/sci/ - Science & Math » Thread #11321346

26KiB, 354x499, 41zb-1cQ0zL._SX352_BO1,204,203,200_.jpg

View Same Google iqdb SauceNAO

Why do people like Rudin

Anonymous Wed 22 Jan 02:54:13 2020 No.11321346 View Reply Original Report

Quoted By: >>11321667 >>11321676 >>11322224 >>11322353 >>11322543 >>11322545 >>11322796 >>11323636 >>11323738 >>11323764

Why do people like Rudin's principles of Mathematical analysis?

We've been working with it on my real analysis class and quite frankly the book is fucking garbage

>Completely cryptic writing style
>Every single proof so far depends on tons of unproven shit
>Tons of formulas are pulled straight out of rudins ass with no explanation to why he needs that formula, where its from or why it works
>90% of the time you dont really know why he is doing something until hes done with it, effectively making what he is doing insanely hard to understand whilst reading

Maybe Im just too new to pure math or just straight up retarded.

Anonymous

Anonymous Wed 22 Jan 2020 02:55:23 No.11321350 Report

Quoted By: >>11321521

>Why do people like Rudin's principles of Mathematical analysis?
Rudin is a meme.

Anonymous

Anonymous Wed 22 Jan 2020 04:11:01 No.11321521 Report

Quoted By:

>>11321350
Why?

Anonymous

Anonymous Wed 22 Jan 2020 05:53:58 No.11321667 Report

Quoted By: >>11322203 >>11322796 >>11323639

>>11321346
>>Completely cryptic writing style
No.
>>Every single proof so far depends on tons of unproven shit
Because you're supposed to fill in the gaps
>>Tons of formulas are pulled straight out of rudins ass with no explanation to why he needs that formula, where its from or why it works
valid criticism sometimes but you're still brainlet
>>90% of the time you dont really know why he is doing something until hes done with it, effectively making what he is doing insanely hard to understand whilst reading
Happens in a lot of books. Skim once and then thoroughly read.

Anonymous

Anonymous Wed 22 Jan 2020 05:58:26 No.11321676 Report

Quoted By: >>11322203 >>11323111

>>11321346
Honestly I think Rudin's book was written with students in mind from a different period in American history where you were expected to have seen formal delta-epsilon proofs, proofs in highschool geometry, to have understood formal logic and have been exposed to fairly rigorous mathematical education well before university. Its over 60 years old now, and standards have fallen quite a bit since the time when it was published. If you come from a typical public school background there is a good chance it will be too difficult to learn from before you've been exposed to a good amount of rigorous university level math classes, but I still think it is the easiest to comprehend of the standard intro analysis texts. Tao and Pugh are just nowhere near as readable or beneficial to one's intuition

Anonymous

Anonymous Wed 22 Jan 2020 12:01:02 No.11322203 Report

Quoted By: >>11322353 >>11322516 >>11322517

>>11321667
How is his writing style not cryptic? This is how a rudin proof usually goes:

>Prove a = b
>Let $0<\frac{a^{n-bm} + \frac{1}{b^{n+am}}{5ab+1/n}<a<b$
>As $a^{n-bm} > 0$ then obviously $a = supB$
>But $\frac{5b+a^{n/m}}{a^2b^2} > b$ so a cant be supB therefore we have a contradiction and a = b

>>11321676
>American history where you were expected to have seen formal delta-epsilon proofs, proofs in highschool geometry, to have understood formal logic and have been exposed to fairly rigorous mathematical education well before university.

Im pretty sure this was never the case, boomers and the like have no fucking clue what a rigorous proof is.

Anonymous

Anonymous Wed 22 Jan 2020 12:14:14 No.11322224 Report

Quoted By:

>>11321346
I feel like with Rudin you learn slick proofs and how to think like an analyst, but you don't learn that much analysis though.

Anonymous

Anonymous Wed 22 Jan 2020 13:48:33 No.11322353 Report

Quoted By: >>11322516

>>11321346
>Completely cryptic writing style
If this is the first "serious" math class you've taken, that's why the writing seems cryptic to you. For some people, real analysis / measure theory is the first class where they really have to go in-depth.
>>11322203
>Im pretty sure this was never the case, boomers and the like have no fucking clue what a rigorous proof is.
He's exaggerating, but the "proofs in high school geometry" and "logic" parts of his list are correct, at least -- the fact that this stopped happening is a common lament. I doubt that most high schools in the 40s and early 50s even offered calculus, though, let alone a rigorous version of it. That push came with the New Math movement a few years later.

Anonymous

Anonymous Wed 22 Jan 2020 15:07:03 No.11322516 Report

Quoted By: >>11322572 >>11322609

>>11322353
>that oush came with the new math movement
No it didn’t lol and I was talking about those who actually went to university which was a significantly smaller portion of the population.
>>11322203
Fucking retard

Anonymous

Anonymous Wed 22 Jan 2020 15:08:31 No.11322517 Report

Quoted By: >>11322572

>>11322203
also you stupid fucking monkey never post about math on this board again

Anonymous

Anonymous Wed 22 Jan 2020 15:18:00 No.11322543 Report

Quoted By:

>>11321346
>Why do people like Rudin's principles of Mathematical analysis?
it's redpilled
>Completely cryptic writing style
*epic
>>Every single proof so far depends on tons of unproven shit
brainlet

Anonymous

Anonymous Wed 22 Jan 2020 15:20:53 No.11322545 Report

Quoted By: >>11322572

>>11321346
Historical reasons. The first edition of Rudin was published in 1953. It had essentially no competitors for quite a while, so it took over the market, and at this point it's become that everyone uses it because everyone else uses it.

Anonymous

Anonymous Wed 22 Jan 2020 15:34:00 No.11322572 Report

Quoted By: >>11323140

>>11322516
>>11322517
>Retard
Seriously, just look at the very first example where he proves that sqrt(2) is irrational and then shows that there's "gaps" in the rationals, he pulls a formula right out of his ass, only until much later you relalize hes using a the secant method to approximate sqrt(2).
My point is not that the proofs are incomprehensible, but that he comes up with a lot of stuff, critical to the proof, that he doesnt bother to explain at all.

>>11322545
This makes sense

Anonymous

Anonymous Wed 22 Jan 2020 15:53:05 No.11322609 Report

Quoted By: >>11322784

>>11322516
>No it didn’t lol
It did. Few high schools had calculus classes before that. It's not the first thing that comes to mind when you think of "New Math", but earlier calculus classes were part of the same period and movement.
https://www.csun.edu/~vcmth00m/AHistory.html

Anonymous

Anonymous Wed 22 Jan 2020 17:03:13 No.11322782 Report

Quoted By:

You're meant to think for 3 seconds about why a given step he makes is true. It's not even bad at all after the first chapter, stop getting pissy over that. From the second chapter onward everything is very easy to understand on a first pass.

Anonymous

Anonymous Wed 22 Jan 2020 17:05:39 No.11322784 Report

Quoted By:

>>11322609
Not talking about plebs

Anonymous

Anonymous Wed 22 Jan 2020 17:15:49 No.11322796 Report

Quoted By:

>>11321346
>>11321667
>Because you're supposed to fill in the gaps
This guy gets it. You look at the proof, and fill in what needs to be filled in to YOUR standards. If you want every little detail inserted, go ahead, if you only need 1 extra argument, thats fine too.

I am biased, this book turned me from a no-life pothead to a real mathematician (just got Ph.D last year).

Anonymous

Anonymous Wed 22 Jan 2020 19:36:40 No.11323111 Report

Quoted By: >>11323292

>>11321676
>to have seen formal delta-epsilon proofs, proofs in highschool geometry, to have understood formal logic and have been exposed to fairly rigorous mathematical education well before university.
what kind of shithole is america now?
This is taught in my hs, and delta epsilon is studied like 3 semesters before analysis in my college

Anonymous

Anonymous Wed 22 Jan 2020 19:47:35 No.11323140 Report

Quoted By: >>11323278 >>11323287

>>11322572
he never showed gaps in the rationals, he showed there's no biggest rational less or more than sqrt of 2.
holy fucking brainlet.
these are the kind of people who complain about Rudin

Anonymous

View Same Google iqdb SauceNAO Screenshot_20200122-164945.png, 333KiB, 1920x1080

Anonymous Wed 22 Jan 2020 20:50:22 No.11323278 Report

Quoted By: >>11323287

>>11323140
Youre a retard

Anonymous

Anonymous Wed 22 Jan 2020 20:54:03 No.11323287 Report

Quoted By:

>>11323140
>>11323278
Moreover:

>he showed there's no biggest rational less or more than sqrt of 2.

1 is rational and less than 2, 3 is rational and less than 2 as well, what he proved is that the set given by:

$A = \{ t \in \mathbb{Q} : t^2 < 2 \}$

Has no supremum in the rationals.

You're the brainlet, retard.

Anonymous

Anonymous Wed 22 Jan 2020 20:55:35 No.11323292 Report

Quoted By: >>11323625

>>11323111
Don't know what he's talking about, formal proof based geometry was taught in my public middle school

Anonymous

Anonymous Wed 22 Jan 2020 23:18:42 No.11323559 Report

Quoted By: >>11323593

Is this for an undergrad real analysis class? If so, what i recommend is writing the proofs in your own style, to your own satisfaction. Use the book if you get stuck, but the point of the class is really to learn how to write quality proofs, under the pretense of analysis. If it's grad, idk we used Folland, but at that point you should be able to write a simple ass proof about open covers or some shit.

Anonymous

Anonymous Wed 22 Jan 2020 23:40:47 No.11323593 Report

Quoted By: >>11323625

>>11323559
Yes, this is for babbies first analysis course.
I
>Write your own proofs in your own style to your own satisfaction

This is pretty much what ive been doing, I use the book in order to see what the main idea behind a proof is and then work on it on my own and write down a step by step breakthrough of the proof, it can get really hard to do so sometimes, so when Im completely stuck I look at Abbotts analysis (which is far more mundane) to see how abbott does it.

Anonymous

Anonymous Thu 23 Jan 2020 00:01:14 No.11323625 Report

Quoted By: >>11323852

>>11323593
why are you complaining about Rudin if you feel your coursework is beneath you? It should be easy to do all the exercises in the first 3 chapters if the concepts are trivial. In which case you had no reason to make this thread.
>>11323292
You have no idea what you’re talking about, they don’t teach math at all the same way they used to at good schools decades ago. Everything is stripped to its bare computational form and taught specifically so students can perform well on standardized tests. This isn’t a suspicion or boomerism its a fact you can look up

Anonymous

Anonymous Thu 23 Jan 2020 00:09:28 No.11323636 Report

Quoted By: >>11323852

>>11321346
>Why do people like Rudin
Humble bragging
They pretend to like it even though nobody really understands it. But they own it as a fetish.
>look at me i recommend rudin so y'all will think i am really smart

Anonymous

Anonymous Thu 23 Jan 2020 00:10:30 No.11323639 Report

Quoted By:

>>11321667
>Because you're supposed to fill in the gaps
Nah thats not how it works

Anonymous

Anonymous Thu 23 Jan 2020 00:57:43 No.11323738 Report

Quoted By: >>11323769 >>11323852

>>11321346
Here's a question sort of related to this topic so I'm not gonna make a separate thread: what do you people think about the meme of early transcendentals? I haven't read Rudin but most other books I've come across on calculus/analysis don't give a rigorous definition of the trigonometric functions; they just use intuitive and informal geometric arguments to work out the basic properties like the addition formulas and some important limits like sin(x)/x when x tends to zero, and then use those properties to work out the derivatives of the trigonometric functions and study their behavior. I feel like mixing together rigorous proofs and heuristic arguments based on diagrams is a scam and a cop-out. It makes things harder to understand rather than easier. The exponential is usually defined with limits of powers of rational numbers in books of this kind, which is more rigorous than the way the trigonometric functions are handled but in my opinion it's awkward to do it that way. It's much easier to define the logarithm of x as the integral ?dt/t on the interval [1, x] (and as -?dt/t on [x, 1] if 0 < x < 1) and then define the exponential as the inverse of this function (after showing it's strictly increasing and thus one-to-one). The same can be done with arctan(x) by defining it as ?dt/(1 + t^2) on [0, x]. You end up being able to define sine and cosine only on the interval [-?/2, ?/2] if you start off with the arc tangent, but it's easy to extend them to the whole real line. Compared to using power series or differential equations, these definitions for the elementary transcendental functions are much easier (they only require integration) and much more rigorous than the approach of early transcendentals (especially in the case of the trigonometric functions).

I feel like not being able to understand how transcendental functions work is a major stumbling block for people just starting out with calculus/analysis.

Anonymous

Anonymous Thu 23 Jan 2020 01:11:46 No.11323764 Report

Quoted By:

>>11321346
it's because the book is dense and doesn't fuck around explaining a bunch of unnecessary shit. It's meant to explain the basic concepts of analysis, not meant to be a step by step wikihow guide on how to do the problems.

I think math teachers mainly like it because it's small and easy to carry around though

Anonymous

View Same Google iqdb SauceNAO 1567537026253.jpg, 591KiB, 2000x2987

Anonymous Thu 23 Jan 2020 01:14:48 No.11323769 Report

Quoted By:

>>11323738
Also wanted to add, Spivak kinda does it in his own way when it comes to defining trigonometric functions. He uses only integration but he makes use of the area of the unit circle instead of using the arc tangent. His method is probably closer to our intuitive notions about sine and cosine but it becomes a little overly complicated compared to using the arc tangent which is more straightforward.

Anonymous

Anonymous Thu 23 Jan 2020 01:49:20 No.11323852 Report

Quoted By:

>>11323625
>You think your course is beneath you
Not at the slightest, I said babbies first meaning im an analysis/pure math baby and this is my first analysis course

>>11323636
This could be a reason too

>>11323738
>Unnecessary shit

My main qualm is that he the shit he doesnt bother explaining is usually central to the argument he is making to the point the proof quite literally depends on it.
I get it that if youre already a full fledged mathematitian with very deep insight developed thru years of study than its trivial shit, but as I believe the great majority of people reading rudin are doing so on their early analysis classes then the book is poor on its explanations

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches