#alg theory

[rigelmejo]

Basically... no one online who's policing what's pure ALG or not is putting themselves out there to prove what they say with their own results. The ALG schools are, in that you can find teachers to ask about the ALG program (like David Long). But of course, when you find actual student results they tend to be B2 (which is great! Excellent results! Just not "like a native speaker" like marketed). I personally would recommend Not doing ALG unless you are doing an ALG school/program (and if you are - there are people you can find on youtube and reddit Thai subs sharing their experiences so far so you can see what to expect).

Dreaming Spanish has a lot of people sharing their experiences and results, so I personally find the Dreaming Spanish Roadmap useful if you're planning to use it as a self study plan, and want to do mainly extensive listening to comprehemsible input as your study activity. You can see on youtube and reddit many people who share their experiences during each Level in the roadmap, and get an idea of what's worked for people and what's realistic.

[anecdochees]

not physicsy enough to physics and not mathy enough to math

[thedawningofthehour]

I was a middle schooler when COVID-19 decided to ruin everything and now I'm a highschool junior and failing math

You're good I did that too. I took a logic class in college so I wouldn't have to take math again.

It's okay, once you're out of school you will never use algebra ever again.

[jupitersflytrap]

in one of those phases where i listen to all my demos and go "why did i think these were bad this is a straight up banger" but unfortunately will not be able to act on this creative impulse as i'm fully booked tomorrow trying to read rob roy in one sitting.

[m---a---x]

I've come around on my opinion that all those excellent yt vidos on 1-3 semester math classes are an universally good thing.

They are not.* Hear me out.

*For people who want to learn mathematical research. Not talking about applied maths here.

At the begining of their studies every math major has a course on linear algebra. (I'm gonna talk about linear algebra, but the same argument applies to analysis and stochastics as well.) The point of this course is not for the student to become really good at linear algebra. Of course lin alg is useful for topics like representation theory, but a majority of mathematicians will not use it in their research.

Also lin alg serves for a lot for examples for other concepts. Everyone loves teaching adjoints with forgetful and free functors between vector spaces and sets. But that is just because everyone knows lin alg (or topology or group theory or whatever).

Most of the work in math research (at least for me) is building internal models in my mind. Finding and sharpening intuitions as well as translating between them and formal notation. Lin alg allows you to learn doing this.

So why does everyone know lin alg, analysis and stochastics? Why not teach those concepts with knot theory? Well, most math students will not end up doing mathematical research. And for applied math, software engineering and management/financial math those subjects are the alpha and omega. So we might as well kill two birds with one pidgeonhole.

So, should a math student use these good yt vids? One must weigh the prospective benefits against the likelyhood of either career of course. And even when one strifes to become a researcher, as long as they don't rely on predigested intuition for all of those first few big subjects it's probably fine.

I'm interested to hear you folks' thoughts on this.

[real-real-numbers]

5, 6, and 20 for the math asks!

hiya thanks for asking!

next year I'll be entering grad school (hopefully!) so I'll probably retake some courses to get good foundations. definitely need to give topology a do-over bc my prof was terrible. also hope to get more deeply into alg geo!

this year I started learning alg geo and also did some homological algebra and category theory (mostly teaching of the latter). it was good stuff

I already dropped a LaTeX trick for the previous ask (colonequals) but another one is the realhats package which turns \hat into a real hat :)

[rigelmejo]

I don't know why ALG enthusiasts shoot themselves in the foot by saying "it will make you like a native speaker" when 1. People will immediately try to prove if that claim is wrong 2. They're not making money from ALG courses so it's not like there's a profit motive to claim something so extreme. 3. Marvin Brown's book... does not say most adults will get results like native speakers, I read his book... it says most adults WON'T get perfect results. 4. Most people don't want to commit to doing a study plan that they feel is lying to them about the results they'll get.

If you are a teacher trying to sell ALG courses, then I'd see the reason for downplaying the idea of permanent damage Marvin Brown mentions - caused by any concious analysis of any language. You can't get paid if you undermine your own marketing ploy to convince people to try your teaching method... banking on the hopes that by the time the student has realized they Wont achieve native like fluency, they'll be invested enough to use the language for their personal goals (and take more classes if they need to for their goals). But if you're not a teacher trying to sell a product... there is no reason to claim ALG will result in native speaker fluency for an adult. (It just makes me feel like these people didn't read Marvin's book... which they probably didn't, I'm kind of a nerd that way, delving into whatever I can find, I assume what they think of ALG is based on ALG Schools marketing - which is where that exageration comes from).

[hojungwrites]

Where I Learn to Deal with Failure (or I just copy and paste choice parts of a really nice email from a former professor)

Originally featured on Korean American Story.

Beginning each morning by writing a to-do list, I feel immense satisfaction whenever I cross things off. It signals that I finished this, that I made something of my day. This compulsion for constant productivity, I am sure it stems from the way I was raised. Famously coined by legal scholar and writer Amy Chua, the term “tiger mom” refers to a parental figure with an incredibly authoritative child-rearing style—in other words, my parents. Like many other Korean parents, my mother and father were tiger parents for sure. Never accepting anything less than the best (my best was not enough, for I had to be the best out of everyone else as well), I strived to live up to their expectations.

I hold a memory from my early childhood, perhaps in the first or second grade, sitting around in a semicircle with the other school children. Having just read us a story, the teacher scribbled some questions onto the whiteboard with her thick black Expo marker. My mother happened to be in the classroom that day, along with the other parents. Her presence made my hands quite clammy, and each breath I took was so frustratingly unrefreshing. While the other kids excitedly raised their hands to answer our teacher’s questions, I sat idly by.

Under my mother’s watchful eye, I imagined the possible scenarios that could play out. If I answered a question correctly, I could earn a smile perhaps. But I also imagined what could happen if I said the wrong thing, and my mouth remained shut. I kept waiting for a question I could comfortably answer. I’ll just wait for the next one. No, not this one. The next. The one after this. The thing is, for every single question, I correctly predicted the answer before the teacher chimed in. My silence wasn’t a result of ignorance; I just hadn’t trusted in myself enough to speak up.

At the end of the school day, my mother and I walked to the car. As I watched her slim fingers turn the key in the ignition, a thick silence grew between us. Looking straight ahead, barely audible over the rumbling of the engine, my mother asked me, “Why didn’t you answer any of the questions?” But umma, I knew all the right answers, I wanted to say. Yet I was rendered mute by stinging nerves, and once again, I said nothing at all.

According to the Implicit Theory of Intelligence (Dweck & Leggett 1988), people hold one of two mindsets—growth or fixed. Following this theory, those with a growth mindset believe their intelligence can grow over time, while those with a fixed mindset believe there is a natural limit to their abilities. What I find interesting is this theory’s implications on failure. Seeing it as an opportunity to grow, those with growth mindsets react positively to failure. In comparison, people with fixed mindsets will apparently fall into the depths of despair.

To shape a growth mindset in a child, the theory stresses the importance of praising effort and not the outcome. For me, growing up in a Korean household, the outcome was all that mattered. In that classroom, in front of the whiteboard, in front of my teacher, and especially in front of my mother—what did it matter if I knew the correct answers if other people had no idea I knew them?

Fortunately, or perhaps, unfortunately, out of sheer willpower (or spite) I did meet these expectations for the majority of my childhood and teenage years. Several afternoons and evenings of my life were devoted to after-school tutoring sessions to ensure I would perform slightly better than my peers. I felt compelled to attend a high school I was not zoned for, with a bus stop at 5:15 am, to participate in their “academically rigorous” International Baccalaureate program (which is complete bull, by the way. If any high schoolers are reading this, just take AP.) I even joined the mathletes, although anything above basic algebra easily brings me to tears. I wanted all these special certificates, diplomas, and various badges of honor to my name to prove that my efforts meant something.

My tiger parents taught me that when successful, I could reap intense satisfaction. Because they reacted so well to my achievements, I ended up placing so much of my self-worth in academic validation. However, my parents skipped the lessons on how to deal with failure. Instead of an opportunity to grow, a failure was simply a failure, nothing more. It was something to brush aside and hide away, in the hopes that a greater accomplishment could mask it. As a result, achieving something felt really, really good. But failure led to equally high, possibly higher, levels of distress.

Because I based my entire identity on being the “smart one,” I had no idea what to do with myself when this label was seemingly taken away from me. Since the end of my school career, I have failed many, many times over. I failed to get a high-paying job at a consulting firm like many of my friends, I failed to get into graduate school my first time applying, and I failed to reach any of the milestones I arbitrarily decided were necessary to feel like an actual adult. Truthfully, I felt—still feel—incredibly behind. My younger self imagined I would have accomplished much more by my mid-twenties. I think I am very good at giving the appearance of being okay, but in reality, I am frantically flailing underneath the water’s calm surface.

I think the toughest lesson life taught me is that putting your best effort into something will not guarantee success. X does not ensure Y, because there are a million factors Z completely out of my control. This lesson highlights the problem with tying up self-worth in something external because I had no idea what to do once this external validation disappeared. As a postgraduate, to squeeze a few years into one short sentence—I was rather nihilistic for a while. I became so tired of trying anything at all because I was so tired of failing.

I love being Korean American. Sincerely, I do. Nonetheless, as I psychoanalyze myself, I am made increasingly aware of how certain aspects of my cultural background have, perhaps, in terms of mental health, screwed me over. It is so easy to be a victim, stay a victim, and relish in feeling bad for myself. But then what?

Not trusting myself to find the answer to my question, I reached out to many others to figure out what to do next. There was one message in particular that stuck out to me. According to my old statistics professor, Dan Player, “It’s an endless treadmill [to chase after success]. It’s really remarkable to talk to people who have achieved amazing things. Some of them are still chasing the proof that they’re successful because no matter what they do, someone else has done something better… I’m telling you, you can’t win at that “proving yourself” game.”

To “succeed” in life, I have to let go of this notion of success entirely. I have to let go of this obsession to prove to other people that I have value. I am learning and growing and (hopefully) becoming a better person, and it does not matter if other people cannot see it. All that matters is that I see it. As Dan says, I am Hojung, a “filmmaker/artist/author/scholar/general fascinating human being,” and I am fine just the way I already am.

My life has been full of so many disappointments, yes, but it is also a record full of acts of kindness, moments of grace, and dreams for myself. It is full of warm kisses, hugs full of longing, the laughter of friends, and eyes that met to share a brief moment of connection. This is my life, a life that is worth living simply because it is mine. My self-worth is something I give to myself, so it cannot be taken away, even if I never achieve something momentous or do not leave behind a huge impact on this earth once my time has passed. It is enough that for a moment, I was here. I existed. This is my Korean American story.

Extra Reading: (1) Chua, A. (2011). Battle Hymn of the tiger mother. Penguin Books. (2) Dweck, S. C., & Leggett, E. L. (1988). A social-cognitive approach to motivation and personality. Psychological Review, 95, 256–273

[positively-knotted]

I'm sure all of this is already in the notes but this is such a crazy poll to me:

No geometry? One of the most fundamental areas of maths and one that is actually taught at highschool?

Measure theory being separated from analysis

Also graph theory from combinatorics

Linear algebra winning? Tbh if I was making this poll I would probably not have included it

"Abstract algebra" I think I know what you mean but I'm also not really sure

The brave (but maybe correct) choice of No Stats

Actually just, no applied at all. Wild. Although it is harder to split up I suppose

Mostly for the exercise of creating a poll like this, here would be my version. Feel free to vote in it (who doesn't love a poll) but I'm not trying to supplant op:

"Hard" analysis is classical analysis, analysis of PDEs, dynamical systems, etc. "Soft" analysis is functional analysis, operator algebras, etc.

RIP numerical analysis you did not fit, but I also doubt anyone misses you. I would also have wanted to split geometry and topology up but with only 12 options it seems a bit unnecessary.

That maths poll was interesting but I'd love to hear from people who chose to study maths at a higher level. No "i hate maths" option.

[tototavros]

interesting to see new pl developments of the kind “yeah you can do most of the basic dependent type stuff an industry programmer might want, but no you don’t get full dependent types” 

[actuallylorelaigilmore]

i genuinely don’t understand why i’m attracted to chris evans in knives out and i’m so disappointed in myself for it but here we are 

[niconiconwo]

I have a stack of five text books, and the unrealistic belief that I can read them all before dawn in any meaningful way.

[xuune]

@lily-claw ima reply to ur comments thru this reblog for anyone else that wants this info bc idt ppl check comments. also bc my response is long again:

i didnt have extensive formal art courses specifically for painting illustrations either. i only had 3 semesters of painting (gouache, acrylic, digital), so a lot of what i know is personal learning and trial and error through studying other artists. giving yourself exposure to other artworks and deconstructing, analyzing, and studying why pieces work and speak out to you helps you understand a lot how you want to create your own art and what you want to see in it! its incredibly valuable.

tbh, idk how common it is for people to teach stuff like layer modes in digital art courses in formal schooling. in my digital painting course, my professor rarely explained that. it was more that we should learn how to paint without relying on tools like layer modes so we first understand technicalities and thought process behind how you use color and how to think when you paint. i understood how to use layer modes better by fucking around in my own art, so there really is no "right" way to go about learning this stuff.

(btw my pronouns are they/them 😅 alg tho)

this answer has two parts: 1) lighting affects color choices and 2) you have creative freedom to fuck around

1. LIGHTING AFFECTING COLOR CHOICES: you're on the right track when you say "adapt it to the place," which in this case, its lighting. specifically and especially lighting affects what colors are used in your piece. lighting will influence what skin tones will look like in it and everything else. the time of day, what your light sources are, whether its cool/warm tone lighting, determines this (but there is always creative liberties to push your colors, it really depends on what you want). my biggest recommendation for this and putting it into practice is to do color studies. color studies can either be: a) MASTERCOPIES of existing artworks (take whatever existing illustration exists, and do your own copy of it to study it). we do this in school all the time, its great practice especially when you want to understand how other artists choose their colors. obviously if you're gonna do this, either keep these mastercopies to yourself or if you want to share online, post with credit to the original artist (but first and foremost ask for permission to do a mastercopy, especially if the artist is someone you can contact and ask lol. i'd feel weird if i randomly came across someone doing a mastercopy of my work posted online. i'd feel flattered that someone wanted to study my work, but still. you get what i mean?)

b) PHOTO REFERENCE STUDIES. straightforward enough. you take a picture and do a painting of it. can be some photo/video/film you found online, or from your own photos. equally as valuable as mastercopies since you're still practicing observation skills and looking at how lighting works and how colors are affected by it. free real estate for you to experiment and push the colors too.

this leans more towards your concern of getting skin tones right when characters are in dark places. what makes it a dark place? is there straight up no light? is it dim lighting? whats the tone of the light source? is it cool/warm? are there multiple light sources? is there rim, split, rembrandt, fill lighting? ideally, if you know these answers and you can replicate it yourself in person, then you should take your own reference photo. but again, dont forget that you can push your colors in your own art! dont be a slave to your reference.

2. YOU HAVE CREATIVE FREEDOM TO FUCK AROUND:

aside from lighting, color palettes/schemes can influence what colors are used on things like skin tones. if you're making your own palette, you make rules for what gets to be what color. its one way of learning to limit the amount of colors you use and be more decisive about your color choices. this also goes back to general color theory stuff, like monochrome, analogous, complementary, etc.

stylistic/experimental palettes work greatly too. here's an example of this artist's artwork. main takeaway from these artworks is that they intentionally limit extreme uses of pure black and white and predominantly keep their colors in its strongest hue. ima be fr, nothing about this makes sense to me on what their exact process is. certain segments seem like its using a triadic scheme, but other areas they're basically using the entire color wheel. in one section, skin tones are blue and purple, but in the next its orange and red. i have no clue. but the illustrations work, are readable, and are appealing. sometimes certain colors surprisingly work out in your favor, so allow yourself to play with it when you can.

hope this helped!

Hii first of all, I FUCKIN LOVE YOUR ART! ITS GORGEOUS AND IM SURE EVERYONE CAN UNDERSTAND YOU REALLY GIVE YOUR SOUL INTO THAT🤧 Your color palette looks so good, What do you pay attention to when painting? (Like when do you think its better to use multiply or something like that and etc.)

first off, I'M HAPPY YOU CAN TELL THAT I PUT MY SOUL INTO MY ART!!! im genuinely in love with drawing and am always finding ways to make creating art enjoyable and impress myself with what i can achieve and learn :D

second, thanks for asking your question!! i dont mind answering it, but my response is quite long. here's my thinking process:

(you specified layer modes like multiply, so im gonna gear my answer towards that a bit) 1. REFERENCE SEARCHING IS KING. color is actually extremely hard for me, so i search around for artworks with palettes i'd like to use and study how an artist uses it. some situations i have a clear idea of what i want, but usually the images in my head are extremely vague, so i borrow palettes from various other artworks that fit the vibe of what i want. an example is this one. my main palette reference were from these artworks. im looking at this artist's use of high saturates and how drawings are overlayed on top of each other. while looking at references, im asking myself how is this artist using warm/cools, where are these warm/cools placed, if their illustration used any form of texturing (like halftones, hatching), how do they use their palette to render form/shape/gradient, when/where do they saturate/desaturate their colors. those questions inform my decisions when using colors too.

2. USING LAYER MODES WHEN NECESSARY. i used to be reliant on multiply for everything, which atp i dont do since i can definitely push colors more first before using layer modes. only when i feel like my current colors are lacking do i start tinkering with tone curves and/or brightness/contrast/hue/saturation/luminosity settings. and if that doesn't work, then i start using layer modes. using layer modes do help with achieving certain effects, color corrections, or when i want to fuck around and find out. i think having a better understanding of what these modes can do makes you more decisive on how you can properly utilize them and to achieve a particular look (like using multiply for a cel shaded style). here's an example:

this leads into my next point:

3. BALANCING OUT VALUES. big thing that makes an illustration hard to read is if values blend together which affects the hues and contrast. i check for what elements need to be distinguished from one another and if it can be read clearly. using layer modes can either help with this or not help at all. it's very dependent on the type of layer mode. here's this example where i applied pin light:

back to #2, there are various instances where i'm using layer modes for quick color corrections and/or to help with readability:

other times, i start off having my entire subject in gray and to figure out main shadow/lights (similar to the multiply cel shaded process i linked ealier). im thinking about what this should look like if i only used 2 value tones:

when in doubt though, i check my artwork in grayscale to ensure values aren't overly blended into each other, especially if i didnt start with grayscale like this one:

painting for me takes into consideration a lot of different aspects. im thinking about how colors should interact, where/when to give contrast, checking/balancing out values, etc, but im also making it a time to study off of how other artists use their colors through the references i collected.

hope this answered your question! lmk if there's more :]

[rigelmejo]

I have realized there's very few people actually doing Automatic Language Growth as Marvin Brown made it, pretty much only Thai AUA and ALGworld and Comprehensible Thai (on youtube) and their related school/teachers. So if you aren't studying Thai then you probably won't run into pure ALG lessons/study program unless you make it yourself. Pure ALG is only going to be reasonable when doing a program, if you happen to already be in an ALG school. I have found very few people doing pure ALG on their own, outside of ALG programs, and few have posted results and experiences. (So if you wish to read/hear about experiences, David Long on youtube who did ALG Thai, and a few other youtubers and redditors doing ALG Thai, are the best resource).

Dreaming Spanish is not purely ALG according to certain ALG enthusiasts, but it is the closest thing you'll find that's hugely popular in the English speaking sphere. Dreaming Spanish is welcoming even if you have taken classes before, and even if you still use other study methods alongside it. So I do recommend it if you like it. With the caveat you Remember that for goals involving listening, reading, speaking, writing, you DO eventually need to do things to practice all of those goals. Dreaming Spanish Roadmap mentions starting to read and speak at Level 6 of the roadmap, and anecdotally learners on r/dreamingspanish mention eventually reading 1-3 million words, speaking 200 hours, and working with a tutor/friend or a WritingStreak writing group for practicing writing in prep for B2 or C1 tests. So if you plan to reach goals in all 4 skill areas, eventually you will want to do those things too.

(And I would say that most people who have done Dreaming Spanish who are going viral lately for 1000-2000 hours and can't speak well, probably just haven't practiced 200 hours speaking yet, or have not read 1-3 million words yet. I'd argue a lot are actually A2-B1 level already in speaking even before 200 hours of speaking practice, but since a lot of people claim they'll "speak as well as a native speaker" they're getting torn to shreds online, because A2-B1 - or even B2 to C1 after 200+ hours of speaking - is not as good as a native speaker. I think Dreaming Spanish changed it's roadmap as it now has B2 level skills as it's Level 7 description. But certain ALG enthusiasts love to say perfect pure ALG results in speaking as well as native speakers, and then those enthusiasts say Dreaming Spanish is NOT pure ALG enough and that's why the results are imperfect. But B1 is fucking GREAT for never having spoken before, and B2 after 200 hours of speaking practice is excellent as far as I'm concerned. Dreaming Spanish roadmap is 1500 hours for B2, and FSI Estimates 1200 hours for B2 in Spanish when accounting for 40 hours a week - self study and class time - at 30 weeks. Those estimates are in the same ballpark. Expect it to take 1000-2000 hours to get to B2 in Spanish no matter what route you take to study.)

And don't get me started on the purist ALG enthusiasts... I read Marvin Brown's book. And I honestly think he did NOT guarantee you would become as good as a native speaker! I think the ALG schools may market themselves using such language though, so maybe that's where the misunderstanding comes from - and David Long in particular did pure ALG, runs an ALG Thai school, and definitely claims he speaks as well as a native... though I'm not sure. I've seen other anecdotal reports of students who did ALG Thai school, and they got B2 active skills results (C1 comprehension) in around 2000-3000 hours - Pablo Roman, and ALGWorld blog posts. Not "results like a native speaker," B2-C1 level. I think Marvin Brown himself... himself... thought any adult learner could NOT learn to speak as well as a native, due to all the years they've learned about grammar in their native language and in other languages. I think Marvin Brown's theory of permanent damage and a learning ceiling, was based on his own experience of fossilized mistakes and things he could not stop mentally thinking about before speaking/could not spontaneously produce. Basically, I think Marvin Brown did not claim any adult learner could learn to speak just like a native speaker... I think he said theoretically IF you did ALG perfectly, and had no prior experience analysing languages then maybe you could get the best result possible. But almost all adults have done grammar revision on essays in school, so they already have a ceiling on the results they can achieve, according to his theory. Maybe Brown's ALG school claimed it could give students "native speaker like results" and it's false marketing is still plaguing ALG theory. I'm going to say... probably. Hey if a school says THEY can give you native like results, sure do it if you want to spend your money, and hold the school accountable if the results are worse than they claimed. But if you're doing ALG on your own? Expect B2 overall results if you do the hours they recommend, then speak for a couple hundred hours after you feel ready to speak (after 1000 hours of listening), read a lot once you've done a lot of listening, and practice writing once you are practicing speaking. Expect realistic results - B2. Not "as good as a native speaker," and you can't be let down later.

[inkoflethe]

I’m pretty sure one of the best feelings is when you think of a nice, clean proof for a program you’ve been struggling with and it ends up being rigorous. 

[hermadamejustice]

Good Morning! Madame Justice here.

Hope you had a wonderful weekend and that you're looking forward to the week ahead. Here are some of my tips to start the week off on a good note, as well as a few of my study music favourites and an absolute tune if you feel like you need a boost of energy to start off the week in style.

Block out set times in the morning and afternoon for emails- I know I'm guilty of spending more time than is necessary responding emails. Set out 15 minutes at the start and end of the day to deal with these pesky messages Try some power poses- If you are unsure of what a power pose is, think "Wonder Woman" stance or the type of poses other superheroes might do. I find they do wonders for my confidence, especially on big days with exams or interviews. Create a plan for the day- Whether you have swimming practice or a lecture, creating a rough or detailed plan can help you maximise time as well as ensure that you create a good balance

My go-to study soundtracks-

The Theory of Everything [Johann Johannsonn]- this is by far my favourite music to work to. Dark Academia vibes and all-round stunning pieces of music.

Hidden Figures [Hans Zimmer]- This is a beautiful film following three amazing African-American women who worked for NASA during the space race. A wonderful and empowering film with an equally inspiring soundtrack.

The Duchess [Rachel Portman]- A wonderful soundtrack I was lucky enough to study at A-Level. Portman is a brilliant female composer and I would definitely recommened her other works too. (Trigger warning- this film contains depictions of rape and domestic violence. Please take caution when viewing and research the triggers in this film further before choosing to watch.) Finally, something to get you hyped up in the morning-

Perfect Day- Chris Lord Alge Mix, Hoku There is a reason this one may be familiar. If you are a fan of Legally Blonde then you will certainly recognise this as its iconic opening song. This is a must have as a law student.

That's all from me for now, have a good day and I'll see you soon!

Yours faithfully, Her Honorable Madame Justice x