If you're not capable of going through this at the age of

>>8144680

Thanks for letting us know.

I can probably go through it, but I can't buy it in my country

Thanks for the opinion m8

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>>8144680

Please. Rubin is baby tier. Anyone who hopes to be able to make an impact in math should internalize pic related by the age of 10 at the latest.

>>8144680
Mathematical Maturity is a thing.

>>8144680
I know this is a joke, but is it possible to develop mathematical intuition at any age through shear practice? Maybe at 16 even? 25?

>>8145038

Yes. I was shit tier at Math during high school (school didn't let me take AP Calc AB cause math grades were low), but became obsessed with it after taking calc I. I seriously spent all day doing proofs because I wanted to be the best in the department. It's a lot of work but very rewarding.

https://betterexplained.com/articles/developing-your-intuition-for-math/

http://math.stackexchange.com/questions/109976/what-is-the-best-way-to-develop-mathematical-intuition

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>>8144680
Fucking dorks

>>8145078
>but became obsessed with it after taking calc I
Same for me. I literally hated math until calculus, but after taking it I found myself reading article after article about different branches. I've never spent a whole day doing proofs or anything, but I think it was just that calculus was the first time I felt like I was actually doing something.

Highest math I took was algebra 2. Never really applied myself in math. Isn't math just plugging things in the correct format? Step by step processes? Not in school at the moment but I want to brush up on my math skills for the fuck of it.

>>8145100
>Isn't math just plugging things in the correct format? Step by step processes?
Solving textbook problems is, which is enough to get good grades on College.

But understanding its underlying concepts, why things are the way they are, requires effort and logic.

>>8145107
Once you get to maybe upper level undergrad or lower level graduate material things stop being so much about "compute x when y" and start being more "assume x and y, prove z." When you're doing a proof, there normally isn't some set process, you have to think about what your assumptions apply and how the definitions of your terms relate.

>>8145118
*assumption imply
sorry

>>8145118
>Once you get to maybe upper level undergrad or lower level graduate material things stop being so much about "compute x when y" and start being more "assume x and y, prove z."
Dude what the fuck. My math department is dogshit and even it has only proof-based classes. I can't imagine how awful a university must be to have math classes asking you to compute shit

>>8145128
For me nothing the basic Calc sequence was basically just computation. They would teach proofs, but it was never tested. I go to a mid-tier 'murrican school so that might have something to do with it.

>>8145038
Of course it is. Only people with serious self esteem issues will tell you the only people who can do math are some special elite of high IQ swag.

>>8145128
Really? Your calculus classes were proof-based?

>>8145128
>I can't imagine how awful a university must be to have math classes asking you to compute shit
It's how things work most places. They train students to solve problems, but not to understand concepts, proofs et al.

Proof of that being most of my class struggling with Lin Alg when the teachers starts using "letters instead of numbers" (as they put it).

>>8145128
I like to use "Math" to refer to the Autismal proof shit, and "maths" to refer to calculations. Except in "do the math". I should start saying "do the maths".

As an Engineer, only the CEs would take more proof oriented classes. EE, ChemE, ME would be maths. Civil would get their education from middle schoolers.

>>8145086
>>8145078
I don't know anyone that went through Pre-Calc and came out the better for it. I was permitted to skip it in HS for AP Calc, started CC at Calc II, and only learned some of it through tutoring students who were taking it.

Pre-Calc is literally the worst class I have ever seen. Epsilon-delta faggotry, synthetic division, Descartes Rule of Signs, holy shit. It's all so Autismal. Like get real nigga long division and numerical methods lol

Don't even get me started on when they're supposed to expand shit like cos(8x) into a fuckload of terms.

>>8145137

Some schools have an honors section. It varies widely. I wish I knew beforehand about mine, but it wasn't a true proof based class. It was basically just some harder level calculus problems and more "theory." My friend took it and said the curve was crazy because all honors college kids had to take it and a lot of them were lib arts majors.

But some schools have serious freshman analysis classes. UChicago and Harvard come to mind.

>>8145150

Seconded. At least my teacher was amazing and got me interested in math.

But ya, it was basically college algebra only worse.

>>8145150
I don't even remember anything from pre-calc aside from the unit circle, which I learned earlier from my sister anyway. I will say though that pre-calc was definitely less motivated than calculus and was the apex of "hurr just do this thing because" tier math classes.

>>8145038

Don't worry dude. I'm in my 20s and have no prior math experience past middle school. I restarted with elementary school stuff, and just through practice alone, I was able to understand some baby additive number theory stuff. You'll get there. It is literally just about practice. I spent all of last week just doing thousands of addition worksheets. When I wasn't doing the worksheets I was playing arithmetic games online. My intuition for addition got better after that. Big surprise huh. Don't listen to the kiddies telling you otherwise. They're usually coasting on whatever skills they inherited from their parents. Kids of engineers do well in engineering, kids of mathematicians do well in math, kids of lawyers do well in law, linguistics, kids of artists tend to be better at art. It's more unusual to find someone who's good at something that their parents, grandparents, ancestry, have no experience in. You don't have to be a genius to see the pattern. Practice a lot and maybe your kid will be "talented" at the thing you spent your whole life practicing. The whole IQ thing just tells you how many more hours you're going to spend practicing than other people. But even that- who gives a shit if it takes you longer. You're going to have to do something with your life, so why not pick something you want to do, or that's challenging? Worth it even if it takes a long time imo.

>>8146404

/thread

This is what recommending self-studies from Rudin does to kids that just completed Calculus:

>Be master at computing integrals
>Be master computational monkey
>Know calculus well
>Don't know proofs yet
>Open up Rudin
>Don't know basic logic yet
>Try to do homeworks
>Thinks proofs are correct
>Doesn't realize errors in proofs cause no way to check their work
>Continue with Rudin practicing bad math and developing bad proof technique
>Become horrible at proofs due to no feedback
>Yet think of themself as a pro due to no feedback.

Thanks /sci/!

>>8146441

Literally. I don't know how someone with no introduction to proofs could just open Rudin and go through it.

Rudin isn't even the best text for RA.

>>8145151
Math 55 seems like no joke desu.

>>8146472
I had a prof who used to wear her Math 55 shirt to class on occasion.

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>>8144680
No one here will make a big contribution to math because they didn't even get close to getting into the math olympiad. If you weren't in the Math Olympiad, consider your legacy dead. You might make an average career out of it, but you'll be a nobody in the math world.

>>8146441
Reading more proofs -> Writing better proofs

>>8145151
Michigan and Stanford have pretty intense freshman sequences as well.

I went on to study something entirely different from analysis, but I get such an enjoyable rush of nostalgia from flipping through my copy of baby rudin. I've been thinking about going through it this summer just for old time's sake

>>8146803
Projecting.

>>8146837
literally who?

>>8145038

Everything takes determination and practice. I've had classmates in their late 20s and early 30s that came back to school to get a math degree. If it takes you longer to understand a concept, take the time to understand it and don't push it to the wayside. That's how you build holes in the foundations of your knowledge.

>>8146445
I've been looking for a good introduction to proofs book. Haven't even taken Calc 1 yet.

Want to be able to finish it this summer, got any recs?

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Same book?
if yes wtf im 19 years old its not that hard just normal Analysis 1/2 stuff you get in university

>>8147369

How to prove it is the best. No prerequisites really.

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>>8147369

My professor suggested this one and they use it at my universities proofs class.

>>8147386
Was machst du um diese Uhrzeit auf /sci/?
Lernst du im ernst um knapp 6 Uhr morgens Mathe? Dazu noch auf die Rudin-Meme reingefallen? O boi

>>8144680
This book is shit. I don't know why people praise it so much

I was at a physocologist the other day and was doing some tests. They said that I have learning disadvantages with maths. Atm I am doing really shit in a mathematics course at my HS because I have like no motivation to study and I find it all super hard. Do I still have a chance?

>>8148162
Ye of course you do mate just stop wasting your brain on trivial shit and start trying to learn math

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>>8147415
This book is the shit especially if you've never been exposed to formal logic or set theory. It is also a good intro to what "real maths" is kind of like.

>>8148163
Thanks for the advice but it's just, I have just dug myself into an abyss of bad habits. Im going to see someone about these soon. You guys got any recommendations or advice?

>>8147386
Ich würd dir Amann, Escher 1-3 empfehlen, ist viel umfangreicher

>>8147415
How does this book compare to "Book of Proof - Hammack" and "How to Solve It: A New Aspect of Mathematical Method - Polya"?

>>8148168
>algebra before euclidean geometry
>arithmetic before euclidean geometry
>elementary combinatorics after algebra

This chart is bad and you should feel bad for posting it.

>>8148317

Polya Polya Polya. If you want to learn how to write proofs, you can get pretty far with just Polya. He writes for people so they can understand it, and isn't abstruse in the slightest. Down-to-earth mathematics, my favorite kind!

some of his books:
-Mathematics and Plausible Reasoning
-Induction and Analogy (one of my favorites)

If you want to understand what the point of a proof is, you should read about the history of proof writing. Read and study the types of proofs used by the greeks, then by the scholastics, then in the 18th, 19th, 20th century. Supplement this with some philosophy of language, history of language, general history of ancient math, and you'll get a much nicer perspective than what you would get from only reading the modern texts (which pretend, or at least try very very hard to exist in a vacuum (the french at least)).

Personally, I'm working right now through Euclid's Elements in it's original ancient greek (heiberg's translation). Originally I started with Velleman's book, but the set theory was so frustrating (from a semantics/linguistic perspective (it didn't seem like math OR logic, just stupid and redundant)) that I ended up going back to the original greek texts, which was much more satisfying. Also, what's great about Euclid, is that once you make it back to the modern era, and start reading Hilbert's foundation of geometry, or peano's writings on geometry, you'll have a much better background to explain their reasoning, the motivation for their ideas.

Math does not exist in a vacuum! Don't be fooled by the intellectual posturing of modern mathematicians. Good luck in your studies!

>>8144680
>you will never make it. no ifs, no buts, no excuses
If you talk like this, you are a plebeian