjects and looking for online learning resources.

Synchronised
Messages
47
Reaction score
0
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.
 
Physics news on Phys.org
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?
 
Last edited by a moderator:

Similar threads

  • · Replies 1 ·
Replies
1
Views
660
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 18 ·
Replies
18
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K