/sci/ - Science & Math

I've never felt the need to take notes. If I happen to forget something then all the professor says is in the book. I normally just doodle while I listen.

>>9133219
You probably won't be able to read all of those in a year, and I suspect you got those specific books from that shitty infographic that's been floating around. Some of them are good, but you need to read them in the proper order, and some of them are just bad.

I should probably get around to making a proper infographic for studying pure math, since there are no good ones at the moment.

For now, go read Smith's "Logic: The Laws of Truth". It's a pretty lengthy book, but it covers basically all the pure logic you'll need to do math. It'll also give you a better perspective on the logic used and notation used when you read other formal texts.

Can anyone explain to me why [math]\mathbb{R}^2 \nsubseteq \mathbb{R}^3[/math] is true? Surely any plane is contained within the 3D space.

>mfw this entire thread

It's pretty cool recognizing all these words and still having no idea what they mean in this context. It lets me imagine I know what's going on.

How do you go from proof to intuition in math? I can quite easily (most of the time) go from intuition to proof.

However, most of the time when I'm presented with a proof - while I can see that it's correct - I don't quite "grok" why. I don't intuitively see why. Is there a method to going from proof to intuition?

About 70,000 years ago the cognitive revolution happened and homo sapiens started thinking more deeply than their contemporaries

Then there was the agricultural revolution, everyone was a farmer, farming community, farming economy

Then after that, you can blame imperialist and capitalist ideology

>>8696816
OK! To be honest I'm finding it a little hard to distinguish when things are "clear enough" and when they're not, at least in edge cases like this.

Mathematical Logic is my first love, and no mathematical proofs seem really rigorous to me compared to the logical stuff I normally study.

Do you have any good rule of thumb for when something is not clear enough, perfectly clear, and when it's getting too verbose?

Also, what did you think of this attempt:
>>8696789

>>8507148
good shit faggot. can't wait to see you fail when you get enrolled

>>8281514
what this guy said

>The book has exercises
>It doesn't have the answers
JUST

When we say mathematics is rigorous, exactly what do we mean? Is it the fact that it is unambiguous? That we make a assumptions clear? But both those definitions are problematic, since I can easily keep asking for further assumptions, and anything can be classified as ambiguous if we pull if far enough.

I have no problem doing rigorous mathematics, I have problems seeing exactly what we mean by it. It doesn't seem to have a clear definition, or a clear way to measure or distinguish rigorous from non-rigorous.