Proofs

For me, it's Mathematical Proofs by Chartrand et al.

I don't know why you got so many weird answers. Guess no one studying math was here, and you had terrible luck with your replies.

The staples are "How to prove it, a structured approach" and "Book of proof".

Transition to advanced mathematics is better, and one guy posted a picture of laws of truth but didn't recommend it, its a great book but only if you really care about your foundations

At that point read a fucking analysis textbook like Rudin.

Where are you from? If you are a competitive person, you should seek your local IMO committee.

en.wikipedia.org/wiki/International_Mathematical_Olympiad

What an awful fucking recommendation. Maybe Tao, which is friendly and slow-paced, but comparing Spivak to baby Rudin just makes you look retarded

"one guy" here, I recommend Laws of Truth, it really helps building intuition etc. Transition to Advanced Mathematics is a good book for applying proof methods, but it's very basic in the subjects it covers to be honest.

yeah, this, get into math olympiads as soon as you can, they'll be very rewarding to you (even if it's local competitions)

Op here, this is way more replies than I was expecting and I seriously appreciate it so much.
I've been recommended this before, but I wasn't serious about this yet so I didn't read it. Thank, user
My only experiences with logic and proofs are geometry in 8th grade and googling proofs for specific things so I am super fuzzy on how to structure one myself and understand the more difficult ones. Thank you for the suggestions
I'm more interested in the real math behind it. Engineering is cool but number theory and pure math are what I'm really interested in (even if I might end up being an engineer for my job because money and more applications)
Thank you! I'll look into it
These both sound like basics I would need. Thank you
Both books sound promising! Will look into them, thanks!
From the US and this looks really really interesting. I've never heard of it before but I could still qualify. This is a really really great suggestion thank you for bring it to my attention

Thanks to everyone who has helped so far! This is just what I needed

>Hurr durr, read Stewart->Spivak->Apostol->Courant->Abbot->Tao->Pugh->Rudin->Apostol->Munkres->Spivak and take 12 years to learn basic calculus and analysis

Why the fuck is this meme so popular? Rigorous calculus books only make sense if that's your first time learning calculus as a gifted student.

Instead of gaining mathematical maturity by studying the same damn thing over and over again with slightly more difficulty, study other easier areas and expand your knowledge while building the maturity needed for Rudin.

Calculus -> Proofs -> -> Linear Algebra -> Point-set Topology -> Real Analysis with Metric Spaces -> Analysis on Manifolds

How to prove it by Velleman

>Girl, actually

U-uh hell-
>I'm in highschool

O-oh...

But in all seriousness, Velleman's is as close to god-tier as I've yet encountered. The two other prominent ones, 'Book of Proof' and 'How to Read and Do Proofs' are good as well, but imo Velleman's is the most accessible if you're a noobie in the subject. It's very cheap on Amazon, and you should be able to find it for free online via PDF if that's your style.

Also, pic-related is for you, i-it makes me think of us...

i've just read:
Mathematical Proofs: A Transition to Advanced Mathematics
Really liked, lots of examples and also chapters devoted to specific areas like analysis and linear algebra

>greentext some idiotic things
rudin is a shit book for self study. use tao after calculus and (optionally) proofs. that's it.
I disagree with topology before analysis as well, topology is dry and unmotivated if you haven't done analysis

This, also for anybody interested, the point of universities dumping all incoming students into Calculus is so they can fix their basic math skills. It's a good one-size fits all course sequence, and TAs are deployed en masse to bring up students skills to basic college levels since our high school math is such absolute shit these days and can't be trusted as a basis for undergrad. That's why you often see people shilling these book sequences because it's the norm for building 'maturity' but there's no reason to do multiple Calculus/Analysis books unless you want to specialize in Analysis.

Spivak is a text for high school students, or first year "honors" calc students who wish to re-learn Single Variable Calculus rigorously, but also be exposed to various tricky proofs. It's more of a showcase book, 'hey look this is real math'. It doesn't even really teach you Single Variable completely. It's a """fun""" book for a motivated highschool kid with extremely difficult exercises to start then they become incredibly easy exercises.

Apostol is the book you use for 'Mathematical Maturity(tm).' By that I mean rigorous introduction and complete reference of Calculus Single/Multi/basic Linear Algebra. This is the book you want if you are returning to math as an adult and wish a rigorous drilling in trig identities and basic algebra, because with all the exercises Apostol has you doing you will absolutely gain a firm grasp of the basics of elementary math. You start easy and progress in difficulty. He routinely has you prove things, but not tricky or showcase proofs. You do enough of them so that you are aware of all the basic proof strategies and are now ready to take an advanced class where tricky and creative shit is deployed. You can tear through these books just doing the exercises, and only referring to the reading material if you get stuck. Fantastic way to fix your elementary math.

you have to be 18 or older to use this website I will direct you to a safer place reddit.com

sad beta loser

Look what website you're on buddy.