Any autodidacts in here? Tell me your experiences in self teaching...

What general principles have you grasped?

I already learned numerical analysis in my program. I don't know what linear programming is but I learned how to program in my program as well. I'm also doing a research project that has me programming in matlab. I'm learning these subjects because I enjoy it.

ohh thats adequate analysis for dynamical systems.
that's cool then, carry on.

linear programming means linear optimization. that is, the study of the simplex method, which invariably leads to the study of convex optimization problems. it's usually called "Operations Research" or "Linear Optimization" or something like that

OP here, what math do I need to know to study real analysis? Also what do I need to know for differential geometry?

Yes the definitions right off the bat like Liaponuv convergence and whatnot were very much in the range of Analysis. I understand your concern.

nothing for real analysis, it's actually a good subject to be your first. I recommend Terence Tao's Analysis 1, which includes an introduction to natural numbers, set theory, and the construction of rationals and reals. it's very didactic for someone just starting to get into math.

for differential geometry you need a semester / year of real analysis and a good foundation of linear algebra. for example, books Analysis 1 and 2 of Tao and Hoffman&Kunze for linear algebra. it's good if you know some algebra by then too.

Righto. I thought about that for grad school. Really I'm split between something in combinatorics or something in dynamical systems leaning more towards dynamical systems (either math biology or control theory probably). What do convex optimization problems entail?

For real Analysis you really only need basic logic and math knowledge like what a proof by contradiction is and how to do basic algebra. I know less about differential geometry but from talking with a prof before taking the course, it seems like you need linear algebra and calculus. At least the way he's doing it, it's a continuation from calc for the most part (hopefully not in a shitty way).

This fellow is not me , he is right about the dinosaurs though. I am interested in ecology, evolutionary biology, nutrition, philosophy, non-technical chaos theory and complexity science, history, psychology, sociology, religion, warfare and a little bit of neuroscience and linguistics.

So while I understand certain things, it is mainly a kind of encyclopedia knowledge. Practical knowledge I have only in terms of what I eat.

I am thinking of doing courses in statistics. But maybe when I get bored I will download some textbooks and give it a try myself. But due to a lot of reading I have developed concentration problems.

I also have developed a habit of selective reading, often I read fast and seek out new information, instead of critical slow reading.

youtube.com/watch?v=McLq1hEq3UY&list=PL3940DD956CDF0622

>non-technical chaos theory and complexity science

fucking kek
it really sounds like you think you're learning many things, but in reality you aren't learning shit. consider putting some actual work into learning anything.

Sweet thanks!

Depth is important my friend. Don't get too caught up on learning "as much as you can" while you're actually sacrificing any sort of deep appreciation for anything.

I graduated with a math degree several years ago and haven't used any of it since and have since forgotten most of it. This summer I started reviewing Abstract Algebra and picked up on Category theory. I found that even though I forgot a lot of math or never learned some of what I'm reviewing now that I'm picking it up much more quickly than when I did as a student.

I determined I want to go back to school and get a PhD after working an office job. I want to get a PhD in CS, but found I don't care about a lot of things CS'ers do and instead found myself more interested in pure math.

I'm hoping to find connections between pure math and CS in algebra.

But anyway, to answer your question OP... yes I learn MUCH more through self-studies than inside a classroom.

Your critique is fine. Note though, I am more interested in the implications of things like chaos theory and complexity science. I do not claim to really learn it.

If the book or paper is deep itself it will work. Philosophy is a problem since it requires critical reading but because it doesn't use much examples from other fields I get easily bored.

what implications are you interested in, exactly?

well my notation sucks so ill try to express broad patterns im seeing like an retard

I broadly get the relationship of electricity and magnetism, and space time relativity.

I have a fuzzy working understanding about linear/scalar theory and its relation with first/second order shit ie
>photons : EM : : gravitons : time/space : : first order/x^1 : second order x^2 (or is it x^x)

I get what something being quantized means and plank values, and somewhat suspect how eigenvalues relate to sweetspots FUCK i have trouble explaining without solid maths
tldr course graining enables geodesic/eigenvalue acceptable accuracy because we cant detect/dont reasonably need to care about smaller variations in the same way that newtonian movement laws work fine for most things but are unequivically false representaions of reality (that is, a non—coursegrained reality if such a thing isnt strictly virtual)

This gets into metalogic ahit.that id love to dive.into but cant in good conscience without really understanding mathematecally all the other shit first

I dont subscribe to spooky actions and have checked out many specific thing like entaglement, i get how it can be used as a cypher generator and its non magical .

Regarding QM genarally, i would consider anything in existance as an observer (unlikely im sure but this is an.example of how/where i need more knowledge to understand heavily abstracted principles without breaking down and going awry)

This is a reasonable depiction of my more general inquiries but i regularly get caught up in other things (last night was casimir effect) at my interest/will. What i really need is to set my foundation straight, then autodidact specifics til i pass out

Something along the lines of what Yaneer Bar Yam and Nassim Taleb have been saying. They state that increased complexity needs more decentralization decision making.

And so now I am studying ecology, often within nature conservation you see policies with unpredictable side effects. I want to see what those sciences say about that.

From what I've gathered so far we can hardly predict stuff but we can somewhat make it controllable by making small changes to the system instead of large ones.

A lot of money in conservation in the Netherlands is wasted on questionable policies.

To add of my above comment. Think of this:

postgenetic.com/Postgenetic/Yaneer_Bar-Yam_-_Notes_on_Complexity.html

One can learn from those notes without knowing the actual technical science behind it no?

>One can learn from those notes without knowing the actual technical science behind it no?
no, you can just repeat his quotes to other people

Maybe you are right and that is what will happen.

I was familiar with algebraic topology (and all that goes with it), general relativity, quantum mechanics etc. before I started university, but I found it difficult to teach myself more modern stuff.
I was able to build up a nice broad range of mathematical and physical knowledge while at uni - lots undergrad and beginning graduate topics.

Teaching is good to show you a direction, but in the end you should study by yourself. Although at a certain point you should be able to go your own way.

youtube.com/watch?v=CelHevoZHuA

>unless someone knows what he's doing is helping you or giving you advice
This is actually more than most people have during university studies.

That's the whole point. Get lost, make mistakes and always try to make sense of the chaos you threw yourself in to. You'll have a far deeper understanding because you needed to figure it out yourself, you're forced to discuss and doubt your assumptions because you understand that there's so much more that could be potentially out of your current understanding.

I personally regret that I started so late. That I simply took the linear path that professors paved more for so long.

What do you mean by "more modern stuff"?

can we start a book list? My most engaging has been

>the quark and the jaguar, murray gell—mann

Just picked up qed from the thrift store today, 70 cent

Also nonsci, but hero with 1000 faces is maybe the most compelling nonfic ive read

Holy shet that looks good. Quark and jaguar gets into complex adaptive systems but is maybe more like a primer on the subject. Id read that before reading your link.

you could same the same thing about the math.

stop being an elitist stupid cock, thanks.

I'd like to point out that you didn't, "teach yourself quantum mechanics," if you hadn't yet learned linear algebra. Quantum mechanics is entirely built on linear algebra.

Care to recommend a calc book?

Spivak

no, you couldn't. when you learn math you're supposed to understand the concepts and be able to prove new things based on what you learned.

stop being a lazy imbecile and go study something worthwhile

apostol / spivak if you want tons of rigor. if you're just starting out something like ocw.mit.edu is better

>ocw.mit.org
fuck yes thanks, this is a great resource

Did Tesla drink coffee?

Are you me? I'm exactly the samr, down to the non critical reading. Maybe its a consequence of lack of dicipline because we learn wat we want to learn, and if intrest is lost we just stop.

For a second I've thought that's supposed to be a book title.

I'm currently teaching myself Russian, speaking with a native every now and then to make sure my pronunciation is correct but I control my own learning. I'm also self-teaching myself programming, starting from the basics. I am also teaching myself biology, chemistry, physics done through a program which I can manage my time, and learn however I want and they send the materials.

I do enjoy reading, and learning new things but they're so diverse and the extent of my reading into them varies considerable, so I wouldn't consider them topics that I was self-teaching. I like to keep my projects to a minimum so I don't have them left incomplete as my interests change. Persistence is key.

Topics which I enjoy are a bit like what said, although I don't find much interest in religion anymore since I hold it in especial contempt, and see it as a waste of time now. I do, however, enjoy languages and will teach myself German once I have finished with Russian.

I am sure there are more of us.
I want to, like says, exchange books. A new trick lately was using the goodreads "others like" book suggestions. It is better as Amazon.

But I would like to read more textbooks. Anthropology has my interest too, and I am starting into economics. Will probably have to ask redditors.

Math is certainly worthwhile and important. But I wouldn't say that it is the only thing that is worthwhile.

Also, economics wanting to be like math sorta turned it into shit.
Well my own idea is that religious thought lives on without religion. John Gray, whom I consider to be more of a thinker, likes to point out that contemporary thought has religious undertones.

I am now looking into the anthropology of myth and psychology to see if they have something to say about this. So far found little.

I enjoyed Big Gods by Ara Norenzayan, but there was already critique on his idea before I read it.

If you go to college, much of your learning will be autodidactism; you will just have some heat under your foot

I'm learning how to write poetry and enjoy philosophising in my spare time. I want to get into linguistics at some point, but that will have to wait.
At the moment I'm learning quantum mechanics with an eye to understanding neuroscience. I'm a bit confused about the quantisation of angular momentum, however. My book doesn't explain it; it is just introduced. Bit frustrating cos I reeealllyyy need to understand atomic and molecular orbitals.
After I get the chemistry down I want to get into computational neuroscience. Gonna learn logic properly.. haven't looked much further ahead than that.