#algebraic geometry

[spectrallysequenced]

I started a blog series (Which will be accompanied by a video series soon) on schemes. The first chapter is on classical algebraic geometry, and the first notions of a generalisation to arbitrary rings. Unfortunately, since tumblr doesn't have LaTeX integration yet, I decided to do this off-site on Functor Network, so that means you will have to go through the mental anguish of clicking a link:

I hope it's worth it.

Edit: Associated video going live tomorrow on youtube:

#math #algebraic geometry #Youtube

[eka-mark]

The central notion in commutative algebra is that of a prime ideal. This provides a common generalization of the primes of arithmetic and the points of geometry.

Introduction to Commutative Algebra, Atiyah & MacDonald

#math #algebra #commutative geometry #algebraic geometry

[measurementcat]

I am attempting to learn “real algebraic geometry” (schemes) and it is the most brutal. The density of new concepts is like, 5 times as high as any previous math class I’ve been in. It took us about a month to define what a scheme even is (using locally ringed spaces). I’m somewhat hoping the difficulty / density of new concepts thins out from here, but I’m not sure if it will or not. 

I do have this wondering about, learning about sheafs and categories and so on so far doesn’t feel super directly related to what schemes actually are (this is a bit silly, I suppose, since a scheme is “mostly” “just a sheaf” (plus the Zariski topology)). But I can’t help but wonder whether I’m feeling this overwhelmed because I’ve done the equivalent of learning assembly before learning C, instead of learning C or better Python and then opening it up under the hood. I do expect we’ll be using a lot of category theory and some sheaf theory though. The first big proof we’ve done so far was the proof that the global sections functor is adjoint to the Spec functor, which both is a theorem of category theory as well as using a lot of category theory in the proof. 

It is definitely the first time a math class has made me wonder if I should make flashcards to memorize things though. 

#mathblr #math #algebraic geometry #anki

[tokinanpa]

I've been reading stuff on modern algebraic geometry (scheme theory and the like) and it's been completely impenetrable to me for the longest time.

I've never really been able to comprehend any of it... until like 5 minutes ago when it just

clicked

I get it now. it makes sense.

love when that happens

#math #mathematics #algebraic geometry #tokinanpa

[jugdyzucchini]

Preface of 'The Rising Sea' by Ravi Vakil

#mathematics #maths #algebraic geometry #ravi vakil #mathematician #matrix

[encryptiondecryption]

It's funny cause it is true!

#math #mathematics #algebraic geometry

[euler-of-a-leonhard]

2022-09-05

#algebraic geometry #affine varieties #monoids #north sámi

[cecilias-cool-stuff]

You know, when I started doing math I thought I wouldn't have to write essays. I was wrong. The essays are just fun now.

#math #mathblr #studyblr #studyinspo #maths #algebraic geometry #and the essays are much less comprehensible to anyone but me

[spectrallysequenced]

I learned more about descent today it's such a cool concept I love algebra so much I inexplicably want to vlog about this even though I neber vlogged.

#In particular i'm talking about galois and étale descent. #algebraic geometry #algebra #math

[gayvampyr]

ok so i think i’ve noticed a trend between preferences for types of math and science while talking to other people so i want to try and test out a hypothesis

obviously there are more types of science and math but i want to test the correlation between these specifically

#polls #science #math #geometry #algebra #chemistry #biology #i think the connection is whether you’re more of a visual learner and grasp physical concepts #or you’re more of a theoretical thinker and don’t have issues with intangible ideas or things #which is why i prefer algebra and chemistry. i find biology difficult because there’s just so much memorization involved and you can’t #really think or puzzle your way through it the way you can with chemistry #i mean you can but. it’s a different process #idk

[chatnoirwithblackhair]

I have a very love-hate relationship with math. On one hand, when I get and understand it, I love it, and I feel proud of myself for understanding it. And when I don't get it, and have to spend long hours having one problem explained to me, I want to burn it, think it's stupid, and who the fuck made up rules like that, they barely make sense?? What were they on when they made those rules??

Like on one hand, as an alter, I hold dyslexia, and apparently that makes math easier for me and "lowers" dyscalculia, but on the other hand, who made these and can I have a friendly chat with them.

#i hate math #mathblr #mathematics #math #calculus #high school #school #algebra #geometry #dyscalculia #dyslexia #neurodiversity #neurodivergent #neurodiverse #learning disability #audhd #dyslexic #dyscalculic

[isomorphismes]

`y³ = x • (x–2) • (x+2)` rotated to show all three branch points at once by Dan Piponi

#branch points #surfaces #manifolds #algebraic geometry #commutative algebra #mathematics #maths #Dan Piponi #ramification #ramos #polynomials #roots #polynomial #cubic

[romanceyourdemons]

whenever i go to a boba place and they’re speaking mandarin behind the counter there’s a part of me that thinks i could do it, i could be the white boy who SHOCKS staff by ordering in FLUENT CHINESE. but first of all why would i do that. whom does that help. and second of all i don’t know how to say 70% in mandarin which means i would need to get full-sweetness milk tea and i’m not strong enough for that

#my mandarin vocab is Limited especially in terms of math #my high school german teacher was teaching us full math lessons in german algebra geometry etc #and in mandarin i can barely do more than count lol #ryddles

[transrevolutions]

"more sense" doesn't necessarily mean you got a better grade in it, just that you felt you understood the concept best.

"algebra" can include any algebra-aligned math (such as abstract and linear algebra) and "geometry" can include any geometry-aligned math (such as trigonometry). however if you don't know these just go with which category makes most sense to you.

(rb for bigger sample size because I have a theory and I'm genuinely curious to see if it holds up.)

#math #pigeon.txt #poll #algebra #geometry #tag your answers if you'd like! #academics

[sportsandlaughs]

#math #life #number #geometry #algebra #trigonometry #calculus #spreadsheet #excel #job #work #chart #graph

[somethingusefulfromflorida]

I plan to go back to school next fall, so I have a little ovet fourteen months to master all seven subjects. I won't need two full months for algebra 1; cracking open the first chapter, it's all stuff like "here's what a plus sign means" and "variables look like letters, but they really stand for numbers!"

It won't hurt to brush up on factorization, but I think I can bang this one out in a week or two. All the better, because calculus kicked my ass in high school and it's not gonna be any easier now that I'm my own teacher. I passed it once (by the skin of my teeth), but have forgotten almost everything about it in the last decade, so I'll need the extra time to really get it down pat. I have to be able to derive and integrate in my sleep if I'm to stand half a chance at earning an astrophysics major. Astronomy would be slightly easier, but not by much, so I may as well go for gusto. The very first class astrophysics requires is calc 2, so I can't enroll until I'm 100% sure I know calc 1 forwards and backwards. Physics too, but physics and calc feel like two sides of the same coin, so I'll try to work on them at the same time (again, I managed to pull it off once, I'm sure I can do it again).

Chances are these Dummies books will be insufficient for me to grok all this math in one year, so I'll end up buying more textbooks, workbooks, study guides, SAT and AP prep, etc. I had plenty of cram sessions in my first go around at college, but nothing quite like this. This will be a herculean undertaking compared to the easy-A humanities program I coasted through originally. I had no motivation back then, no drive, no goal for "the real world" upon graduating. I went to college because it was expected of me, and I was told I needed it to get a good job. What I wasn't told is that not all majors are created equal; there's not a lot you can do with an English degree besides, well, teaching English. I just hope 14 months is enough time, because I would really prefer not to take another year off; 2024 is the ten year anniversary of when I started college the first time, so it would mean so much more to me if I started again that August rather than put it off until 2025.

I guess it doesn't matter in the end. If I'm not ready, I'm not ready. I can't force myself to start an extremely advanced program before I've mastered the pre-reqs. If I need to start later, so be it. As long as I'm consistently working towards my goal, it shouldn't matter how long it takes.

#my plan #college #math #maths #algebra #algebra 1 #geometry #algebra 2 #trigonometry #precalculus #calculus #physics #calculus 1 #physics 1 #science #astrophysics #astronomy #i got this #2024