Is it possible? I have been trying to read textbooks and doing the exercises, but it is not going very well.
I learned many kinds of mathematics with the help of Khan Academy.
Don't skip prerequisites. Do practice problems. Watch lectures.
>>1
What are you trying to learn, and how mathematically mature are you?
You put three lemons into the basket, then you take out one lemon. Now you have infinite lemons.
Yes it is possible. I'm balls deep in mathematics right now.
lol
Are there cases where learning higher order mathematics gave some interesting dividends? Maybe genuine consciousness expansion or wisdom or something of the sort?
>>8
That depends on what you mean by "higher order mathematics."
>>10
Disciplines of mathematics not usually covered in a STEM-grunt's education - more theoretical too, I suppose
I'm learning mathematics on university, and on this first semester we have four disciplines: Quantitative Geometry I, Introduction to Calculus, Laboratory of Mathematics I, and Foundations of Arithmetics.
It's a bit of a slow start but I'm hoping it will pick up later and I'll learn a lot.
Here is the curriculum: https://cagr.sistemas.ufsc.br/relatorios/curriculoCurso?curso=222
>>11
I don't read Portugese, but the last few semesters make this program looks more interesting than the one I'm about to complete.
I was hoping after I wrote >>4 OP would provide further details about their situation. As that did not occur, to speak in generalities, I would say making the leap to proof theoretical mathematics would be difficult without feedback (further if one was able to teach themselves these skills, there likely wouldn't have ever been much of a leap to make). Without feedback you're liable to mistakenly believe you are correct and fail to develop the thinking dispositions needed to prove effectively. I suspect there is a similar difficulty in transitioning to research mathematics. Beyond these two leaps it seems to me that mathematical progress is necessarily self directed.
you're liable to mistakenly believe you are correct
I think I have the opposite problem.
>>14
That's interesting, a much less serious issue I would imagine. If this is actually the case practice may be sufficient.
Anyone played with Mizar?
There's a ton of resources online. "The Organic Chemistry Tutor" has tons of math videos on YouTube. Used his videos to teach myself math all the way through college You can watch them through tube.i2p if you don't wanna watch through the clearnet.
>>16
No, but I did read The Little Prover and played with Coq.
>>17 thanks for the eepsite bro very bro of you bro
>>18
Were you using constructivist type theoretical foundations? I worry that this would put too much burden on students, even if it solves the mentioned issue.
* https://tutorial.math.lamar.edu/
* Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by George F. Simmons
>>20
I am not well versed in these things but Coq is based on something called the Calculus of Inductive Constructions, so probably yes. There are attempts to use it to teach proof heavy things, you can find papers about how successful these courses are, like these:
https://www.cis.upenn.edu/~bcpierce/papers/plcurriculum.pdf
https://dl.acm.org/doi/10.1145/3105726.3106184
https://cs.pomona.edu/~michael/papers/coqpl2019.pdf
I am trying to learn the maths needed for SICM.
Can spaced repetition systems like Anki be used for mathematics? Or who do you make sure you remember all those theorems and definitions?
>>24
Repetition is the key to learning. I learned using Khan Academy and it is easy to repeat the learning materials over and over again.
>>24
SRS is a stupid idea.
Without ranting at length about srs' flaws, mathematics is an organic discipline. You're balls deep into the industrialized production model if you thing bulk-memorizing definitions and theorems leads to any knowledge. Either get your shit straight or go find another discipline where mass memorization techniques are an asset, if there is any. Maybe law.
Without ranting at length about srs' flaws [...]
But please do! Not for mathematics, but would you disagree that it is an aid for, say, vocabulary memorization in early language learning, when you're trying to bootstrap a reasonable understanding of common vocabulary and idioms? Or the point was more just that applying mass memorization (with the aid of SRS or otherwise) to every discipline is a shit idea in general (but is acceptable in certain specific cases - and, transitively, so is SRS)?
bulk-memorizing definitions and theorems leads to any knowledge.
But it is not supposed to?? SRS are meant to aid you in retaining knowledge, it is to prevent forgetting. The number one golden rule of every SRS is that you are only supposed to commit things to memory that you already understand. They are just sophisticated reminders.
What techniques do you use to make sure you remember mathematics? What is your alternative?
Can spaced repetition systems like Anki be used for mathematics?
Sure.
[How] do you make sure you remember all those theorems and definitions?
Why memorize statements when it's the understanding that makes the math?
>>26
Mzybe I was a bit too harsh in my statements. I do get irritated when people talk about "memorizing theorems" and I also strongly dislike SRS
>>27
Well, I can see it being helpful in some cases, maybe for a beginner in languages, or for learning a new alphabet. But for languages especially I think SRS is more a problem than a solution. A language is also an organic entity, and to "learn" it by isolating words and playing a memory game is ineffective, and it doesn't really cement those words. Soon the srs session becomes a chore, one that pays little and unnecessarily taxes the brain. A far better solution is just reading. It's not hard to see why it's a much better option, in so many levels, than simply checking flashcards. Plenty of graded readers are available now for many languages.
>>28
They are just sophisticated reminders.
What techniques do you use to make sure you remember mathematics? What is your alternative?
Notebooks. I can only advocate for flashcard study if you have an exam tomorrow.
As with vocabulary in languages, how are you to know how relevant a theorem is going to turn out in the future? The time spent taxing your mid-term memory with flashcards is better spent reading on, where the theorems show up in their natural context, where you will either remember them or they can simply be checked from your notes; their repeated use will be exactly what SRS tries to emulate, refer to my note on the previous paragraph on reading.
I don't remember most trig identities, and they have seldom been relevant to me outside of a few applications in calculus (proofs where they are just a step in the process), but at least the laws of sines and cosines are so common that I simply remember them without ever actively comitting them to memory.
Programmers and mathematicians always say "I don't do arithmetic, that's the computer's job". The exact same principle applies to memory, and you don't even need a computer.
Keep in mind that this is in the context of the autodidactic student. Not everyone is lucky enough to be able to study mathematics full time. It must be nice to make use of your maths knowledge so frequently that you don't have time to forget anything, but it is not the reality for me.
In my experience with language learning, Anki does not feel like a chore and is not taxing at all. It is actually fun and takes less than 5 minutes a day. It will take longer if you have tons of cards to review, but it is pretty easy to manage the workload so that it never happens.
I guess everybody learns differently. I don't study mathematics "full time". I just don't think it makes any sense to "memorize theorems". But there's not point arguing why, if that's how you want to do it, go ahead. Why ask at all?
I asked because I am aware that it is frowned upon. Memorizing anything in mathematics other than maybe the multiplication tables is seen as a cardinal sin, and you are supposed to remember mathematics by doing lots of practice problems. But I am doing them and I still forget at an embarrassing rate. Maybe my brain is just defective. Maybe mathematics is just not for me and I would be better to do something that is more fitting my brain. But right now all the time and effort spent studying mathematics on my own feels like a huge waste as it produces absolutely no results.
doing something for the love of it is not a loss.
>>33
Have you tried spaced rather than massed practice? Have you considered memorizing and refining understanding such that any forgetfulness can be compensated with derivation (hinted at in >>29)? Do you make sufficient use of visualization in understanding? Do you attempt to understand things from multiple perspectives? Have you considered using the method of loci?
Maybe mathematics is just not for me and I would be better to do something that is more fitting my brain.
Very few people are perfectly oriented towards the study of mathematics, even most professional mathematicians have flaws they have overcome. You should not give up after finding a single flaw, especially given memory is one of the easiest of our fundamental capabilities to improve.
>>33
To be honest, mathematics can be very frustrating. I too struggle with it a lot more than I would be willing to admit. The best thing that has worked for me is as >>35 said, where I get different views of a single thing, from different sources and different subdisciplines (eg algebra, or analysis).
I might have failed to grant memorization it's value. Calculus is heavy on memorization: memorize the chain rule, memorize most derivatives, memorize binomial coefficients. But I just keep those things in a notebook. Maybe as you said, flashcards are just fancy notes.
I decided to ignore conventional wisdom and your warnings and started doing Anki cards. I think of it as an experiment on myself and I'll update you as it goes or when I give up on it.
I wonder where you get the time for doing anki flashcards. Most of my mathematics study time is gone on a handful of excercises each day.
>>37 good luck man! I would like to hear a report.
>>35
How do you space practice? Do you have a method to it?
Open rando wiki math article and click through definitions if you don’t know a word. It’s not that hard to get a gross overview, but actually doing something useful takes practice and time.
>>40
A simple way would be to use one of the super-memo heuristics to select a chapter, or section of a book and then use a random number generator to select a problem. Taking more advanced courses (building on the previous) and conducting systematic review of problems from previous courses also works.
https://www.dw.com/en/murderer-solves-ancient-math-problem-and-finds-his-mission/a-53895884
https://www.popularmechanics.com/science/a32502357/inmate-math-discovery-prison-continued-fractions/
https://interestingengineering.com/can-you-solve-this-prison-inmates-viral-math-riddle
https://www.popularmechanics.com/science/math/a35520893/havens-math-horizons-problem/
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy
https://www.youtube.com/watch?v=I4pQbo5MQOs
So if I want to get good at maths, I have to murder someone?
>>42
What if I want to work through all the exercises in a textbook? For example, I would read a chapter, do some exercises, read the next chapter, do some of its exercises, go back to the previous exercises, do some of them, etc. Is there some easy method for this that does not depend on having a teacher do the scheduling for me?
>>45 don't murder me. I beg of you don't murder me. Please don't murder me.
>>47
I might have a bit extra weight on myself but I can assure you I am nowhere near six hundred pounds of sin.
In what discipline are vector fields studied in a proof theoretical way? Topology?
>>49
Bumping for this.
>>49-50
I'm pretty certain now that this is covered in Topology, and Analysis on Manifolds. I was thinking I might study it sooner than later but my Calculus review is going slower than I would like (I have hope this situation will improve however), and I also now plan to review my two Analysis courses as well before continuing (probably using David Bressoud's books to keep things interesting).
Maybe you should try this company for help : http://justequations.org
Why is analytic geometry so much work? It is not even that complicated, just lots and lots of work.
>>37-39
I'm too lazy to write a proper report, but I am still doing the Anki cards. I review them every morning along with my other cards. I have been doing this with other cards for years consistently so this was not an issue. According to Anki, I spent 4 minutes a day on average reviewing the maths cards, for that amount of work I think the benefit is well worth it. I convert my notes in org-mode to Anki cards, it mostly involves copy-pasting LaTeX equations and selecting parts of them for "cloze deletion", it is not that much work. I add new cards slowly as I don't want the new cards to overwhelm me.
As for the results, it is nothing life changing, but I have to look up things a lot less and it helps me keep honest with myself.
Is it possible?
Sure it is, but you have to moderate yourself and know especially *what* to learn, not just the abstract subject. You might find a roadmap like this useful: https://github.com/TalalAlrawajfeh/mathematics-roadmap
Why's diff such cake? I just did two weeks worth in an afternoon, shit makes Escoffier look like Poincare praise be his holy name.
Just do it ~
https://www.youtube.com/watch?v=iSNsgj1OCLA
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A STUDY HAS SHOWN THAT SCIENCE HAS WHAT'S CALLED A REPRODUCIBILITY CRISIS WHERE MANY SCIENTIFIC STUDIES CAN'T BE REPLICATED."
BREWSTER ROCKIT : "CAN THE RESULTS OF THAT STUDY BE REPLICATED?"
DR. MEL : "UHH..."
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