/lit/ - Literature

Autism, unironically.

>>15799867
Awesome. I've heard really good things about The Book of Proofs (https://www.people.vcu.edu/~rhammack/BookOfProof/)) but I just feel like an asshole doing homework on my own without anyone to talk to about it/get help from/compare with.

How should I evaluate myself on some of the more algorithmic (for lack of a better term) aspects of math? Like I can watch a video on 3blue1brown about linear algebra and be like "okay I get the gist" without really showing mastery. I guess I could just study and then pass an exam I find online, but it feels aimless if I am just doing it to feel like I am allowed to move onto the next, more interesting thing.

idk if you know that feeling.

>>15799947
Extremely helpful response. Thank you so much. Please let me know if you ever need resources on history or philosophy and I would love to reciprocate. I have always found Riemann's work really interesting, and would love to learn how to do analysis.

It sounds like this is my rough to-do list before attempting Hardy's book (which I think I actually picked up a copy of at a yard sale):
*Make sure I can still ace a Calculus final
*Make sure I can pass a final on Linear Algebra
*Book of Proofs (or should I do this later?)
*Algebraic structures (I'm aware this is a huge field so I dont know really how to approach it in an effective way)
*Real Analysis
*Complex Analysis
*Topology
*Then the stuff I don't even know what it is, like Measure Theory, Integration, and Fourier Analysis.

I notice that the way these topics are broken up varies a lot by institution, just looking at random colleges I am familiar with. Is there any grouping you find most standard?

Also, anyone have specific book recommendations on any of these topics to help guide my study? I have access to a really good academic library and I'm pretty used to pirating things as well so don't be shy. Obviously I will supplement it with 3b1b and Khan Academy etc.

>>11433261
Yeah, I'd say it goes like this:

>Ignorance: "1+1=X" And I don't know X
>Opinion: "1+1=2" But I don't know why
>Knowledge: "1+1=2" And I know it because of pic related

Although I barely finished with the greeks so take my post with a grain of salt

>>10464024
Yes, here is a small piece from Russell's Principia Mathematica

Proofs can go on for many steps just like any other mathematical proof.

>>7264837

https://en.wikipedia.org/wiki/Principia_Mathematica

Russell and Whitehead. 4chan likes to throw around the insult "autism". You don't have the first clue.

The Principia Mathematica (not to be confused with Newton's text on physics, written about two hundred+ years earlier) is one of the most autistic texts of all time, bar none. It's 1500-ish pages spread over three volumes, and it all, /all/ looks exactly like pic related. I've flipped through an edition a few times, even locating the famous "1+1=2" passage toward the back of V.1. The idea was to formalize the entirety of mathematics and (being simplistic, now) remove all paradoxes of logic; the whole project of this well-over-one-thousand pages (I wanna say 1200-1500, 4-500 per volume) was scuttled about 17 years later when Gödel did his thing that took all of 36 pages.

So although the project was doomed, it bears mentioning that mathematicians and logicians have though long and hard about the "why", contrary to some above posts.

Per wiki, they wanted to do a fourth volume on geometry, but they copped to intellectual exhaustion. For those of you who have read or want to read the Tractatus, /this/ work is what Wittgenstein spends much of his time responding to, even using the same logical notation (in particular, the backwards C-looking thing as the "implies" operator, what we now usually denote by → )