Anyone here taken Real Analysis yet?

[luke8ball]

Real Analysis will be the most rigorous, proof-based course I've taken for my math major, and I'm concerned because a lot of people at my school HATE the course.

Any tips on preparation? Surviving?

 

[SteveL27]

Real Analysis will be the most rigorous, proof-based course I've taken for my math major, and I'm concerned because a lot of people at my school HATE the course.

Any tips on preparation? Surviving?

Well I loved the course. The very best thing you can do is get a great instructor. The other thing you can do is clear the decks in your life and plan on spending a lot of time on the course.

Anyone who hates real analysis wasn't cut out to be a math major. That's a fact. Engineering or physics, ok. But how can you love math but hate the rigorous study of the real numbers?

 

[genericusrnme]

Anyone who hates real analysis wasn't cut out to be a math major. That's a fact. Engineering or physics, ok. But how can you love math but hate the rigorous study of the real numbers?

It depends...
When I first looked at real analysis I hated it and most textbooks made it feel really unmotivated. Now that I know what I'm doing though it isn't that bad.

Any tips on preparation? Surviving?

Don't start with Rudin. Apostols analysis book is pretty nice, try that.
Examples make your own examples and get some kind of picture of what is going on and look for alternative definitions for things. Funnily enough I can't think of any off of the top of my head right now but I remember when I first looked at the subject the definitions of certain kinds of sets seemed really artificial and pointless but after looking through different textbooks and different sources I found some better (but equivelant) definitions that got to the point of what the set is.
Once you've got the sets part down the functions and sequences part of it isn't really that hard.

 

[luke8ball]

Thanks for the responses. Sounds like it's just a matter of seeing the bigger picture rather than getting caught up in any particular difficult definition.

 

[00Donut]

I've never actually taken a course, but I've self studied it for about 7 months now. Granted, this is the only rigorous, proof based part of math I've ever done, but I've never enjoyed studying anything more than this.

I started with Understanding Analysis by Stephen Abbott, then I moved on to Principles of Real Analysis by Aliprantis and Burkinshaw. The Aliprantis book is much harder than the Abbott one, but I've managed to work through about half of it on my own thanks to the excellent preparation I got by studying from Understanding Analysis first.

So if you want a book to prepare you for your Analysis course, I strongly recommend you get Understanding Analysis. Basically, if you're willing to put in hours and hours of work into understanding stuff you don't get, and into doing hard problems, you'll be fine.