there is nothing that makes me feel closer to divinity than doing my Abstract and Discrete Mathematics coursework unaided
puzzling out the proofs for concepts so utterly fundamental to math by myself that it’s like if Genesis 1:3 was And God said, 'Let there be integer,' and there was integer
I remember my discrete math professor getting to Aleph Numbers and thinking "My God, it finally happened! THEY RAN OUT OF GREEK LETTERS!"
Wait until you hear about ω1CK
Algebra is the great innovation of humankind, prove me wrong.
And then you study foundational Maths and you are convinced of the Demiurge.
Cantors diagonal argument and the continuum of the reals is my demiurge. It'd be one thing if it was like a weird tangential fact about the reals, but no, you have to accept choice to construct them in the first place, and then that means that there has to be a well ordering on any subset, and of course, wtf is a well ordering on (0, 1)
I've been obsessing over axiom of determinacy as a potential replacement for axiom of choice.
If you are already familiar with calculus but not with topology, I recommend you take a look at the latter.
I'd suggest doing introductory analysis prior to topology. Having a bit of concrete experience with the topology of R helps motivate a lot of the basic definitions and results.
I want to understand math but my adhd makes it hard to study (plus i dont even know like, how to study effectively on my own with no direction)
That was the only math class I did well in. Everything else was straight Bs lol
I barely scraped by in Discrete Mathematics, but it was definitely neat when I understood what the hell was going on. I love that aspect of it--that you're basically bootstrapping a logical framework for doing math. But boy does it feel bad when you're taking an exam, staring at the proof prompt, and going, "I have absolutely no idea where to even start." My experience was that in Algorithms I could at least fudge an answer for partial credit, but I got plenty of big fat zeros in Discrete Math.
If you're doing CS and enjoy the math aspect, definitely take a gander at a cryptography elective if that's an option! Formal math wasn't my strong point but I still loved that class for helping me actually understand the mathematical primitives behind modern crypto. Not math based, but I also enjoyed compilers for that same bootstrappy aspect (admittedly I am also one of those masochists who enjoys working with assembly).
On the note of CS and the rest of math, there are also computer graphics and artificial neural networks.
Computer Graphics was also a lot of fun! It's amazing how satisfying it is when you've wrestled with your twenty lines of GLSL for hours and then you're finally like, "Holy shit! My teapot is reflective now!!" Definitely gave me a newfound appreciation for people who work with graphics down at that level. I only learned the basics, but it's definitely a topic I'd be interested in learning more about at some point.
linear algebra was my favourite class in CS. I also loved assembly:)
Ooh, that was another good one! I didn't find it to be too difficult, and there's something super satisfying about doing all those matrix operations by hand. It was really cool to take cryptography and computer graphics later on and see just how powerful a tool linear algebra can be!
"God created the integers, all else is the work of man"
What the heck is abstract mathematics?
Are they like "a number that might be 2 + the number that most invokes the season of fall = 14"
Edit: and discreet mathematics?
"Okay, I'm not saying 2 was added to 4, I have not comment on whether that happened or not but I am saying =6"
it's when you ask "okay but how does division work on a fundamental level, it's definitely physically intuitive yeah but what's the maths behind it, like multiplying is adding a number to itself x amount of times, dividing is unmultiplying by a number, but it's not subtracting a number multiple times, at least not one that's always present in the equation, what's going on here, how did this happen" and it all goes downhill from there
Really getting into studying things like that always feels so good. Once I almost understood the Maxwell equations. Feels good. Grasp the divine!
That's so cool. I hope you enjoy it!
I really lament not being mathematically talented enough to get that far with math and feel that divine aspect of it. I have other strong suits though. Can you please recommend any books discussing philosophy of math, if you know any?
i remember the lecture i decided to ignore and instead see if i could figure out the golden ratio just knowing a golden rectangle could be subdivided into another golden rectangle + a perfect square. it took me basically the whole class and that was just simple algebra and substitution, the shit you're talking about may as well be heiroglyphs to me
I really liked my "Sequences, Series, and Foundations" course which was the core proofs course for my University.
As someone specializing in graph theory I am greatly enjoying this thread 😄 what a treat
discrete maths is fun as hell
it's all like lil puzzles and stuff (indeed most puzzles can be described as problems in discrete maths), it's real satisfying
I had a guy for abstract algebra that was one of those truly brilliant dudes. Just constantly doing little math puzzles in his head, gave really cool problem sets with interesting results.
