/sci/ - Science & Math

>>11197647
if you're just starting math is not going to be beautiful to you for a long long time.

>>11197647
>but gave up not because it was hard but because it required way too much boring memorization
calculus requires almost no memorization. perhaps you are just stupid.

Start with calculus if you already know high school level algebra lmao

>>11197647
>Where should i start?
PROOFS
after you have mastered proofs start from arithmetic and work your way up
if you can't prove it, you don't understand it

>i tried to learn calculus
>But it was too much to memorize
Math is not for you Anon

>>11197647
Calculus is boring as fuck and not at all beautiful, so that's actually a good sign.

I think the best place to start gaining an appreciation for the "beauty" of math is applied math, specifically economics, linguistics, biology, and philosophy (mainly because they're more accessible than physics) and concrete math, i.e. elementary number theory, combinatorics, formal logic, and basic group theory. Most importantly though, if you're doing this on your own, realize that ypu probably wont get very far with just textbooks. You'll also need YouTube videos or something pike that because most maths textbooks don't provide any intuition or motivation for the subject.

I would also reccomend getting into monographs and research articles as soon as possible (the best place to start is with so-called "review articles" or "historical surveys"). E.g. if any anons know logic and have any interest in philosophy, I recently read a great monograph called Knowledge and Belief by this philosopher Jaako Hintikka.

>>11197689
>Calculus is boring as fuck and not at all beautiful, so that's actually a good sign.
You had a shit teacher/textbook.

>>11197647
No math requires memorization. Try out some introductory descriptive topology.

>>11197769
Probably a shit textbook. The teacher was great and actually I really love sequences, series, covergence, and also applied diff. eq, but just not how it was presented in (my) calculus without proofs or drawing any connections. I love how that stuff is treated in the context of say combinatorics or analysis though.

>>11197769
This is also a very good point, and desu I think teaching the concepts and providing a general understanding is more efficient even for teaching people like engineers, etc.

>>11197786
>>11197769
>>11197689

Thanks. Any books/videos recommendations on Topology/Fields in applied math/Formal logic?

>>11197647
Fractals.
Play around with a fractal viewer. Read up on the Sierpinski triangle and other such easily drawn fractals.

Golden ratio.
The irrational number found everywhere in nature from seed pods to galaxies.

But the beauty is really in the simple rules producing the output. Learn how formulas were constructed from several lines or pages of math down to a memorizable formula for finding some point on a graph for example.

It really is BEAUTIFUL, even if it isn't always visual.
An example of both conceptual and visual beauty:
https://www.youtube.com/watch?v=b7FxPsqfkOY

Watch 3blue1brown essence of calculus playlist

>>11197647
If you want to see beautiful math, read Serre

>>11197647
Try study linear algebra, done right, and Lisp.

>>11198290
This. And also topology.

My area of expertise is more in statistics and probability than topology, fractal geometry, or calculus, but understanding the concepts intuitively is incredibly satisfying. Whenever you make the transition from using predetermined formulas and methodologies to really grasping what each variable represents, it feels like you've gained insight into reality itself.

>>11197660
literally this. OP probably hasn't even done real math before.

>>11197647
What is one and what is two?

Homotopy groups of spheres.

Thanks anons. I think i'll start with Topology, it looks pretty interesting from the brief videos i've seen. But where should i start tho? Any books/videos for somebody who's almost completely new to pure math?

>>11197665
anon, which proof book would you recomend?

Just do Tao's Analysis. He literally starts from the basics(Peano Axioms) and builds them up much greater than those brainlet Engineer Calculus courses.

>>11197647
Watch https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
Then when something pick your interest go deeper

dude you need to learn calculus and linear algebra, that alone is enough to keep you busy for several months.
anyone telling you that you should start with topology is completely out of their mind.

>>11202488
Why do you need calculus or algebra in basic topology?

>>11201431
a transition to advanced mathematics

if you're trying way too hard to learn a thing and it quickly feels more like a job (not enjoyable at all, virtually a job) after you invest some time rather than a hobby then learn a skill that is valuable in a way that you know it will pay a nice amount of cash for the total amount of effort you're pulling, for instance programming could be a neat idea.

You probably don't like complex math, if that's the case then just quit it, it's not useful for a job. Try something that fits you and do it for enjoyment. Jobs will be jobs and hobbies will be hobbies, you define which is which.

>>11203969
you don't need calculus or algebra per se, but you need mathematical maturity, and the only way to gain mathematical maturity is to do math, and you can only do math that you're capable of comprehending. based on his background, I'm guessing that OP doesn't even know stuff like mappings and equivalence relations, do you actually think that he can open a book on topology and understand more than a preface ?

>>11203974
awful awful awful

>>11204408
Ok, that I agree with, sure. I'd say that elementary number theory and elementary group theory are also good introductory topics to boost 'maturity' at early stages.

NOOO not duh scaewy calc 2

>>11204443
What do you suggest?