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/sci/ - Science & Math

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14732858 No.14732858 [Reply] [Original]

Any good resources for dumbies to learn real analysis?

I'm taking RA as a summer class and I've hit a brick wall. Our professor rushes through the lectures and she doesn't really give us much time try to absorb everything. I've never had trouble with any other math class but this one just has me stumped. I'm so lost with understanding all the definitions and I have no idea how to even approach writing a proof for many of these problems. It doesn't help that she's a very strict grader.

We're using Jiri Lebl's Basic Analysis I which is a free book and we do the end of chapter problems for our assignments.

>> No.14732867

>>14732858
>real analysis
many such cases I got a C in this class and i nearly switched majors bc of it bc i thought i was doomed in math

>> No.14732881

>>14732858
The math section in stack exchange
Paying an actual competent teacher who knows how to teach, even (especially) if he will use a different book to teach you
Paying a tutor is most likely your best shot. It could even be an online tutor

There are things that can be self taught. Unfortunately real analysis isn't one of them, because the books are terrible at teaching. Real analysis books are incredibly anti-pedagogical
You could teach yourself nuclear physics before real analysis from books. I hate math books, well most of them at least.

>> No.14732883

You could maybe check if there's an open courseware class for it, as supplementary material. But damn, real analysis by yourself is tough.

>> No.14733428

Problems in Real Analysis - A Workbook with Solutions

Charalambos D. Aliprantis, Owen Burkinshaw

>> No.14733430

>>14732858
My favorite books on that subject are Fichtenholz (hard), Zorich (harder), and Amann-Escher (hardest)

>> No.14733433

>>14732858
Its a weed out course. If you can't get over the hurdle maybe your in the wrong business.

>> No.14733455

>>14732858
I looked at the book. You could try speedrunning Spivak’s calculus, as it’s meant as a 1st year course but actually contains most of this material

>> No.14733538

>>14733430
seconding amann and escher, tough but very valuable

>> No.14733832

What is so hard about analysis? Never understood the complaints.

>> No.14733904

>>14733832
Doing the stinking proofs.

>> No.14734251

>>14733433
Maybe the Analysis profs are the hitmen of the university and receive a bonus per student filtered?

>> No.14734275

>>14732858
You sit through the lectures and take notes and go rewrite your notes to look clean and reprocess afterwards. Come back the next day with questions from the previous lecture. Do the homework problems to process the material in new ways.

>> No.14734280

>>14732858
If your professor is going too fast for you, read the chapter material beforehand so you know what's coming up and try to actually teach yourself from the book. Then class will seem normal paced and you can process the material in class because not everything is new to you on the spot

>> No.14734303

>>14732858
>have no idea how to even approach writing a proof for many of these problems

Did you take a look at Hammack's Book of Proof? (It's in the literature list of the Lebl book you use) On the first glance, it looks quite nice to me, going really slow and easy.

http://www.people.vcu.edu/~rhammack/BookOfProof/

>> No.14735639

>>14733433
I'm not a math major.

>>14734303
I'm looking at the calculus section right now and it does have some nice simple examples for epsilon-delta proofs.

>> No.14735703

Most intro calc books actually do have a section on epsilon delta proofs, it’s just that most intro calc teachers skip it. So find it in your calc book.

Besides that just get a copy of Rudin’s Principles of Real Analysis and just copy it by hand 5 or 6 times and you will have god like analysis skills

>> No.14736283

A Problem Book In Real Analysis by Aksoy and Khamsi.

Tons of great examples for beginners.

>> No.14737732

Rudin or failure

>> No.14737756

>>14735703
>get a copy of Rudin’s Principles of Real Analysis and just copy it by hand 5 or 6 times and you will have god like analysis skills

Nigga, is you serious?

>> No.14737759

>>14732858
Unironically, try to draw pictures of the theorems and definitions in question so you have an intuitive understanding of the concepts. Also do exercises, but try to use basic results in the book as little as possible, only using a theorem if it's a major one (Intermediate value theorem, Mean value theorem, FTOC, etc). This way you won't just be memorizing a bunch of theorems but actually understand the concepts.

>> No.14737766

>>14737756
Nta but it’s true.

>> No.14737804

>>14732858
>learn basics of Real Analysis
Well, you can bullshit your way into a C and get over the semester but if your IQ is below 145 there is just no way you can actually learn it.

>> No.14737812

>>14737804
Kek a bit self delusional aren't you anon?
Analysis isn't any harder than calculus. It's just that the approach that analysis takes, being proof based, is something that people who aren't math majors or didn't prepare to be one, simply have no experience with.
It's a completely different way of thinking and that's what's difficult about introductory real analysis. People simply didn't have any exposure to proofs before.

>> No.14738178

>>14732858
There is no royal road to Real Analysis.

>> No.14738990

are there any cool intuitive visual animations of real analysis concepts?

im talking something similar to 3blue1brown's videos on linear algebra

>> No.14738999

>>14738990
lol no is just calculus but boring

>> No.14739296

>>14732858
sit you lazy ass down and study on your own. things you learn autodidact will be engraved in your smoothbrain until you die

>> No.14739314

>>14735639
>I'm not a math major.
so?

>> No.14739387

>>14737732
Rudin is a meme book for mathfags, just as Landau Lifshitz is for Physicists. Please keep in mind that OP specifically asked for the easiest way to learn the basics!

>> No.14739430

Bro its literally just calculus with a few more proofs..... you could have read baby rudin as a supplement during Calc I-III....

>> No.14739724

>>14739314
People shouldn't be tormented with proofs and shit unless the actually chose to become mathfags. Makes no sense.

>> No.14741445 [DELETED] 

>>14739430
Shut the fuck up you dumb faggot.

>> No.14741547

>>14739724
it teaches you how to think. if you dont want to take the course then get through it and never touch a proof again

>> No.14742108

>>14733832
It’s not hard, but the first few chapters are always extremely boring. You spend so much time proving things you have been using since you were kindergarten. This burns people out the point they don’t want to continue further.

>> No.14742114

>>14732858
It depends, do you intend to got further in math? Then you really should work your way through difficult books like Amann, Escher; Rudin; Zorich.
However, if you don’t care about that, you could just go for Abbott. Though I warn, you really should use easy books like these only if you’re in some sort of time constraints. You lose a lot of opportunity for mathematical maturity, when you read these books which hold your hand throughout.

>> No.14742358

>>14742114
Not OP, but what do you think about Pugh?
To me it feels rudin is a boomer meme. At least baby rudin, i don't know about papa
If anything, i think for baby rudin you need a good professor (not just a professor, a good one, or a very good TA, or both)