#learning is not linear

[sodacowboy]

crocheting without a tutorial/pattern is HARD because sometimes you spend a whole day working on something only to realize that It’s Not Working and it’s Unsalvageable and you’ll have to scrap it and then you’ll have to talk yourself out of thinking that you wasted a whole day when the fact of the matter is that you didn’t waste shit because you actually spent the whole day learning and learning isn’t about how much you got done

[paul-newmans-sauce]

this fucking no named freak wont leave me alone what do i do guys

[mrsthunderkin]

Consistency? Who's she?

Part 2 >>> Part 4

[shivroy]

kendalling in oil

[welcometogrouchland]

I understand that literature nerd Jason Todd is kind of overblown in fanon compared to it's actual presence in canon (a few issues during his pre (and post?)crisis Robin tenure that highlight it) BUT consider that I think it's hilarious if the unhinged gun toting criminal has strong opinions on poetry

[skunkes]

old drawings i found and enjoyed while looking for something else

[algebraic-dumbass]

this might be a dumb question but like. how do you learn math without a class/curriculum to follow. i have a pretty solid calculus understanding and I want to pursue more advanced math but like im not sure where to start. what even is like category theory it sounds so cool but so scary???. do you have any recommendations on specific fields to begin to look into/whether its best to learn via courses or textbooks or lectures/etc.? any advice would be super appreciated!! dope blog by the way

thanks for the compliment!

first of all it's not a dumb question. trust me i'm the algebraic-dumbass I know what I'm talking about. okay so uh. how does one learn math without a class? it's already hard to learn math WITH a class, so uhhh expect to need motivation. i would recommend making friends with people who know more math than you so you have like, a bit more motivation, and also because math gets much easier if you have people you can ask questions to. Also, learning math can be kind of isolating - most people have no clue what we do.

That said, how does one learn more advanced math?

Well i'm gonna give my opinion, but if anyone has more advice to give, feel free to reblog and share. I suppose the best way to learn math on your own would be through books. You can complement them with video lectures if you want, a lot of them are freely available on the internet. In all cases, it is very important you do exercises when learning: it helps, but it's also the fun part (math is not a spectator sport!). I will say that if you're like me, working on your own can be quite hard. But I will say this: it is a skill, and learning it as early as possible will help you tremendously (I'm still learning it and i'm struggling. if anyone has advice reblog and share it for me actually i need it please)

Unfortunately, for ""basic"" (I'm not saying this to say it's easy but because factually I'm going to talk about the first topics you learn in math after highschool) math topics, I can't really give that much informed book recommendations as I learned through classes. So if anyone has book recommandations, do reblog with them. Anyways. In my opinion the most important skill you need to go further right now is your ability to do proofs!

That's right, proofs! Reasoning and stuff. All the math after highschool is more-or-less based on explaining why something is true, and it's really awesome. For instance, you might know that you can't write the square root of 2 as a fraction of two integers (it's irrational). But do you know why? Would you be able to explain why? Yes you would, or at least, you will! For proof-writing, I have heard good things about The Book of Proof. I've also heard good things about "The Art of Problem Solving", though I think this one is maybe a bit more competition-math oriented. Once you have a grasp on proofs, you will be ready to tackle the first two big topics one learns in math: real analysis, and linear algebra.

Real analysis is about sequences of real numbers, functions on the real numbers and what you can do with them. You will learn about limits, continuity, derivatives, integrals, series, all sorts of stuff you have already seen in calculus, except this time it will be much more proof-oriented (if you want an example of an actual problem, here's one: let (p_n) and (q_n) be two sequences of nonzero integers such that p_n/q_n converges to an irrational number x. Show that |p_n| and |q_n| both diverge to infinity). For this I have heard good things about Terence Tao's Analysis I (pdf link).

Linear algebra is a part of abstract algebra. Abstract algebra is about looking at structures. For instance, you might notice similarities between different situations: if you have two real numbers, you can add them together and get a third real number. Same for functions. Same for vectors. Same for polynomials... and so on. Linear algebra is specifically the study of structures called vector spaces, and maps that preserve that structure (linear maps). Don't worry if you don't get what I mean right away - you'll get it once you learn all the words. Linear algebra shows up everywhere, it is very fundamental. Also, if you know how to multiply matrices, but you've never been told why the way we do it is a bit weird, the answer is in linear algebra. I have heard good things about Sheldon Axler's Linear Algebra Done RIght.

After these two, you can learn various topics. Group theory, point-set topology, measure theory, ring theory, more and more stuff opens up to you. As for category theory, it is (from my pov) a useful tool to unify a lot of things in math, and a convenient language to use in various contexts. That said, I think you need to know the "lots of things" and "various contexts" to appreciate it (in math at least - I can't speak for computer scientists, I just know they also do category theory, for other purposes). So I don't know if jumping into it straight away would be very fun. But once you know a bit more math, sure, go ahead. I have heard a lot of good things about Paolo Aluffi's Algebra: Chapter 0 (pdf link). It's an abstract algebra book (it does a lot: group theory, ring theory, field theory, and even homological algebra!), and it also introduces category theory extremely early, to ease the reader into using it. In fact the book has very little prerequisites - if I'm not mistaken, you could start reading it once you know how to do proofs. it even does linear algebra! But it does so with an extremely algebraic perspective, which might be a bit non-standard. Still, if you feel like it, you could read it.

To conclude I'd say I don't really belive there's a "correct" way to learn math. Sure, if you pursue pure math, at some point, you're going to need to be able to read books, and that point has come for me, but like I'm doing a master's, you can get through your bachelor's without really touching a book. I believe everyone works differently - some people love seminars, some don't. Some people love working with other people, some prefer to focus on math by themselves. Some like algebra, some like analysis. The only true opinion I have on doing math is that I fully believe the only reason you should do it is for fun.

Hope I was at least of some help <3

[piratadelamor]

skip and loafer ch. 53

shima seems to see romantic love as a combination of different attraction factors, where liking someone as a person (for their personality) can be compensated for other things, therefore your standarts are lower when you're romantically attracted to someone. the way he sees it, the highest form of steem you can have for someone is to like them as a person, where these other factors don't matter and what you truly value is solely their personality.

i think it's interesting how mukai introduces this conversation by building a hierarchy of feelings, where romantic love stands on top of the feelings of friendship and of liking someone as a person, because that's one concept i've been personally focusing on deconstructing in my life. it's precisely by differenciating these types of feelings and putting them on a hierarchy that so many people end up in romantic relationships with people they don't really like, or why so many people drift away from their friendships when they start dating someone.

through everyone else's eyes, shima's feelings are romantic, and he doesn't feel like they are, because romance to him means something else. the lines between liking someone as a person, as a friend and as a lover are blurred. and listen, that's how they're supposed be. to love someone as a lover is supposed to mean you love them as a friend and as a person as well. a friend and a lover shouldn't be too different, and liking them as a person is supposed to be the core of both feelings.

i don't think shima is being innocent, like i've seen so many people saying on twt since the chapter came out. i think he's touching something very deep about relationships in our society that so many stories that focus on romance fail to address. in most of these stories, romance is the final goal. that's where most of them end. that's not the case here. i was already surprised when mitsumi and shima started dating, and even more surprised when they went back to being friends. that's not the usual narrative for this kind of story. because here, it doesn't seem like this hierarchy matters. and i think it's beautiful and i think it's HUGE how both shima and mitsumi value their friendship above everything else. not only them, because friendship is one of the main themes of this story. both as a dynamic and as a type of love as well.

but people have different perspectives on love and how love feels for them. it's different for mitsumi, for shima, for mika, for fumi. the way you're taught about love in your family or as a child in general has a big role on shaping that. we saw the matter of mitsumi having received lots of love in her family and childhood friends being brought up before as an explanation for her confidence. then, on the other hand, that's why we see shima acklowledging this on the next panels:

we know a few things about shima's family and their complicated relationships. shima never realized his little brother liked him because he saw his behavior as coldness or indifference, when he was actually being considerate of the distance shima was putting between them himself. he felt the need to please his mother by acting in order for her to love him, or for him to be worthy of her love, because their relationship was too anchored on exploitation. his father was having an affair, which not only made shima watch the failure of his parents marriage but also perceive romantic love as something superficial (as in "people break up and move on to the next person") and possibily as something that pushes people away. then shima's first girlfriend only liked him because of his looks, and so many others confessed to him without barely even knowing him. how could shima trust his own feelings after all of that? if he spent most of his formative years in an environment of appearences where love was tied to selfishness, interest, volatility, coldness, pain? shima learned to supress all his feelings and be a people pleaser as a survival mechanism. don't get too attached, live up to others expectations, keep your distance, smile and wave, bottle it all up. he is a kid that doesn't know a single thing about love and is scared as hell of it. love feels as if something is about to break.

that's why liking someone as a person feels more important to him. and that's not only the highest feeling he can have for someone else, i think this is the highest form of feeling he thinks someone could have for him too. it's the kind of feeling he thinks his own mother couldn't have, because acting was more important to her than who he actually was. it's the feeling he unconciously doesn't allow others to feel for him, because he never shows people who he truly is. so shima understands mitsumi's words as a love confession back in chapter 41. she didn't say "i love you", she said "that's what i love about you". and he asks her out, not only because he already knows mitsumi is different, so it seems more reasonable to give it a try, but also because he thinks this is how it's supposed to go. this is what he thinks it's expected to give her in return.

when society puts romance on the top of the relationships/feelings hierarchy, it builds an insane amount of expectations around it. i think it's crazy how friendships feel so free while romantic relationships feel so enclosured. they have too many rules. you're supposed to do this, and that, and behave in certain ways. if you start dating a friend then suddenly your friendship dynamic changes. a boyfriend or a girlfriend have responsibilities that friends don't have. it's a weight. i can't imagine a person like shima feeling any other way about a romantic relationship. for him, this is a big, big weight. that's why he puts an emphasis when he says "i thought that i could be a 'boyfriend' too". a boyfriend is a social role. when he phrases it like that, he's using the word "boyfriend" as an outside concept: he doesn't know what it means to him, he only knows what it means for everyone else. and that's not something he can do.

mukai is absolutely right when he tells shima he shouldn't be going out with anyone. shima isn't ready to be that close to anyone, not even his closest friends. i can't even describe how sad i felt when mukai said this to him:

shima is just so, so lonely...

but this doesn't mean that shima's supposed to become ready to be a "boyfriend" on those terms. i just think he's still trying to figure out what all of these things mean to him. and the good thing is that mitsumi is also trying to figure out these things too. the difference between them is that mitsumi is a few steps ahead, because she already understands what friendship love feels like. and when it comes to that, she gave us one of the most special love confessions i've ever seen.

so many people talked about this scene already, but now, in the light of chapter 53, her saying "i really like this person" has a whole new meaning. this is the most honest love shima has ever received from anyone. no romantic confession could top that. no romantic feeling could heal his wounds the way these words from mitsumi can. this is a treasure shima can't afford to lose.

we're taught that romantic love will save us. that it will make us the happiest, that it completes us. we grow up believing that we can't survive without it. what we really can't survive without are our friends... skip and loafer is putting friendship above everything else, but more than that, it is questioning how romantic love is supposed to feel. some people feel it, some people don't. i think most of us don't really know what it is. we think we do because we read enough, we saw enough movies, we listened to enough love songs. i think i felt it a few number of times in my life but everytime i felt it for someone new i asked myself, was it really love before? what is it, really? if i never read those books or saw thoses movies or listened to those songs. would i recognize it? would i know it better? would it even exist?

aren't shima's feelings for mitsumi already valuable enough? big enough, true enough? would they change if he called them romantic? mitsumi has SO much to teach him about love, about himself, about others. their encounter is so beautiful and so rich. we see how much he's changing, how many new things he's finally starting to understand about himself, how many important steps he's taken since they met. is finding romance at the end really the most important thing for their story?

[ruminate88]

In 2025, I thought I would be out of my little hibernation that I created last year where I spend as much time by myself as I can but guess not. I’ll get back to normal life again when it’s time. You can’t rush yourself. Our brains run on the clock but our bodies don’t.

You have to learn to love yourself (something you never did before by spending alone time with yourself.) You move slower, eat slower and rest more. You’re calming your nervous system and creating trust within yourself again. You’ll still have moments of being triggered and you’ll have moments of hyper-vigilance. This is all part of it. Healing is hard and there’s no deadline becuase it’s not a race or a project. It’s the chapter of your life that you’re in.

This is not about isolation or becoming selfish. You’re not trying to push people away and hurt them but you are finally taking care of your needs. You need to test your trust by getting back out there with people. You can’t hide forever and live in fear but process the lessons of the past. Use your lessons for future relationships. Your body will know when it’s time to push yourself harder. Right now, just take it easy. ❤️‍🩹 4/15/25

[evil-jennifer-hamilton-wb]

A course on number theory? Please, I know what numbers are. Smh

[plounce]

tbh i dont need every important detail about a character to mentioned in the main story. im okay with certain details being "optional"/"missable" side content. does it break the flow of the story? does it fit in with the themes? is the creator willing to devote as big a pathway as certain stuff would need in a main narrative to be explored as seen fit? or - does the relatively greater obscurity of the character detail within the story allow the "missable" nature of the trait to connect the reality with the fiction? in a game, would you have to put a lot of work in to find out this trait because the character would never say it outright? is the character relatively minor? or - is this a great reward for people who seek out more things to learn about the story/characters/world? are you rewarding interested readers for caring and for reading? not everything has to be immediately accessible in the main text. some things are fun as optional content, and being so allows that and the main story to breathe easier.

[bragganhyl]

Deadfire is a game of all time, that's it, that's the post

[datasciencewithmohsin]

Simple Linear Regression in Data Science and machine learning

Simple linear regression is one of the most important techniques in data science and machine learning. It is the foundation of many statistical and machine learning models. Even though it is simple, its concepts are widely applicable in predicting outcomes and understanding relationships between variables.

This article will help you learn about:

1. What is simple linear regression and why it matters.

2. The step-by-step intuition behind it.

3. The math of finding slope() and intercept().

4. Simple linear regression coding using Python.

5. A practical real-world implementation.

If you are new to data science or machine learning, don’t worry! We will keep things simple so that you can follow along without any problems.

What is simple linear regression?

Simple linear regression is a method to model the relationship between two variables:

1. Independent variable (X): The input, also called the predictor or feature.

2. Dependent Variable (Y): The output or target value we want to predict.

The main purpose of simple linear regression is to find a straight line (called the regression line) that best fits the data. This line minimizes the error between the actual and predicted values.

The mathematical equation for the line is:

Y = mX + b

: The predicted values.

: The slope of the line (how steep it is).

: The intercept (the value of when).

Why use simple linear regression?

click here to read more https://datacienceatoz.blogspot.com/2025/01/simple-linear-regression-in-data.html

[aefensteorrra]

next year I'd like to learn more maths !

[mentalknot]

What I thought my trajectory as a math major would look like during the fall of my freshman year:

Semester 1

Take linear algebra + multivariable calculus… maybe intro combinatorics if I’m feeling “wild,” but taking it easy to learn the ropes

Semester 2

Take number theory, maybe some CS classes to work on the double-major side plot… pretty chill semester again, to adjust to college ofc

Semester 3

Take abstract algebra and a few more CS classes, maybe an extra little elective? Time to be adventurous!

Semester 4

Take real analysis + finally start finishing my distribution requirements… lol

Semester 5+

Topology and purely unknown vibes, maybe research at some point? Who knows!

Reality, three semesters later lmao

Semester 1

Took linear algebra and combinatorics + a last-minute remote internship + intro CS, and discovered research seminars for the first time

Semester 2

Took abstract algebra, number theory, and multivariable calc + data structures + started my first math research project, …and had an eight-day medical emergency side plot (oops)

Summer

Finished first math research paper, attended six conferences + more seminars than I can count, worked part-time at a pizza place, and my friend, imposter syndrome, said hello

Semester 3

Taking advanced linear algebra and real analysis, working two interdisciplinary research jobs because I was ready to “take a break from retail,” experienced my first “philosophical bender” after severe anxiety that spawned a “potentially novel” family of graphs, attempted to prove some goofy old conjectures and convinced myself that I was going crazy in the process… and enjoyed combinatorics seminars with my friends!

I’m never letting my autistic brain have free will to decide my schedule again… 😭

[gxlden-angels]

do you have any thoughts on the story of abraham and isaac? my parents talk about it and praise abraham for being willing to kill his son which..... scares me to say the least, and i'd love to hear your perspective as someone who seems more well-adjusted

Where I am now, it disgusts me more than anything. The interpretation of "I'm willing to sacrifice your life if I was told to" feels like the step before "I put you into this world and I can take you out of it." It's entitlement to a child, who is an independent individual, just because they are dependent on you for survival. I prefer the interpretation of understanding the actions you're taking and the reasons why (like how there's multiple religions that don't eat pork because it was so unsafe to eat at the time), especially if it's at someone else's expense.

Where I was in the thick of it all, it gave me morbid comfort that scares me now. I had fantasies of being a martyr for the church and the idea of being the next Isaac was just so appealing. Being a hand-selected sacrifice chosen by the Good Lord Himself? Sign me the fuck up, babey!

I think if I admitted that to my family, they'd be horrified.

It's another one of those stories or beliefs where I think the majority of christians just regurgitate what they've heard. It's a point of pride and devotion, but there's no personal reflection or cross-cultural awareness of it. Lean not unto your own understanding and whatnot. It's the potential that scares me the most, like the Quiverfull movement with the Duggars or Turpins. I'm sure there's stories now, but I can't remember them off the top of my head

(Also I will be telling my therapist someone on Tumblr called me "more well-adjusted" thank you anon)