RUDIN BTFO

[Anonymous No.14812146]

>Vladimir Arnold, one of the champions of the “organic” approach to mathematics, reportedly called the book (in comparison to the lectures of Vladimir Zorich) “Bourbakian propaganda, stripping and sterilizing analysis of any soul or meaning beyond the symbols.”

[Anonymous No.14812196]

>>14812146
I don't need to know shit about physics. Mathematics is its own thing. Who cares about the real world. Besides, are physicists even doing a good job describing the real world?

[Anonymous No.14812207]

>>14812196
Well then read a book for people who think like that. Should be easy to find.

[Anonymous No.14812224]

>>14812196
and this is exactly why you will never discover anything profound. String theory is the most interesting part of math these days

[Anonymous No.14812246]

>>14812224
>String theory is the most interesting part of math these days
It's also completely insane schizobabble.

[Anonymous No.14813595]

>>14812146
Honestly, this makes a lot of sense. This book single-handedly sucked the soul out of real analysis for generations of students.

[Anonymous No.14813625]

>>14812146
This is one of those books I think about when I wonder why people have these lists of highly recommended books to go through in order to become a mathematician. (The other is Calculus by Spivak.) I understand that a lot of these books are influential or elegant, but books like these expose me as a puny brain lol. My applied math bachelor’s program didn’t even use Rudin at all for real analysis. Instead we used the text by Abbott. Gee, I wonder why.

[Anonymous No.14813650]

>>14812146
Does Vladmir Arnold have any books on analysis?

[Anonymous No.14813708]

>bitter author criticizing more successful author
Yeah, that tracks. Have you read anything by him? He pulls out fucking group theory in the first chapter of his mechanics book and then pretends it's the easiest way to learn.

[Anonymous No.14813730]

>>14813708
Wtf I’m interested now.

[Anonymous No.14813736]

>>14813730
Check them out? They're not hard to find. His full name is Vladimir Ivanovich Arnold (unless I've massively fucked up and am talking about a different guy)

[Anonymous No.14813737]

>>14813625
Spivak is actually really fun though, and has a lot of character. much different than Rudin and sorry to hear about your small brain.

[Anonymous No.14813742]

>>14813708
You're referring to the book called "Mathematical Methods of Classic Mechanics", arent you? Well no shit he'd do something like that with a book named as such.

[Anonymous No.14813762]

>>14813742
Yep, that's the one. I'm not saying it's wrong, I'm saying he needs to stop pretending he's not
>stripping and sterilizing [mechanics] of any soul or meaning beyond the symbols
In fairness, it is a graduate book so there's that.

[Anonymous No.14813771]

>>14813625
Rudin is taken as a graduate course in some places, obviously following the /sci/ meme of using it as an intro to analysis would end up miserably

[Anonymous No.14813801]

>>14813737
Thanks haha. Yeah I remember reading a little bit of that Spivak textbook and thinking some of the exercises were fun and new. Like especially the riddle about the professors who had an agreement with each other and a Dr. X who spills the beans on them.

[Anonymous No.14813846]

>>14812146
The major problem I had with Rudin was that several proofs consist of him pulling an expression out of his ass and providing no explanation to its derivation. It Just Works!

[Anonymous No.14814387]

>>14813762
>>stripping and sterilizing [mechanics] of any soul or meaning beyond the symbols
but the rest of the book gives you deep geometric insights into mechanics and introduces you to symplectic geometry. I don't think you quite get what Arnol'd means when he refers to symbol-pushing.

[Anonymous No.14814405]

>>14812146
>doesn't know Russian
>thinks he can study real analysis from a text with no solution manuals and that's only used in CIS countries

[Anonymous No.14814509]

>>14813846
You're supposed to figure out how he got that.

[Anonymous No.14814618]

>>14814509
Nothing to be gained from that

[Anonymous No.14814627]

>Bourbakian propaganda
BVSED

[Anonymous No.14814648]

>>14814618
>t. brainlet
Books with complete proofs are for absolute beginners who have never done proofs before. It's always these fags who aren't meant to read Rudin that complain about it.

[Anonymous No.14814856]

>>14813625
Spivak is a waste of time.
Just breeze through Anton, Stewart, or some other such brick book to get complete coverage of Calc I - Calc III (Spivak is too patchy even for Calc I and Calc II), and then move straight to Rudin.

[Anonymous No.14814863]

>>14812196
>Besides, are physicists even doing a good job describing the real world?
Yes. you didnt get the memos because youre not swimming in those deep waters. The ones that do read about others. Its fun. Like handing someone a solved puzzlebox and your job is to figure out how it disassembles.

t.Theotetical Physicist

[Anonymous No.14815308]

>>14814648
Again, there's nothing to be gained from that. You have never demonstrated anything substantial on that front, all you have is insults. Rudin has nice problems, that's it.

[Anonymous No.14815635]

>>14812146
There's no real mystery to the popularity of Rudin. When it was first published, it had some of the best problems available in an intro analysis book. Professors are lazy and liked that they could just sign homework from the book. Writing good problems is hard and they want save those for the tests.

There are plenty of analysis books with good problems now, but professors are lazy and they don't want to bother creating new grading rubrics or looking up another book unless there's a good reason. For example, I didn't learn analysis out of Rudin because my prof had us use a book published by the company that published his book.

If you ever want to know why something exists in undergrad math education, it can usually be explained by: profs are lazy.

[Anonymous No.14815987]

>>14815635
there are official solutions http://libgen.rs/book/index.php?md5=E1D24A0D164F7355C94AAE858551BEF9

[Anonymous No.14815992]

>>14814856
Spivak isn't a waste because it's fun, and bridges the gap between the computational style in Stewart to the proof based stuff in Rudin.

[Anonymous No.14816034]

Problem with minimalists texts is that often they do it wrong. They use things that are not yet defined, appeal to common sense and context and ambiguous text. With added text you can fix small errors in your head but when a "rigorous" author makes a mistake then nothing makes logical sense and theres no long verbal explanations and examples to highlight where the failure was.
This is of course much worse in physics

[Anonymous No.14816255]

>>14816034
no problem at all, that books are designed to be used in a classroom not for self study

[Anonymous No.14816709]

>>14815308
>there's nothing to be gained from that
kek

[Anonymous No.14816852]

>>14816709
Again, there's nothing to be gained from that. You have never demonstrated anything substantial on that front, all you have is insults. I can name at least 6 Analysis books with much better texts. All Rudin has got is great problems, that's it.

[Anonymous No.14816853]

>>14816255
In other words: they're lecture notes parading as a book. Great, we cleared that up.

[Anonymous No.14816856]

>>14812146
Yeah, Rudin is terrible. Awful exposition and intuition. The topology section is especially awful considering how unintuitive it really is. I don't know what he was smoking for the last two chapters. Does he really think his approach to differential forms makes sense? At least the problems are good. I struggled through this for a semester until I picked up Rosenlicht's book and read 150 pages in a weekend, then immediately I understood what I was doing and how crap Rudin was.
There's no point in reading the book. Just do the problems, that's it.

[Anonymous No.14816864]

>>14813771
There's no point in taking PMA in a graduate course since, at that point, the material will be far too elementary

[Anonymous No.14816866]

>>14815992
Not that anon, but I never saw the point in books "bridging" two subjects. I know when I first started analysis, I struggled hard but eventually, I got used to proofs. I don't know if a book "bridging" these two subjects would've been of any help

[Anonymous No.14816877]

>>14812196
My god, you really are too far gone.
>Who cares about the real world
Real people? Why don't you care about the real world, you suicidal faggot? Humans are very visual creatures. There's absolutely no point in pretending your intuition for certain subjects isn't gained from thinking about it in the "real world". There's a reason so many parts of math are geometric. Why do we take the distributive property? Because that's how side length and areas interact.

[Anonymous No.14816954]

>>14812196
Actually, math can really be seen as a branch of physics. More specifically, it can be seen as a branch of empirical ATQFT. I recommend Landau-Lifshitz - An Introduction to Quantum Field Theory as a basic introduction and Sakurai - Algebraic Geometry of Black Holes to get a better physical feel for the deeper empiricism involved. After that, you can easily read Shankar, Lurie - An Introduction to Non-Perturbative Algebraic Quantum Field Theories which contains a deep empirical proof of the cobordism hypothesis using nothing but our innate child-like physical intuitions. While these so-called "mathematicians" still can't provide proof of their homotopy "hypothesis". It's laughable.
Modern string theory is just a branch of empirical TQFT. It's better to start with that so he can get to the physical proof of the cobordism hypothesis as soon as possible.

[Anonymous No.14816973]

Vladimir Arnold, a brainlet neverheard russian shitman, criticizes the logical mathematican Rudin for not being "organic" as in organic food product.

[Anonymous No.14816974]

>>14816255
I could self study Rudin.

Rudin is THE great brain filter.

[Anonymous No.14816976]

>>14812146
So what is actually the steelman for this dry, unmotivated, visual-free style of teaching mathematics? Why emphasize formal symbolic manipulation over intuition, over historical approaches? Why present "polished" proofs that are as concise as possible instead of ones that at least give some hints as to how the reader might have come up with it himself?

[Anonymous No.14816982]

>>14816974
it's rather just a time waster

[Anonymous No.14816992]

>>14816976
The reason was very simple: analysis takes analytical solutions: often the interesting function points are ill behaving and any visual loses meaning, the answer will be found from the symbolics. For example, what is "lim x->0 sin(1/x)"? If you still need visual calculus, read calculus books.

[Anonymous No.14817001]

>>14816976
because otherwise, the analysts would be out of a job because physicists and engineers would be better than them.

[Anonymous No.14817003]

>>14816852
The absolute state of /sci/

[Anonymous No.14817004]

>>14817003
Keep on shitposting, you malicious retard. That's all you can do.

[Anonymous No.14817042]

>>14812196
Your situation is pretty common among "mathematicians". It's not surprising that a subject that tries really hard to push out any semblance of physical intuition from entering it is facing such difficulties with motivation. I would recommend stepping back from the insane level of abstraction and gaining a basic fundamental understanding of the use of fields in physics (this is useless formally and only useful for gaining intuition). That way you can develop your base physical intuitions so that you are better prepared to tackle stuff like QFT and TQFT in the future. Then and only then should you return to your walls of notations and unnecessary abstractions. Recommended reading - Jackson - Classical Electrodynamics, Landau-Lifshitz - Classical Mechanics.

[Anonymous No.14817057]

>>14817004
Rudinhaters permanently BTFO

[Anonymous No.14817074]

>>14817057
Nobody here is hating on Rudin, you tribalistic smooth brain. People here simply recognize the fact that the text is terrible from a pedagogical viewpoint and its problems are its sole good feature (and even that is not a novelty anymore, these days). Riddle me this, faggot, why aren't you reading EoMS books if you only care about content? Surely, you'd be "big-brained" enough for full abstraction. In fact, Rudin has got absolutely nothing on Bourbaki when it comes to "clarity" and being brief.

[Anonymous No.14817085]

>>14817074
>it is terrible because it does not hold your hand through every proof
Let me guess, you also seethe whenever a proof is left as an exercise.

[Anonymous No.14817092]

>>14817085
It's hilarious to me that you think that this is what my argument is even about. You're such a lobotomized chimp. You've got NO understanding of pedagogy in any way, shape, or form.

[Anonymous No.14817116]

>>14817092
You're just a malding mathlet who is seething because you got filtered by one of the greatest texts in Analysis.

[Anonymous No.14817119]

>>14817116
Again with the shitposting. Rudin isn't even rigorous.

[Anonymous No.14817172]

>>14817119
>it's not rigorous because...because...I just said so, okay!

[Anonymous No.14817175]

Does Amann & Escher cover all the three Rudins? Does Zorich?

[Anonymous No.14817181]

>>14817172
Taking his treatment of the Taylor series as an example, Rudin fails to appraise functions approximating errors the way that Courant or Zorich had done so in their "Introduction to Calculus and Analysis I & II" and "Mathematical Analysis I & II" and, in truth, Rudin's approach lacks much in rigor. Zorich, for instance, actually derived a general expression for the remainder as a consequence of the properties of a sufficiently differentiable function over a compact set for the real numbers, then derived both Cauchy's and Lagrange's form of the remainder immediately without problem by mere substitutions, page 220, volume I.

He just states the popular theorems and lemmas as can be found in every other high-quality text on analysis, and without the examples, motivation, intuition, and rigor, he makes them seem exceedingly bland. Zorich derives various inequalities (e.g. Minkowski's inequality, Hölder's equality, etc.) and uniquely employs the use of the "base" (in the sense of Bourbaki), as a topological notion to replace the classical Ɛ-𝛿 notion from a more general perspective (hence, a topological notion not just merely limited to the reals). In fact, the style of Zorich shows in his great generality and power, as, as examples, with the use of the big-O little-o notation or in his great expository style of vector analysis. Or, that Courant consistently brings a historical Göttingen charm to him while reminding us of a number of useful mathematical devices as taken historically (e.g. Euler's tangent half-angle substitution etc.) — Walter Rudin is just too bland, sorry.

[Anonymous No.14817192]

>>14817175
Zorich starts at a lower level than Rudin but ends at a much higher one, covering many additional topics including manifolds. Amann-Escher is similar but much more abstract (Zorich is thus probably better for physicists).

[Anonymous No.14817216]

>>14812146
>>14813595
>>14813625
>>14816856
you people don't understand the value of Rudin: it's an introductory self-learner text, it's a fantastic *reference*. here's a book that has all of undergrad real analysis (except measure theory, which it doesn't cover properly) concentrated in one book, with neat, clean proofs, great exercises and absolutely 0 fluff; it's my go-to whenever i need to recall something quickly
Rudin really comes alive when it's used as the basis for a course by a competent professor that can supply all the intuition and interpretation in the classroom (i was lucky to have one like that in functional analysis, he used Rudin again; sadly i didn't get to hear his analysis sequence, which i gather was excellent)

[Anonymous No.14817217]

>>14817216
>it's an introductory self-learner text
it's NOT*, fuck!

[Anonymous No.14817219]

>>14817181
>copypasta
KEK

[Anonymous No.14817222]

>>14817216
I prefer this for reference books: https://www.springer.com/series/855

[Anonymous No.14817229]

Looks like I have won.

[Anonymous No.14817241]

>>14812196
Mathematics is (by definition) the study of TQFT and string theory and maybe some AQFT over exotic spacetimes. How the hell is it not buckled into the seat of the empirics train?
Are you brainwashed by Serre and Grothendieck? Please study some basic quantum mechanics to understand the full beauty of physical and empirical reasoning where you can 100% experimentally verify everything being said. In fact, you should probably switch to Mathematical Physics if you wish to gain any deep knowledge about anything meaningful. You're probably studying something invented by the nu-philosophers/nu-mathematicians of our time. Why even bother when you could be uncovering deep secrets of our universe through studying TQFT? We need more people in the field. Please, reconsider and start learning some TQFT. I recommend Sakurai's great book as a prerequisite.
When you are convinced that you truly want to join us, just contact me or my associates here and we will discuss it further. My TQFT group is currently having deep meetings 5-6 times a week. Be aware that you have to be a staunch empiricist to join them.

[Anonymous No.14817261]

>>14812146
>Vladimir Zorich
Zorich's analysis books are incredible. My favorite by a mile.

[Anonymous No.14817267]

>>14817181
Based Zorich enjoyer

[Anonymous No.14817268]

>>14817267
>Zorich enjoyer can't even formulate his own criticisms

[Anonymous No.14817271]

>>14817181
btfo'd hard

[Anonymous No.14817279]

>>14812224
>string theory
>>>/x/

[Anonymous No.14817344]

Rudin is at the same time too terse and hard for begginers and the subject is too basic for anyone else. it serves absolutely no purpose.

[Anonymous No.14817348]

>>14817261
Same. Also got some of my favorite analysis problems. Some are hard as fuck, though.

[Anonymous No.14818906]

>>14817241
kek based physics chad

[Anonymous No.14818920]

>>14817241
what do you think of constructive mathematics, Bittenfeld-kun?

[Anonymous No.14819070]

>>14817241
OK, where's the meeting?

[Anonymous No.14819637]

>>14817181
What's the best continuation of Zorich? It doesn't cover everything.

[Anonymous No.14819646]

>>14819637
Rudin.

[Anonymous No.14819671]

>>14819646
Real and Complex Analysis? Does it have lots of physical motivation and examples as well?

[Anonymous No.14819678]

>>14819671
no?

[Anonymous No.14819680]

>>14819678
Well then it doesn't continue in the same spirit as Zorich.

[Jealous No.14819691]

>>14812146
>stripping and sterilizing analysis of any soul or meaning beyond the symbols.”
I had a glance at Rudin's book and that doesn't seem wrong to me.

[Jealous No.14819694]

>>14812196
>does electricity work?
>I can't tell.

[Anonymous No.14819701]

>>14819691
arnold knew the pre-bourbakian era and here he expresses his opinion of the new mathematics

[Anonymous No.14819772]

>>14817217
It is. You need to be nonmath imbesil to think you need a lecturer to read this introduction book to you.

[Anonymous No.14819773]

>>14819701
Nooooo you cant be too rigorous in math nooooo you need soul nooooo..wheres my images nooo..

[Anonymous No.14819787]

>>14819773
We are talking about pedagogical texts. It is better for humans to first develop an intuition for a subject than to dabble in rigor. In particular, as this guy mentioned >>14816877
>There's a reason so many parts of math are geometric. Why do we take the distributive property? Because that's how side length and areas interact.
You are simply denying the empirical reality of mathematics and why humans are capable of it. That's why you hide behind abstractions and still cannot provide mathematical proof for your homotopy "hypothesis", which is just algebraic wank.
Physicists, on the other hand, have already empirically proven the cobordism hypothesis using nothing but our innate child-like physical intuitions.

[Anonymous No.14819858]

>>14819787
You already should have build it in calculus.

[Anonymous No.14820109]

>>14819858
Terrible post.

[Anonymous No.14820120]

Zorichfags and Amanntroons are always sucking each other off, so you may try that. But unlike Zorich, Amann & Escher is actually a good book.

>>14819787
Yet another faggot who is sole criticism of Rudin is that it is not introductory.

[Anonymous No.14820123]

>>14820120
Yeah, you've never read any of these books. The IP count did not go up, don't even try to samefag.

[Anonymous No.14820126]

>>14820120
What's wrong with Zorich? It has more physical motivation than Amann & Escher.

[Anonymous No.14820131]

>“The textbook of Zorich seems to me the most successful of the available comprehensive textbooks of analysis for mathematicians and physicists. It differs from the traditional exposition in two major ways: on the one hand in its closer relation to natural-science applications (primarily to physics and mechanics) and on the other hand in a greater-than-usual use of the ideas and methods of modern mathematics, that is, algebra, geometry, and topology. The course is unusually rich in ideas and shows clearly the power of the ideas and methods of modern mathematics in the study of particular problems. Especially unusual is the second volume, which includes vector analysis, the theory of differential forms on manifolds, an introduction to the theory of generalized functions and potential theory, Fourier series and the Fourier transform, and the elements of the theory of asymptotic expansions. At present, such a way of structuring the course must be considered innovative. It was normal in the time of Goursat, but the tendency toward specialized courses, noticeable over the past half century, has emasculated the course of analysis, almost reducing it to mere logical justifications. The need to return to more substantive courses of analysis now seems obvious, especially in connection with the applied character of the future activity of the majority of students.

>[...] In my opinion, this course is the best of the existing modern courses of analysis.”
— V.I. Arnol'd

[Anonymous No.14820261]

>>14820123
>If you're not a newposter you didn't read the book
Zorichfags are deficient in logical thinking, as expected.

[Anonymous No.14820268]

>>14820261
Cease the shitposting. See the dot that separates these two sentences? Analogous to the post you're quoting: they are independent sentences.

[Anonymous No.14820277]

>>14820126
The use of delta notation is so atrocious, that it was enough for me to drop the book. The constant muh real world examples is annoying. Everyone who's been to school already knows the real world applications of everything that is in volume 1. What he really should have focused more on is motivation for rigour. His muh unique ways that copypasta talked about is his worst qualities.

[Anonymous No.14820284]

>>14820109
Get filtered.

Rudin is a major filter, no amount of cope or other authors with less difficult prooves otherwise.

[Anonymous No.14820286]

>>14820277
Get filtered.

Zorich is a major filter, no amount of cope or other authors with less difficult prooves otherwise.

[Anonymous No.14820306]

>>14819858
I don't understand this post. So Zorich can be used for both Calculus and Analysis. What's the issue again?

[Anonymous No.14820669]

>>14812146
I have no idea why people insist on making basic analysis as abstract and dry as possible. It's completely pointless at this stage. When you get to Rudin's other books the abstraction is actually useful, but in basic analysis, it doesn't do shit. Just read Rosenlicht, 150 easy pages and you can move on to bigger and better things.

[Anonymous No.14820745]

>>14817116
The point of a textbook is to teach. A book isn't better for being hard.

[Anonymous No.14820754]

>>14820745
That depends on if you're interested in learning or if you're interested in bragging. Image conscious manipulators have different goal in life than legitimate students do.

[Anonymous No.14820984]

>>14812224
>String theory
Aayyyy lmao

[Anonymous No.14820989]

>>14819858
Name a good calculus book for intuition-lets who are not ready for dry, terse proof-chads.
>hardmode: that works even for calc III

[Anonymous No.14821003]

>>14820989
Is it even possible for you to write a single sentence without butchering it with memespeech?

[Anonymous No.14821054]

>>14821003
no, and it's because I'm a product of Baby Rudin

[Anonymous No.14821064]

>>14820989
Spivak's Calculus you can follow it with Spivak's Calculus on Manifolds

[Anonymous No.14821100]

>>14820306
Not only that but Zorich gives you the direction to start off in physics too.

[Anonymous No.14821413]

>>14819637
Zorich vol 2.

[Anonymous No.14821422]

>>14821413
Yeah I meant after that. I found the further reading section in the appendix, so I'll just look at those books. He suggests Dieudonné's analysis as further reading, as well as one I hadn't heard of Jost's Postmodern Analysis.

[Anonymous No.14822568]

>>14813625
Avoid Rudin like the plague. (maybe useful https://math.berkeley.edu/~gbergman/ug.hndts/#Rudin https://bomongiaitich.files.wordpress.com/2008/10/silvia-em-companion-to-rudins-principles-of-analysis-web-draft-1999434s_mcet_.pdf )

Good Books
Postmodern Analysis by Jost
Elements of the Theory of Functions and Functional Analysis, Volume 1 by Kolmogorov and Fomin
Classical Analysis by Marsden, Hoffman

[Anonymous No.14822659]

>>14821422
Dieudonné's later books definitely contain stuff Zorich doesn't mention, not so sure about Jost, though.

[Anonymous No.14822708]

>>14820989
Not spivak. Not american memebooks.

Read Calculus:a complete course, with passion. After it you should be able to take Rudin.

[Anonymous No.14823127]

>>14822708
Why not Thomas's calculus?

[Anonymous No.14824388]

bump

[Anonymous No.14824603]

>>14812196
Based. Physics is for queers.

[Anonymous No.14824630]

>>14812224
String theory is Jewish kabbalah, physics edition.
>there's only 10, maybe 11, sefirot, goyim
>there's only 10, maybe 11, dimensions, mathlet
it's the same shit dude, you let Jews take over all of STEM, and now they're doing insane schizobabble all over the place. its especially bad in category theory
>the most ambitious category theory is literally pioneered by a Jew, Jacob Lurie
>bro what if we did like... infinite abstractions
>modern kabbalah was founded by a man named Isaac Luria
>Jacob is the son of Isaac in the Bible
>Jacob literally wrestles with God, contemplation of the infinite in kabbalah is often referred to as "Jacob's ladder"
I'm really sick of goyim falling for all of these stupid tricks. you show people the obvious and they think you're schizophrenic. I'm thinking about converting to Judaism. I don't want to be on the losing side. maybe goyim really are nothing but cattle.

[Anonymous No.14825825]

bup

[Anonymous No.14827185]

bump

[Anonymous No.14827280]

>>14820745
I feel sad for people like this. They truly will never understand what's it like to work through a book. They need their hands to be held every second, being told how to think, how not to think. Lack of a proper maternal figure may have caused this. It's sad, really.

[Anonymous No.14827324]

>>14827280
To be fair, it would be disingenuous to pretend you're an authority on anything related to pedagogy, let alone psychology (not like you did a convincing job either).

In any case, "working through" Rudin is a waste of time for beginners and too trivial for anyone more advanced.
I can comfortably read through something like Rosenlicht in 2–3 days and thereupon do Rudin's exercises easily. Burn proof sketches you didn't come up with into your procedural memory (common technique for prepping for math olympiads)/make them your own.
If that is too hard for you, then you're simply a terrible student.

[Anonymous No.14827337]

>>14827324
You can only do Rudin exercises easily, because of reading all the brainlet books like Zorich which have already told you how to think with countless examples, and complete proofs. You never came up with the strategies yourself, you never spent time on trying to understand a single proof in Rudin for days, and hence you never furthered your thinking skills. You can only solve problems that are familiar to you, and you cannot do anything about it. The braindead books you have read have permanently spoiled Rudin for you.

[Anonymous No.14827358]

>>14813708
He wrote a pretty good book on differential equations.

[Anonymous No.14827416]

>>14827337
Wrong. You don't even understand what procedural memory is.

[Anonymous No.14827544]

>>14827416
>he learns math by memory

[Anonymous No.14827565]

>>14827544
Procedural memory is linked to math ability https://www.frontiersin.org/articles/10.3389/fpsyg.2016.01318/full
You're incredibly clueless

[Anonymous No.14827585]

>>14827565

[Anonymous No.14827586]

>>14827565
some faggy random paper is absolute truth now, retard go away

[Anonymous No.14827588]

>>14827585
>>14827586
The data speaks for itself. In any case, it's procedural memory that matters for math ability. Not like a retard like you knows the difference between that and semantic memory anyhow.

[Anonymous No.14827593]

>>14827588
psychology is not even a science, im mad

[Anonymous No.14827602]

>>14827593
How about you stop being mad over things you don't understand? How about you finally argue in good faith instead and stop the serial shitposting?
Again, procedural memory has got NOTHING to do with memorization of facts, which is semantic memory.

[Anonymous No.14828296]

>>14827337
Just curious, are you the type of asshole who believes we should be constantly hazed, or do you think there should be at least one prominent hazing ritual in mathematics education to put hairs on your chest, and that happens to be Baby Rudin?

[Anonymous No.14829626]

>>14828296
Putting in hard work to understand something is worth it. Being spoon-fed just teaches you to be like most students nowadays. Quickly looking for an answer instead of spending time to figure out a problem on your own. What are you going to do when you get to the real world problems that no one has an answer to?

[Anonymous No.14829655]

>>14819787
>>14819701
Jesus Christ you guys are retarded undergrads.
Mathematical Analysis is unmotivated? Jesus Christ, it's almost physics and probability, I don't know what to tell you if you need someone to tell you functions describe all concepts about measure like probability or spaces over time. You have to be retarded to not understand it's a worthwhile investment of your time after a first Calculus class and a Probability course.
Build your own intuition bunch of midwit retards.
>>14819858
>>14820120
This.

[Anonymous No.14829800]

>>14828296
>do you think there should be at least one prominent hazing ritual in mathematics education to put hairs on your chest, and that happens to be Baby Rudin?
Yes retard you need to learn hard work in abstract environments. Introductory Abstract Algebra (Group and Ring theory) is way too easy for that, you barely learn any techniques because the structure is too simple, you can learn a fucking ton in a sitting and remember quite a lot on your short term memory. But that's not how big things are made.

You need to learn to rest when you've spent too much time in a problem. You have to learn to move shit from short-term to long-term memory. You have to learn how to lower your stress strategically. If you already knew how to study efficiently, you wouldn't be crying about Rudin. That's the fucking point. You need to be able gather information from texts like that, and solve the problems, without crying. It's like rallying, you have to learn how to do it without the book being your co-pilot. Your co-pilots are the teacher, other students, and the internet. Co-pilot information shouldn't be on the book itself, it's a waste of space in your shelf. You have a book for Physics, and a book for Math, you don't them with a lot of overlap that's gross. You need to learn to study things as their own things, not as frankenstein subjects because it's a waste of time to repeat the same shit over and over. Sure the intuition comes from different places, but the point of being a Mathematician is being able to put the intuition into concrete terms. You should make yourself a machine that turns intuition into concrete statements. "Oh that physical problem? It seems to be properly modeled by this set of equations. The domain and range seem to be like this, etc, etc." You will put shit back into a familiar place called Math, not the other way around. You don't fucking use Physics to learn Math that's retarded, you use it to inspire Math then use the Math back on Physics.

[Anonymous No.14829834]

>>14829626
>>14829800
I agree, I just think the dose can turn into poison.

[Anonymous No.14829859]

>>14813771
>>14817216
Rudin is tough as a first text because it is intentionally terse. The point of the text is to train you to draw your own pictures, to play around with your own examples, and to present the "conclusion" without the details so that you have space to discover them yourself. As another anon stated, it's important to have it taught with a good prof.
Rudin is a lot nicer in his measure theory and functional analysis books. But he's quite mean spirited in baby Rudin.

(I still prefer analysis books by mathematical physicists. They're *carefully* rigorous - unlike theoretical physics books - but generally know about the most interesting and fun problems)

[Anonymous No.14829888]

>>14829859
Would you recommend Baby Rudin or any books that copy the style for the autodidact? Or is the challenge of learning math alone "enough" to build the intellectual grit that Baby Rudin inspires?

[Anonymous No.14829997]

>>14829888
I mean, if it works for you, then go for it. I suspect they Rudin is best done after elementary real analysis (at the level of Abbott). I got a lot out of Rudin while doing it with Munkres - it was basically my metric topology primer + exercises in real analysis after I was familiar with the setting.

[Anonymous No.14830109]

>>14817216
Baby Rudin fucking sucks as a reference. He hardly names the theorems, uses other's ideas without attribution (e.g., Abel's trick), and writes like a four year old. Papa Rudin has way better proofs even if it is a harder text.

[Anonymous No.14830573]

>>14829655
see >>14820306

[Anonymous No.14830580]

>>14829626
Look, faggot, we have already answered this. If you couldn't come up with a solution on your own, you do what all math olympiads do, which is to look at the solution, think about HOW you COULD'VE come up with that on your own, and then burn whatever you realize into your memory.
Another thing I don't get at all is why you pretend Zorich spoon-feeds you. There are legitimately no solutions for his exercises anywhere and they're significantly harder than Rudin's.
>>14829800
And this is a total non-sequitur.

[Anonymous No.14830589]

>>14830580
I wasn't one knocking Zorich. I like it as well. It is wordy and has lots of development done for you, but like you say plenty of problems to do with no solutions.

[Anonymous No.14830690]

>>14830589
I assumed you were the one who posted >>14827337
My apologies.

[Anonymous No.14830740]

>>14830690
I enjoyed several problems in Zorich, and I like the sort of Russian style with physical and geometric flavour. My first analysis book was Rudin and I have fond memories of working through the problems with minimal input, though I did work with some other students on them. I just think people are quick to look for solutions nowadays and that will not serve them when they get to real world problems.

[Anonymous No.14833258]

>>14830580
And this is a total nigger tier post.

[Anonymous No.14833267]

>>14813625
We "used" Rudin. It was a listed book for the course but we used the lecture notes more than anything. It's been that way for most classes I've taken.

[Anonymous No.14833293]

>>14812146
Physics is for Phaggots

[Anonymous No.14833975]

I don't get why people here claim Zorich is a brainlet-tier book. I guess me and my professor are both brainlets since I showed him a few problems I couldn't solve with the theorems that were given to me and he had no idea either.

[Anonymous No.14834604]

>>14812146
If I read all the volumes of Amann & Escher, how much of Analysis would I cover? Would I still need to read separate books on Functional Analysis, and Analysis on Manifolds, and whatever else Analysis there is? Does it cover graduate Analysis? Does it cover Papa and Grandpa Rudin? What to read further? How long until I reach bleeding edge?

[Anonymous No.14834688]

He's in this thread isn't he?

[Anonymous No.14834754]

>>14834604
>If I read all the volumes of Amann & Escher, how much of Analysis would I cover?
2 years undergrad worth
>Would I still need to read separate books on Functional Analysis, and Analysis on Manifolds, and whatever else Analysis there is?
Yes.
>Does it cover graduate Analysis?
No. There is no universal graduate Analysis class anyway. Schools are going to have graduate level classes on topics like Nonlinear Functionalanalysis, PDEs, Harmonic Analysis, Global Analysis and some other special topics but what an university offers will differ from every university and not every class will get offered every year.
>Does it cover Papa and Grandpa Rudin?
It covers most of Papa Rudin (Real and Complex Analysis) but not Grandpa Rudin (Functional Analysis).
>What to read further?
Definitely read a book on Functional analysis at least.
>How long until I reach bleeding edge?
It's impossible to reach the bleeding edge in all subareas of Analysis. You have to specialize.

[Anonymous No.14834959]

>>14834688
are you math sorcerer btw?

[Anonymous No.14835064]

>>14834754
Thanks.
>in all subareas
Wtf how many subareas are there? I thought Analysis itself was a very small area of mathematics as it is.

[Anonymous No.14835196]

>>14834754
Does it cover everything in Math 245ABC and 246ABC at UCLA?