I'm trying to grasp this Analysis book, but I just couldn't. Could you recommend me another book for a brainlet like me?

The only prerequisite for that book is an understanding of basic logic. If/then statements, quantification, negation, and/or.

What do you not get in that book? Its my favorite and really helped me get through my program.

fuck off dude, don't act like there isn't an implicit prereq of sufficient mathematical maturity

theorem proof lemma theorem etc isn't something that's immediately comfortable, if you're truly ignorant to then, at best, you've had an excellent mathematical upbringing but are ignorant

By only prerequisite I mean you should probably have seen at least calculus 1 and 2. Its written so that any pleb with minimal proof background can read it and mimic the proof structure/fill in the missing details.

>he can't into rudin
Literally why study Math then? You're a waste of space and should switch asap to CS or Stats where they study "analysis" with shit like Ross and Abbott

You lack mathematical maturity. Go learn some easier math subjects and come back later. There's little point in doing watered down analysis books.

Thank you for all your suggestions.
I have a masters degree in computer science but I teach mathematics at a sucky college (I have taught Differential Equations and Multivariable Calculus for Engineers). But now I'm trying to learn real maths. As you said, I lack maturity but I don't know what to do. I try to do proofs and understand them but I'm struggling a lot with it. That's why I'll try with some "watered down" books as one of you stated, and try to improve my math skills.

Didnt saw this pic. Ill do that

Level up with:
"Conjecture and Proof" by Miklós Laczkovich
"The Joy of Sets: Fundamentals of Contemporary Set Theory" by Devlin
"Linear Algebra" by Shilov
"Topology" by Munkres

Then try Rudin again.

>reading Papa Rudin before Baby Rudin
What the fuck

In any case, Rudin is incredibly terse. I'm reading through it right now; it's written as an introductory text to topics in analysis, algebra, and topology but it's honestly better paired with an easier, more "watered down" text. Try Elementary Analysis by Ross; what I'm doing is dipping my toes in the water by introducing myself to topics in the latter, then diving in head-first to the real rigorous surveys in the former.

Here is exactly what you are looking for user: math.ucdavis.edu/~emsilvia/math127/chapter1.pdf. Index for the rest: math.ucdavis.edu/~emsilvia/math127/

Lrn2meme fgt pls

>it's honestly better paired with an easier, more "watered down" text.
this.

Really? Even Topology is needed to be leveled up? This is going to be harder that I tought but I'll do it user thanks
These actually looks nice user
And how it has been working for you? Suddenly Rudin is getting clearer?

If I got A's in calc 1-3, ODEs, and linear, am I ready to start with Analysis? The thing that worries me is that the only class that dealt with any actual proofing was my linear algebra class. The calc series was all meant for engineers so it was mostly applications

Yeah it makes Rudin much more manageable. Another thing to remember when doing Rudin is to be patient. Read it far more carefully than you read anything else. It takes me about 3 hours to get through 4 pages.

You're probably fine, but you shouldn't start with Rudin. Start with something like Understanding Analysis by Abbott. You'll need to familiarize yourself with the basic methods of proof and practice them a little bit.

What about Tao? I've heard good things about his books and they have nice reviews on Amazon

You're ready but don't get Rudin. It is great to base a course on but shit-tier if you want to learn by yourself. Get Tao (skip first few chapters) or Abbott.
Also if you didn't use H&K or Shilov for lingebra, you need to go through either of them because you don't know lingebra.

Read a proofs book, then a proof heavy linear algebra book, then something else proof based (set theory, mathematical logic, graph theory, combinatorics, probability, number theory), and then you're mature enough to attempt analysis or algebra.

I used Gilbert Strang, I thought it was amazing compared to the shit-tier book my class had us buy

you should do rudin before you do munkres... why would you study general topology before topology of real numbers, it's also not a very big part of introductory analysis

They are both engineer-tier. If you didn't go through H&K or Shilov, go back to it.
Absolutely no need to do all this junk just to learn anal. If you go through basic calc sequence, you can dive in- we start with Rudin in semester 1 here in yuropoor. If you did lingebra, even better because you already know how to do proofs.

I'm also not at all interested in doing actual proofing, I would just like to deepen my understanding. We used Stewart at my school and he pretty much didn't try to prove any of the multivariable theorems

You won't deepen your understanding without proving theorems. Don't go into analysis thinking you can avoid it. Proofs are the bread and butter of analysis and without them, the theorems are mostly meaningless.
Proofs are worth it though, in every area of math. It helps you build great (accurate) intuition and understand the principles behind theorems, which makes it much easier to see how one would use a theorem.
Summa summarum don't bother with analysis if you want to avoid proofs, you won't get anything out of it.

Is lang good enough for linear algebra?

>Is lang good enough for linear algebra?
Lang is a meme.

Unless you want to prove Stokes' theorem, you can skip general topology and focus on basic topology in metric spaces instead.

No. There are only two viable books, H&K and Shilov. All other books build shit intuition, Shilov builds insanely good image of lingebra, H&K forces you to build a good image too.

>munkres before rudin
what kind of an asshole are you?
there's no way someone is going to understand munkres before basic intro to topology via rudin.

I'm the user that recommended tao above

fucking do it faggot

jk but just compare the texts yourself, you can snag both from libgen.io. But I can't see Tao being beat honestly, that was an incredibly painless introduction to anal

Valenza deserves an honorable mention, that's my favorite intro lin alg book and I own Shilov and H&K

This. Rudin is a great book, but it's trial by fire. Go spend time learning literally anything else and come back and you'll have an easier time. Rigorous linear algebra is a great bridge from baby's first proofs to analysis with Rudin in the sense that you'll develop loads more mathematical maturity

If i skip peano's axioms from tao's book ill be fine? They are so strange for me right now

you can't build the naturals without them, so no

rather, you should identify and address what makes them so uncomfortable. tao was my first exposure to them and i had no problems and my iq is only 55

I'll read it sometimes this year then, you're the third person mentioning it. How does it compare to Shilov?
It's okay to go straight to R for most people since they already know how to construct N,Z and Q from highschool. But since you don't seem to, do not skip anything, do all the excercises- Tao has very streamlined linear progression and you won't ever find yourself struggling with a proof.

Shilov was my first attempt at LA, and it was too much for me. Back then I was new to proofs and real maths in general (I tried Shilov when my maths background was limited only to Stewart's calculus works). However, I found Valenza to have very simple, straight-forward proofs and exercises with a focus on developing geometric intuition, and that made it really comfy as a first look at LA, especially compared to Shilov.. It started with sets, groups and vector space properties, which, being structural properties that the rest of the maths is built on, was great because a familiarity with those makes everything else much easier. I have yet to go back through Shilov, so can't directly compare the two, but after hopping around a few LA books Valenza's really clicked with me. Though the exercises were rather easy compared to other texts (but many were still very difficult for me), I feel they really cemented the conceptual and structural approach that the author was aiming for. and I have doubts I'll glide through Shilov or a more advanced LA text now that I understand these underlying concepts relatively thoroughly.

I won't skip anything then thx

This is the best book. Watch lectures on YouTube on what you don't understand, ask sci at least.