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How I'm able to take notes in mathematics lectures using LaTeX and Vim (castel.dev)
703 points by tambourine_man 63 days ago | hide | past | web | favorite | 221 comments



As a feat in itself this is definitely very impressive, but I wonder if it's really worth anyone's time to spend precious lecture time with your mind fully occupied in the mechanical task of taking notes rather than actually absorbing and engaging with the content. Especially for an extremely content-dense subject like Mathematics, where you need all your concentration just to process what you are reading and follow along the logic.

There is absolutely no dearth of study material on the internet. It's one thing to take notes as part of your study process. There it helps solidify your understanding. But surely taking notes on the fly when you have been barely introduced to the subject isn't going to help with that.


> mechanical task of taking notes rather than actually absorbing and engaging with the content

The mechanical task of taking notes is one of the most important parts of actually absorbing the material. It is not an either-or. Hearing/seeing the information, processing it in a way that makes sense to you individually, and then mechanically writing it down in a legible manner is one of the main methods that your brain learns. It's one of the primary reasons that taking notes is important in the first place. This is referred to as the "encoding hypothesis" [1].

There are actually even studies [2] that show that tools that assist in more efficient note taking, such as taking notes via typing rather than by hand, are actually detrimental to absorbing information, as it makes it easier for you to effectively pass the information directly from your ears to your computer without actually doing the processing that is required when writing notes by hand. This is why many universities prefer (or even require) notes to be taken by hand, and disallow laptops in class.

1: https://www.sciencedirect.com/science/article/pii/0361476X78...

2: https://www.npr.org/2016/04/17/474525392/attention-students-...


Not that it detracts from your point, but I definitely benefited from notetaking on my computer in school. For an AP History class, I typed up—in outline style (I, II; A, B; 1, 2; a, b; etc)—all my notes on the required reading. At the end of the course, I had a few hundred pages of these notes all printed up.

I never had to go back and read any of them. Just the process of typing them up in the first place firmly fixed all the knowledge in my mind. When taking the final and AP test, I could see the notes I had taken in my mind.

Writing or typing didn’t make a difference. Just the rephrasing and condensing alone was enough. (Which, again, reënforces your point. I still had to consciously avoid “pass-thru” regurgitation)


> reënforces

What's it like working at the New Yorker?

(explanation: this is a joke based on the way nobody uses diaresis marks anymore for any word other than naive, except for the New Yorker style guide. https://www.newyorker.com/culture/culture-desk/the-curse-of-... )


Not only that but the common spelling is "reinforces", which doesn't need a diaeresis at all. It's like function_seven went very far out of the way to show that they know what a diaeresis is...


I’m not usually pretentious, but when it comes to the double-e, I lean in :)


History <> Math at all. I'm an electrical engineer (pretty good at math as that's all you do for 4 years in college), but can process a history lecture much much faster and easier. Outlines are great for History (I agree), but this isn't as easy for Math. A single equation can need more explanation than a novel.

Note that I'm not at all belittling the study of history...just trying to show the counter to the parent post isn't 100% relevant here IMO.


I was relating to the parent comment about writing v. typing, so I kinda lost the original point of the article.

Yeah, Math is a much different subject when it comes to notetaking and processing the information you learn. There are a few equations to memorize, but to really excel at the subject, you need to learn more why's than you do what's


I wonder if traditional memory techniques (e.g. method of loci [1]) would have long-term benefits over taking notes by hand?

According to this highly interesting HN thread, Alan Kay apparently doesn't take (much) notes [2]. I also found Warren Buffett's tip to focus on information that "doesn't expire or expires very slowly" an excellent rule of thumb for daily life. Obviously, with decades of books under their belts both of them are outstanding systems thinkers, so it must be true that they just don't need to take notes that much.

I'm a 30-something, but I like to trust my brain's tendency to forget more and more. Most of the stuff I don't remember probably wasn't relevant for my current mental models. If it's important, it sticks in one way or another. (I try to reinforce this by using the aformentioned method of loci, but I'm not as confident with this as I would like to be. It involves creating "sticky" images for the brain, and thus it always requires at least several seconds for me to "store" something that way.)

One probably won't be an A-level student with this approach, though -- but in trying to live a meaningful life, letting things (information) go often helps a lot. It's a great bullshit filter for everything.

1: https://en.wikipedia.org/wiki/Method_of_loci

2: https://news.ycombinator.com/item?id=11809285

3: https://fs.blog/2019/02/compounding-knowledge/


I wonder if traditional memory techniques (e.g. method of loci [1]) would have long-term benefits over taking notes by hand?

Mathematics already is a sort of hierarchical interconnected structure that allow you to easily remember everything, as long as you understand it. The understanding is the hard part, not remembering it. Mathematics is not a set of random facts that you have to memorize.


> There are actually even studies [2] that show that tools that assist in more efficient note taking, such as taking notes via typing rather than by hand, are actually detrimental to absorbing information, as it makes it easier for you to effectively pass the information directly from your ears to your computer without actually doing the processing that is required when writing notes by hand.

This might very well be anecdotal, but in my experience, note taking in class (by hand or on computer) was nearly always how you describe it here. Everyone was expected to copy out every word on the board, from 6 years old to ~20 years old. Maybe it works for some, but to me class was to some extent an exercise in mindless dactilography.


This depends heavily on the country's educational system.

I have gone through most of my middle-school and some high-school in Italy, and after that completed high-school in Moldova. Classes in Moldova were exactly how you described, and I hated it, while in Italy it was exactly the opposite.

Having the teacher explaining and expanding on the content in the course books while students take their own personalized notes is much more efficient and productive.


I definitely agree with this for mathematical notes. Writing LaTeX is so mechanically different from writing down actual mathematical expressions and proofs that I feel like it distracts more than it helps me absorb.

On the other hand for something like a psychology class where the material is mostly in English prose, then I feel like typing does help. Typing English is not so mechanically different than writing down English since each letter is still in a one-to-one correspondence.


I would disagree with you on the benefits of taking notes in higher maths. If I'm taking notes, I can barely follow what is going on in the lecture. If I don't take notes I can fully concentrate on the lecture and logic, but then I have nothing to study/reference. Teachers should provide notes so you don't have to do it yourself, especially if they're just writing off a sheet of paper. They're usually just worried that people then won't show up for class.

I'm sure history is maybe different where the note taking is probably easy enough and reinforces what you learned, but with math you're not exactly comprehending everything you write down at the same speed as human language. When you're in high school: "The storming of the Bastille happened in..." is different than scribbling down the Fundamental Theorem of Calculus and wondering WTH is on your paper.


I often wonder if those studies about "copying the entire lecture by taking notes" are an example of the Simpson Paradox. Breaking them down to sub-groups of students and their experience would surely reveal another picture. At least some students can't benefit from this, as my experience mirrors yours. Courses that required me to write everything down were those where I couldn't remember anything at the end. I just can't write and listen / comprehend at the same time.


Agreed. Either lecture or tell me to read a chapter. I can't multi-task that well with learning something that detailed.


Agreed, sometimes just copying the formula takes very long and you don't want to be making mistakes. Also, sometimes wording for explanation takes me long enough that I miss a few sentences from my lecturer.

The best I think is still to come prepared for class by having read the required readings before hand.


> The mechanical task of taking notes is one of the most important parts of actually absorbing the material. It is not an either-or. Hearing/seeing the information, processing it in a way that makes sense to you individually, and then mechanically writing it down in a legible manner is one of the main methods that your brain learns. It's one of the primary reasons that taking notes is important in the first place. This is referred to as the "encoding hypothesis" [1].

There's almost certainly an advantage to learning to think about math using a publishable symbol set like LaTeX.

We learn by reinforcement; with feedback loops that may take until weeks later in a typical university course.

> There are actually even studies [2] that show that tools that assist in more efficient note taking, such as taking notes via typing rather than by hand, are actually detrimental to absorbing information, as it makes it easier for you to effectively pass the information directly from your ears to your computer without actually doing the processing that is required when writing notes by hand.

Handwriting notes is impractical for some people due to e.g. injury and illegibility.

The linked study regarding retention and handwritten versus typed notes has been debunked with references that are referenced elsewhere in comments on this post. There have been a few studies with insufficient controls (lack of randomization, for one) which have been widely repeated by educators who want to be given attention.

Doodling has been shown to increase information retention. Maybe doodling as a control really would be appropriate.

Banning laptops from lectures is not respectful of students with injury and illegible handwriting. Asking people to put their phones on silent (so they can still make and take emergency calls) and refrain from distracting other students with irrelevant content on their computers is reasonable and considerate.

(What a cool approach to math note-taking. I feel a bit inferior because I haven't committed to learning that valuable, helpful skill and so that's stupid and you're just wasting your time because that's not even necessary when all you need to do is retain the information you've paid for for the next few months at most. If course, once you get on the job, you'll never always be using that tool and e.g. latex2sympy to actually apply that theory to solving a problem that people are willing to pay for. So, thanks for the tips and kudos, idiot)


Glad to see this at the top, agree 100%. I’m definitely going to copy some of OP’s setting and snippets, but not for real time use during a lecture.

A textbook is an infinitely better reference than any notes one could take in class. Read the damn book. Lecture time should be for asking questions when you have a freaking live expert professor literally presenting the material to you. Ask all the small, nuanced questions that you can think of in the moment, which you can’t find answers to easily online or in the book.

Not to downplay the efficient workflow here, but there is zero chance that this person’s notes are actually better than a real textbook.


That's fine amd dandy from a US perspective, but many European universities are different. I don't know about this guy's exact class, but some (many?) undergrad classes are 500 people in a lecture hall with the professor orating, no textbook, and the content on the exam is pretty much whatever was covered during the lectures. So accurate note taking is very important because those notes essentially are your textbook. Hence the small business of students assembling high quality lecture notes and selling them to people who have't been to class (much).


Undergrad maths classes with 500 people? That must be one hell of a course. Either way, all undergrad classes I attended in Germany were based on some kind of textbook (usually (co-)authored by the lecturer, and occasionally self-published, i.e. as photocopies of a set of more or less neatly typewritten pages, with equations scrawled in by hand).


At that point smuggling an audio recorder to the class might lead a better reproduction of the material.


You'd still have to transcribe them, and you'd miss what's on the blackboard.


onenote can transcribe in real time and save the audio recording as well... you can even save notes at particular timestamps so you can mark something you didn't understand for later.

all of these things are solved problems


Note: Europe: the continent where most of the lectures are still not in English. And where are many languages. Not to mention the accents and the dialects in the same non-English language.

I also doubt you are aware how seriously distorted the result of the speech to text conversion would be for a non-professional recording of any non-trivial lecture given in English (e.g. domain specific terms).


yes it was totally my mistake to assume a comment on an english speaking american site would be in the context of american english. also one note picks up domain specific terms just fine in STEM fields...

also remember how i said it records audio and logs in real time? yeah, just listen back to it and correct the one or two words it garbles. works just fine. people want to complain not use the solutions that exist. i'm sure writing in latex is trivial and doesn't have you googling issues every 2 hours lol


audio recording != text book ;) It still would need significant time to transcript, and then OPs workflow comes back into picture ...


The lectures will contain content from text books, even if they aren't referenced. Reading around the topic will give a better understanding and better results.


It does not make too much sense to compare textbooks and class notes, specially when you get to higher level classes where the textbooks are reference textbooks, hardly readable by someone who is not already familiar with the material.

Your study notes will contain parts of the textbook, of course, but also explanations that are not in the book, maybe examples that you find useful and that might not be in the book, counterexamples, doubts, schematics... No textbook will have 100% of the contents you need to study.


>A textbook is an infinitely better reference than any notes one could take in class.

but...

>Ask all the small, nuanced questions that you can think of in the moment, which you can’t find answers to easily online or in the book.

and then what, forget them by the time you go back to the book? Why was the book so good again if it doesn't answer all the questions? It makes more sense to record the answer to those useful questions you ask, maybe in the form of some notes.


Not everybody learns in the same way. For myself, I get essentially nothing out of just sitting in a lecture hall listening to a professor drone on. It literally just goes in one ear and out the other. The only way I am able to learn is by reading and by working through the material on my own, either from notes taken in class or (preferably) a textbook.

So I can appreciate what OP has done here. I took notes in LaTeX for most of my undergraduate math courses (and some graduate ones), and I found it to be a fairly valuable exercise.


But surely taking notes on the fly when you have been barely introduced to the subject isn't going to help with that.

I found that taking structured, detailed notes in lectures forced me to pay close attention & work constantly to keep up with the lecturer. For the courses I did that for, it felt like it was equivalent to doing an entire extra revision session with the lecture material for me - I had to do much less work to go over the material after the lecture in order to make sure I understood it, so it was a far more efficient use of my time that just 'attending' the lectures and then doing revision work afterwards.

Some people can maintain that level of connection with the lecture without taking notes of course, but that’s what worked for me.


I found I couldn’t take notes fast enough. But if learning online, pausing the video and taking notes is very effective for me.


> I found I couldn’t take notes fast enough.

Me neither. However, what I do once in a while is after I've sat through a tutorial (in person or video) I recall and make notes. It helps me immensely to a) Structure my thoughts b) Recall the actual content which reinforces it in my memory.

As a student, I always found that writing notes/answers on a topic/question made me understand the concept that much better as well as connect them to form a larger picture (e.g., connect concepts in math and physics).


It must be admitted that I got a lot quicker at taking notes in a very short time!


Learning is learning. He has clearly learnt how to do something. And do it well.

The entire article is very clear and well thought out. To me it signals a disciplined and methodical mind, that learns from doing. And we are lucky it's willing to share.


Lucky indeed. Who hasn't dreamt of being a stenographer for Math lectures in grad school, using the hardest tools for the job, including the most obscure window manager known to Linux. I mean, if one don't kill a week getting bspm to work on their laptop, is lecture note taking even worth it?


You don't need to demean the effort of anyone to put focus on how to do something better.


I'm not demeaning anyone. Sometimes, we can all look at the things we deify, including obscurity and complexity, and laugh a bit at ourselves. Tell me with a straight face that this article isn't quintessential fodder for the show "Silicon Valley".

I fully agree with your parent comment that this article is a demonstration of multiple positive traits of the author, I respect him/her a lot. But also, I cannot help but laugh a bit at myself and the others who up-voted the article. That in no way diminishes my respect for anybody, including the author.

FYI - I've relied on LaTex for submitting to multiple peer reviewed journals, my thesis and my thesis defense presentation (LaTex Beamer), so I fully understand and appreciate the skill level of the author here

Cheers!


i bet he looks really cool doing it though+whoever convinces him to share his notes is on easy street


I did this in a Biochemistry course minus the Vim. It is definitely counterproductive and I started to do better once I switched back to traditional notes.


OP describes exactly how he abstracts away the mechanical task of writing LaTeX and can focus on the content. I did a similar thing in my classes and after a little bit of practice and tool adjustment you just don't think about LaTeX more than you think what pen to use or how to highlight something when handwriting.

And precisely because math is so content-dense, having your notes is important, as they will be organized in a similar way to how the content is organized in your mind. Yeah, there is a lot of study material but most of the time, unless the class follows a textbook literally, you'll want your own set of notes with only the class contents, and you'll want to organize that in a way that is easy for you to understand.


The only alternative I see is getting the lecture notes from your professor. I had one (math) lecturer who used to make his notes on the fly with his convertible Thinkpad (x230t or similar) and shared those notes with us afterward. In addition, he also had a clean script. That combination was awesome as you could focus on what he was explaining (or take additional notes if necessary).


I remember things much better if I write them down during a lecture, rather than just listen. I seldom actually used my notes afterwards beyond a quick recap, except in a few classes where the lecturer had prepared the lecture very well. Still, just writing it down allowed me to remember better by orders of magnitude.


Exactly. Any decent lecturer is going to give you printed lecture material with this kind of detail already, your written notes are exactly that: notes on the material of important information and extras to help recollection.


I live-TeXed notes for some of my math classes and it was absolutely a great idea.


I don't agree with this. Perhaps it's possible for someone with exceptional LaTeX and vim knowledge, but even after using both for 20 years I wouldn't do this.

The point of the lecture is to assimilate structure and basic understanding, not to produce a neat set of notes instantly. To take notes to this detail means you're putting more time into the note taking than the work.

Use a pen and paper. Write down structure as it happens. Write down things you understand, short hand. Write down things you don't for later review. After 2 hour long linear circuits lectures I regularly waltzed off with a couple of pages of loose A4 for review. A lot of the time, our lecturers would give us a copy of the OHP stack if we asked them as well.

Write your notes up at the end of the day with reference material at hand and no compromises. You can structure, extrapolate and transform things into your own understandable language then.


People are different, the processes in their minds goes different ways. People develops different styles of learning and then they adopt to that styles and adopt styles for themselves. So it is pointless to agree or disagree.

I personally like this idea of vim+LaTeX. It is close to what I did while studying math, though I write notes down with pen and paper. Mostly I wrote down them once and read them once before exam. I remember some issues with this approach, but the one I remember most was due to incomplete recording, not due to "I didn't managed to understand this mess of greek letters while listening a lecture".

I remember some problems due to inability to understand, it was Galua theory, but I solved them by reading books. I had read three different authors on topic, and I think it was the only way, I think that any style of keeping records would not help more then mine.

And I hate to write greek letters by hand. There is one names xi, I never managed to figure out how to write it, so xi looked in my recordings as some messy knot of lines. All my xi's was different, but there was a bright side of this: xi was the only one, that was so messy, so I could understand that it is xi when I saw this mess. With LaTex xi looks nice and clear.


On the point of writing greek letters and symbols I've taken to practicing a Greek letter possibly hundreds of times when I first encounter it. Just write it, write it, and write it again.

At first it's just to understand how my hand has to move to write it efficiently, then I move on to attempting to write precisely. Finally, I write it over and over pushing myself to get it to the speed at which it will not interrupt the rest of the notes when it happens. This approach has be wildly successful for me and while it does take some time it is always time well spent.

Recently, I ran into § and just had to figure it out. Honestly, I was out of my depth in the Wikipedia article and I don't even know what it represents. It was fun, though.


> I ran into §

This is the symbol for section, it means that a new section is starting, or it may be a reference to a section number.


Research shows handwritten notes to generally be far superior to typed notes for memory and retention

https://www.scientificamerican.com/article/a-learning-secret...

So while there are certainly some people who are better with digital notes it is absolutely not " pointless to agree or disagree."


Do they control for handwriting? It's hard to learn from handwritten notes if your handwriting is illegible, especially at speed.


it's the act of writing the notes physically which is helpful


I wholeheartedly agree on the "People are different" part. I for one am never able to process information and write it down. It's always either thinking about the content or "copying down curvy lines that purposely mean something". The worst lectures for me were when the teacher / professor forced us to copy down the lectures, even though they had perfect lecture preparations they could have just uploaded online. Or teachers that gave us the homework of copying down these pages of vocabularies because "only then you will remember them".

If you remember only one thing about teaching: There are multitudes of learning styles and only a minority of students will have similar ones than you. Probably, the (as I imagine) magical experience of remembering after writing something down is so intense that it is hard to let that feeling go and let others have their different styles.

Edit: Xi was the worst for me, too. I think the standard letter form as portrayed in print does not lend itself to quick handwriting. Also, if I compare how much time is spend in elementary school teaching how to efficiently write the Latin alphabet to how there is no introduction in university regarding the Greek alphabet (except if you are lucky a complete table with their pronunciation), it is almost ludicrous. Yes, we are all adults at that point in time, but for some reason I still didn't get the idea to google for "how to write greek letters efficiently" back then [1][2].

[1] https://duckduckgo.com/?q=how+to+write+greek+letters+efficie...

[2] https://www.foundalis.com/lan/hw/grkhandw.htm


I agree that Greek might not be the best for people with a different linguistic background. By the way, did you mean Galois Theory? If it's OK to ask, what other languages do you speak mainly besides English?


Yes, I meant Galois Theory. I speak russian, and 'Galua' just letter-per-letter transcription from russian spelling.


If you read that out loud as if it were Spanish, it would sound like the original French pronunciation for Galois. So, good job! :-)


Russian spelling is mostly phonetic. It tries to keep the idea of spelling that word is a program for sound making machine, which knows nothing about pronunciation of a particular word, just follow simple rules for interpreting letters.

As I understand, Spanish is much like this, it keeps spelling simple. If so, then there are nothing surprising that transliteration from cyrillic into latin make sense from Spanish point of view.


Ah, cool. Funny thing, in Chinese Einstein uses the character for "love" [ai] also because it's a phonetic approximation.


>Write your notes up at the end of the day with reference material at hand and no compromises. You can structure, extrapolate and transform things into your own understandable language then.

As if the average modern day student is going to do this.

I did what OP did and it worked for me because instead of dozing off I was focused on keeping up with the lecturer. It worked for me personally.

More on topic, the standard vim-latex bindings are so incredible, for example "`a" (backtick + a) expands to "alpha", "`b" (backtick + b) expands to beta, then we also have "`/" (backtick + slash) which expands to "\frac{<++>}{<++>}" where "<++>" are called bullet points that you can jump to using <C-j>.

I too, was able to write LaTeX notes in class, it was awesome.


> As if the average modern day student is going to do this.

This is the problem.

Yes I dozed off in lectures too but only when I knew the material already (preparation - another modern day student failing!) or had a heavy night or a starchy breakfast.

Like I said I'm fairly experienced with LaTeX. I've used it for technical documentation for 20 years.

Picking an example, I did an EE degree. I sat there and watched a hundred students scribbling out a lecturer's slide with basic function laplace transforms in it. The lecturer moved on leaving 99 people with half a table of transforms. Me, I'm sitting there with <<laplace basic transform table>>. I took this home, reviewed notes and added a reference to my textbook which contained it, added a sticky note to the book page sticking out of the side. Then I spent some time playing with them and trying them out and building valuable real understanding.

Now I've completely forgotten what you even use a laplace transform for 20 years later but I can find out in 10 minutes with that textbook and my notes which I still have in a concise manor.


If I'd known to do that, I might have made my way through my EE degree instead of dropping out to the (easier) CS degree. 90% of the time I got about 40-50% of the way through transcribing the stuff on the board before the lecturer erased it because 'fuck you, you had 30 seconds'


Ditto, EE too. I bought a copy of Abramowitz and Stegun just for the great table of Laplace Transforms.

If I were a professor, I’d ban all electronics from the room. All the decent professors handed out copies of the notes anyway, or wrote them in real-time on an overhead projector, for easy copying later.


Ridiculous. You're forcing your own preferences and quirks onto a class-full of students. They are adults, they can make their own decisions and do what suits them best. As we can see from this very article what works for some does not match what works for you.


> They are adults, they can make their own decisions and do what suits them best

They can, but do they ?

Given my experience as a student in the US long time ago, it rarely seemed so. I am all for treating them as adults as long as its not disturbing/distracting others in the class.


Then you'd be a terrible professor, because that attitude is not pro-learning. Students take their own notes because writing is an aid to memory. Students take electronic notes because those notes are easier to organise, edit, and search through. Many "decent" professors will not hand out notes, and the writings they put on the projector might be scanned and put online, but those writings have none of the benefits of actually typeset notes. Moreover, since you would ban electronics, students couldn't access those scans in a later lecture anyways.


You know people used to hand-write notes, right?

The act of writing them actually helps one to remember -- I never went back and organized, edited, or searched through notes I took, because I remembered most of the material, and what I didn't was in the book.


Well, I gave up entirely on taking notes in high-school because laptops weren't allowed, and I can barely read my handwriting if I'm quickly taking notes. Whereas in uni I actually used my notes, and have even referred to them years later since they're actually readable and useful. Granted, I would have them 1/2 typed while reading the material before lecture and did a final-draft cleanup after lecture, but typed notes were far more helpful than handwritten notes.

Assuming that everyone learns the same way you do is just false. Some people really like mind maps, I don't find them personally helpful but I don't tell people it's a useless technique or that they're wrong. If a student can't be trusted to have a laptop without spending the lecture browsing Facebook, then why should the lecturer care? That student is only hurting their own academic performance, it shouldn't stop others from being able to learn in a manner that benefits themselves.


Have you ever sat in the back row of a lecture hall and watched what the students are doing on their laptops?


What does that have to do with anything?


A lot.

Laptops are generally disruptive to the entire class, and (anecdotally, but I’ve done a lot of higher learning) almost all of their use is not for note taking or anything related to the class.

So why not ban them? Many professors do.


>So why not ban them?

Because some students are using them to take notes, and banning electronics harms the learning of those students.


They are distracting other students using a computer. Why do you want to ban using a computer but keep permitting distracting other students?


So when you get to the real world and everyone in the meeting is on their laptop? ...


Doesn't work that way in a lot of the real world.


>You know people used to hand-write notes, right?

They also used to write cuneiform :p What's your point here?

>The act of writing them actually helps one to remember

Source for this, in comparison to typing?


It’s been widely reported for several years. Here’s the first link I found.

www.medicaldaily.com/why-using-pen-and-paper-not-laptops-boosts-memory-writing-notes-helps-recall-concepts-ability-268770%3famp=1



> >Write your notes up at the end of the day with reference material at hand and no compromises. You can structure, extrapolate and transform things into your own understandable language then.

> As if the average modern day student is going to do this.

Why wouldn't modern day students do this? It's one of the best way to study that I ever used.


I can understand why people don't do it. We weren't taught how to learn at school or college and when we turned up at university we were expected to know how. It took me a semester of alcohol fuelled hedonism, followed by screwing up, panic, then introspection to work it all out.

I imagine a lot of that could be avoided with some assistance from the education sector along the way.

My eldest wants to be a doctor so I've tried to share as much of my experience with her on how to learn so she doesn't have to make my mistakes as they still don't teach them any of this today, at least in the UK.


This is exactly what I have observed among today's students also, and I am desperately trying to help! Smart students actually get hit harder because they cruise through high school and hit the wall in college. Then they may have a seminar or something on how to take notes and basic time-management (usually delivered through a first-year experience program or something similar), but if they want a real understanding of how to learn they have to get it on their own.


I'm not saying they shouldn't, I'm saying that they are not going to do it, the majority at least. Most people take the path of least resistance, if your path of least resistance is retyping your notes consistently every class more power to you, you are not an average student then. I never typed up my notes, I made flashcards based off them which worked for me, but OK. I'm just saying that if you think the average student diligently types up his notes after every class you're sorely mistaken.


This method of writing notes still seems like a downgrade from using a pen - my optimal way of taking notes would be with a pen, but with some sort of handwriting recognition on a tablet so it could immediately translate it to prose + LaTeX mathematics. Something that does both nicely seems difficult to find though...


> As if the average modern day student is going to do this.

If that is the case, then I fear little from the upcoming students chomping at my old ankles in the jobs market!

Transcribing my lecture scribbles to neater notes later in the day (or sometimes later in the week depending on scheduling) was important in solidifying the knowledge or, more importantly, realising that something hadn't twigged in my head as I thought it had (giving me chance to look up the matter and/or ask the lecturer for clarification next time, instead of being surprised by not understanding when new information was built on that part or it came up in an exam).


My handwriting is terrible,and worse when it comes writing down formulas, this could be a useful way of writing up notes a lot quicker. Also useful for cheat sheets or summarising notes


My handwriting is also awful, but what the parent suggested isn't at all incompatible with taking typed notes: I would type a first draft while reading the material before lecture, add during the lecture, then finish the final draft afterwards. I regret I didn't learn this method of note-taking earlier, and it works for both hand-written and typed. It also doesn't take that much time, but the last step of reviewing and cleanup is critical for actually cementing my understanding of the material.

Another possible method would be taking written notes during lectures, then typesetting them afterwards. However, I found it was preferable to revise my notes soon after the lecture, at least 1-2 days following, while my memory was still fresh.


I have no objection to taking quick notes in lectures using electronic means instead of pen+paper (though the latter would still be my preference).

It was the implication that people don't have and won't make time to review, tidy, and, where relevant, expand upon or question those notes afterwards, that I was responding to.


It is scientifically proven that handwriting is better for your memory because it forces you to process the material more than note taking on a laptop.

https://www.google.com/url?q=https://linguistics.ucla.edu/pe...


That's... not true, and not supported by the study you linked.

In the study, there was no measured difference in memory between the two note taking styles; the groups' factual scores were not significantly different in any of the tests.

Where things vary is the non-memory questions: are the notes helping you understand and apply the material better, and how advantageous are they to your studying?

In both of those categories, handwritten notes win out.

Finally, there is no "because"; the authors can only speculate. I am not aware of any studies that can actually purport to say why handwritten notes are better.


I find handwritten notes far worse. For me, I'd prefer a full set of notes to a be provided if feasible (a lecture, etc.) but that doesn't work in everyday conversational meetings. I instead prefer typing notes because it requires little cognative load to accomplish and is quite efficient.

The point of notes for me is to refresh my memory after the fact because my human memory isn't reliable enough. They are especially useful for capturing finer quantified details.

During a typical lecture or discussion/meeting, I find it far more useful focus most my cognitative abilities on what's being described/presented to me and only commit critical information to memory. The majority of my energy spent is processing the language and concepts discussed, linking language and concepts togethe, connecting those concepts with previous experiences/knowledge, and generating new ideas/relationships... all in what seems a fairly random order as needed. This allows you to ask informed questions when I see things missing in the conceptual structure I have that I might otherwise miss later and have no means to extract that information because my notes may not have the relationship or fact I need.

Later on when reviewing the information, I utilize the critical conceptual structure/framework I created about the discussion to reason through it. If there are pieces of information missing, it's pretty obvious and I can refer to my notes. If I missed the concept I at least have a second shot at recovering the idea from highly detailed and clear to read notes I took.

I could not imagine trying to write LaTeX on the fly during a in depth mathematics discussion, I'd have far too much focus on syntax formulating correct notation structures than the concept at hand when it's far easier to translate using a camera phone or handwriting.


I want to highlight that part:

"Participants using laptops are more likely to take lengthier transcription-like notes with greater verbatim overlap with the lecture"

In other words, there is nothing intrinsically wrong with taking notes on a laptop if you don't copy everything verbatim. If you force yourself to process the material you should have no problem.


But they noticed that most do not go back to their notes as much as they should so a general advice, while typing is easier hand-written helps you learn and retain better using less exposure.

Assuming a class isn't already being recorded (many/most at my university were), the best solution is probably to record audio on your phone and take hand written notes. Then go back and transcribe the hand written notes while referring to the audio in to the computer.


Well, I started taking LaTeX notes in-class specifically because I couldn't refer back to handwritten notes later; my handwriting is atrocious at the best of times and when taking quick notes it was just unreadable. However, I did have to keep a notebook for diagrams as well, and my typed notes always needed cleanup afterwards. My eventual process was to type up a first draft before class while reading the material, supplement them with lecture material, then finish them after class. This won't work for everyone, but after I started doing this I would actually use my notes, whereas before I wouldn't, since I could actually read the darn things. Plus, I can type ~2.5 times faster than I can write.


If you're going to do that, your best bet is probably to take handwritten notes on a tablet while recording using an app that syncs the two.

I sometimes do this; it's also nice that I can snap a photo of a slide with the tablet and insert it into the notes.

TBH, I mostly type notes, in part because my handwriting is really bad and, if I'm going to write something up about an event cutting and pasting is easier. OTOH, I sometimes prefer to have fairly cursory notes knowing that I can always go back to exactly what was said if I need/want to.


Totally agree. Also handwriting is better for your handwriting! About ten years into my IT career my skills devolved into chicken scratch and I can't even read notes I wrote recently now. I need to do something about that.


As another reply mentioned, it seems like hand-written notes are good because the limitations on writing speed force you to synthesize information as it is relayed to you.

Outside of mathematical lectures, I find writing notes in something like notepad++ more fruitful. I can attempt mirror the structure of the speakers' argument using tabs/indentations, and quickly reformat the document as the logical structure becomes clearer.


I've known people who liked using mindmaps for this purpose. Personally, I could never get into them but big fans exist.


Agreed. Paper and pen is hard to beat when it comes to equations and improvising. Hats off to anyone with that level of Vim & LaTex skill though. Now that I'm in the workforce I use OneNote, Notepad, and Confluence for notes and documentation for the most part, but I still use a lot of pen and paper as well... especially when doing complex coding where I need to map out how all the data structures work before hand.


Run away from OneNote quickly. Microsoft are not shipping OneNote desktop any more, preferring the horrid UWP app.

Another vote for paper or neutral formats here. They persist longer than vendor whims!

Case in point I wrote a lot of my work up on TechWriter on an Acorn RiscPC. Where are we now with that. Hmm...


Thanks for the tip. OneNote is one of a handful of things Microsoft has done that I like. Is it really not on Windows10? I haven't upgraded from 7 yet.


It does ship with windows 10 but it's a UWP app and it's rubbish. It's missing on Office 2019. See: https://support.office.com/en-gb/article/onenote-2016-is-mis...

This one totally caught me by surprise for ref when I upgraded, perhaps foolishly. I installed OneNote 2016 and am sticking my fingers in my ears until I have some time to deal with it.


That's awful. I probably have hundreds of pages of notes in this thing. Time to mass PDF export.


I have been using it for about 15 years so am in the same situation. I haven't found a suitable alternative yet.

Annoyingly they're going to EOL the cloud connectivity for it in 2023 and then the product in 2025. I've taken all my notebooks offline and will deal with it at some point, probably in 2025 :D


I've been waiting and looking for a replacement for a long time, but it doesn't seem like one will appear unless I make it myself.


I think the moral of the story is, do not depend on proprietary software ;)


I totally agree. One reason I haven't moved yet is I haven't found something I would consider using that isn't proprietary.


Are you referring to EOL for desktop version or OneNote entirely?


EOL for old desktop version. There's a new terribly crippled UWP desktop version and the cloud based web app available going forwards. They are absolutely terrible bits of software compared to the old desktop version.


Do they not understand customers at all? Except for high performance simulations, I will never use the cloud. Maybe they realize that and want to force cloud adoption?


I think they understand that if you give customers no option they will be forced to comply with their wishes and act as a monthly revenue stream.

However they also misunderstand people's reluctance to put all your eggs in a large basket out of your control that disappears in a puff of smoke if you stop paying for it plus their ability to want to avoid paying a monthly fee.

At some point it'll backfire.


I'm hopeful that the "new" OneNote will follow the same type of iterative dev/release scheme that VSCode has used so well, but for now it is pretty barebones and missing a lot of functionality from the Office app.


Fully agreed. We had two guys in university that would type to Latex the mathematics lecture notes and produced a neat script that everyone else used. They failed the course.


I object to this for completely different reasons. Do whatever you like to learn the material, but when you're sitting in a lecture, please don't have a laptop open -- it's terribly distracting for the other people in the room. You may stick resolutely to note-taking and have no messaging programs, games, or video playing. Even so, your constantly updating screen, your tapping keys, are a magnet for others' attention. And that's a best-case scenario by far. Few students are disciplined enough to stay off of Facebook during a lecture. Laptops have no place in a lecture hall.


Over the years I've audited a lot of math classes and tried various ways of taking notes.

I've found that live-TeXing lets me keep half my attention at best on the lecture. The people I've talked to about it agree. Also, when the professor requests for the class to be transcribed, the live-TeXing duty is rotated among the students as to not unduly impose on one of us.

I eventually gave up and moved to taking notes with an iPad and an Apple pencil, which has the quickness of handwritten notes, and the availability of digitized notes -- if I'm looking for something I can usually find it pretty quickly by navigating to the class and the (labeled) lectures.

Of course if live-TeXing works for someone, more power to them!


If this works for the guy how can you ‘disagree’?


Because it's very much an edge case and he hasn't passed yet. A lot of people get to the end of their course and realise they have thousands of pages of useless words and diagrams and have a nervous breakdown.

It takes a lot of discipline and time to write very high quality notes and to study. I spent more time thinking about things and experimenting with ideas and writing notes than I did in lectures or tutorials or labs.


I did take LaTeX notes for most courses on my math degree, and I passed all of them. In fact, the ones where I dedicated more time to the notes were the ones that I could study more easily as I put in more effort to understand and review what I wrote.


> Because it's very much an edge case and he hasn't passed yet.

I am fairly sure he passed more than one course with this approach. The blogpost says that he started using LaTeX to take notes during his second semester. The screenshots show introductory complex analysis, which is usually taught somewhat later.


Don't you think you could be an edge case too where you went back and studied extra and experimented? Very few college students I know actually did anything like this, and I know I didn't. Obviously it would have helped, but I did not do that then.


No because we formed study groups and did it collectively.


I use pen and paper notes for meetings & discussions. While I love the act of physically writing, not having notes accessible and searchable at the tips of my fingers means I am not able to get the most out of them.

This discussion is timely as I have been researching smart pens the last few days which can give you exact copies of your paper notes into an app. Anyone here used them? Do you like them?


I've never used standalone smartpens but I semi-regularly take handwritten notes in an iPad app using Apple's smart pencil. Some apps attempt to turn cursive into text but TBH my handwriting isn't good enough for the transcription to work reliably.


I did live TeXing for about a year, after only having ~a year of emacs and latex use. It's not as hard as it sounds but yes like you mention, it takes your head out of the lecture and into your editor. However, the idea of 'rewrite your notes at the end of the day', who has the time for that though?


While I agree with you on the notes aspect of this (and have always used pen-and-paper notes), I do think that the setup described here would be quite useful for authoring papers -- I've always found it is way too painful to write out math-mode equations in LaTeX.


I would never write short hand with mathematics, it’s too confusing… do you mean long hand?


Sorry I should have used a different word. Write the name of the equation down / bullet points. Don't write too much. Just enough to jog your memory later or cover anything you don't think you understand.


1700 pages of notes would translate to 9 pages/working-day in a year. That's a lot of note taking. The blog post is wonderful and does show outstanding LaTeX and VIM practical knowledge, but I'd be skeptical that the average student could absorb so much content and still have time to bring it to such a polished final format every day.

Nonetheless, there's definitely a lesson to be learned here with respect to the usage of templates. In essence it seems like OP developed his own shorthand language for both text and mathematics. I'm always curious to hear about approaches that try to solve the bandwidth problem (as we have quickscript [1] for hand-writing and stenography [2] for typing). Most interestingly, I'd be curious to know whether these short-hand notations are actually capable of improving learning and assimilation, and whether they'd work for a general audience.

[1] https://en.wikipedia.org/wiki/Quikscript [2] https://en.wikipedia.org/wiki/Steganography


Looks like you have a typo in your [2] link. I think you meant to link to https://en.wikipedia.org/wiki/Stenotype


That is correct, thank you. Also in the description, I meant stenotype and not stenography.


> which makes for a total of more than 1700 pages of notes

That's an absolutely incredible feat, especially considering that the notes look pretty much textbook-quality!

Although personally, I have never been able to both absorb a lecture and take electronic notes. If I need comprehension, my notes have always had to be pen-and-paper.

Once again, this is an incredible feat.


> If I need comprehension, my notes have always had to be pen-and-paper.

I agree. However, if I want to be able to refer to them afterwards, I really need to take electronic notes.


Agreed. So we have this problem that can only be resolved by taking notes with a pen before typing them up. This has the nice opportunity of reviewing them whilst typing, and puts pressure on you to ensure understanding when making notes.


Or use one of the many handwriting recognition apps and take pictures of the hand notes. You don't actually want to convert the handwriting to text, because there will be errors. But it should be good enough to create a search index.


I use LaTeX for notetaking as a blind person because that's the only way to show my notes to sighted people. Nothing else comes even close. Ascimath would be much better and that's what I'd recommend for most people, unless you're required to send PDF documents and often offline.


Thanks for the ascimath reference. Do you know of any similar technologies for writing equations in a simpler and more readable form than latex?

I've never seen ascimath before but I wish I had because I think I partially reinvented the wheel. I wrote some extensions to Pandoc (and an associated emacs major-mode) for scientific note-taking, with a main portion being a "simplified latex" for writing equations in a more readable way. The key features of simplified latex format are matlab-style matrices, UTF8 support, easy exponents, and better formatting (e.g. functions automatically use roman instead of italics). There are still a few edge cases mine doesn't catch, but I'm in the process of rewriting it in Haskell and rewrite is more stable.

https://code.launchpad.net/~mwshinn/+junk/notes3

or for documentation:

https://bazaar.launchpad.net/~mwshinn/+junk/notes3/view/head...


eqn (part of troff) from 1974, predating TeX, had a very decent syntax! It's not as complete as TeX, and the layout quality is worse, and I wouldn't want to touch the rest of troff syntax. So not really practical, but good inspiration.

Open/LibreOffice math formulas use a syntax that's clearly inspired by it. Unfortunately it's very lacking in documentation.

Another important question is are you looking for presentational or semantic math? For presentational fine tuning I'm afraid nothing can beat the flexibility of TeX combined with a huge body of Q&A (on stack exchange and elsewhere)...


I always found that my notes were effectively write-only.

The process of writing things down on paper helped me absorb the information, but beyond that I never really looked back at the notes.

Generally I could find the information I needed in a better form somewhere else. If anything, the notes mainly helped me review broadly which topics were covered on which days.

For math specifically, I always found that what helped me most was to come up with a general "shape" of how I used the paper when solving a problem of a particular type. Then I would end up with a visual that helped me know which bits of information I was missing and what I needed to do where to find the answer.

It's different from the "draw a picture" thing, really more of a knolling[1] of the problem down on paper. If all the things are in their places, then the answer to the problem is straight-forward to come up with.

Edit:

Mise en place [2] might also be a good way to describe it.

[1] https://en.wikipedia.org/wiki/Tom_Sachs_(artist)#Knolling

[2] https://en.wikipedia.org/wiki/Mise_en_place


This method is beautiful and incredibly complicated. Anyone who has enough determination to build up their tools like this and make them 100% ideal and customized for their situation deserves all the praise they get.

If your use case is similar to the author's, perhaps consider taking your environment and leaning hard into customization. As he's proven, it's very much worth it. Seems like it would be much less useful to copy his configs rather than building your own organic system after years of use, though - which is what he did.

I really like vim, personally, but I encourage my coworkers more familiar with Windows to use nano over vi (nobody wants to type that extra m, for some reason) because they're less likely to mess things up. Better off for them to learn their own way rather than being dumped in the middle of the vi desert with no way to exit.


> Seems like it would be much less useful to copy his configs rather than building your own organic system after years of use, though - which is what he did.

This is a great point and one I've been thinking about more recently. Tools and/or setups like the one displayed in the post with this level of specificity or complexity seem like they would be almost useless packaged up as a standalone. Much more valuable would be the system on which this was built (vim and the collections of extensions he used, not saying this is anywhere near an idea workflow but as you know if you use vim - it is extensible in its own right). Or, rather than that system, to take inspiration in it and design tools with much more intentional flexibility to allow people to build their experience.

I recently had a great conversation about how science educators might wish to have 3 brown 1 blue style animations or experiments, but such a programming tool would be much too difficult to teach to the educators. I think that is totally true, 3b1b generates his videos programmatically and while I believe some version of his tool is open source, he does not offer any support. But there is something to the idea of having one's own publishing tool and workflow to allow the exploration of ideas in whatever field it may be. For Science teachers, they ought to be able to play in a tool like 3b1b uses, but it can't be his exact one, it seems they'd need some well thought out foundation upon which to express their mental models of physics or geometry or whatever it is.

3b1b about page; first item is his modeling approach: https://www.3blue1brown.com/faq

3b1b animation: https://github.com/3b1b/manim


This reminds me of the sole draining * job as a "web developer" to turn word documents into HTML. I imagine such a job also exist in science, but instead of Word to HTML you turn paper notes into LaTeX. He could probably make good money helping professors write papers.

* You coded since you where 15 years old, wrote your own game engine, wanted to cure cancer and save the world, and now your job is to copy text from one document to another.


The best response to having to do dumb work like this is to automate it with regex, bash (and possibly an unzipping tool - aren't word documents zipped xml?) and take the time that people previously gave you to do the task to tweak your scripts and learn things you find interesting. I got through my dumbest student jobs that way, which was almost all of my student jobs.


I got a friend that basically automated his job, the management was not pleased, and forced him to go back to doing it manually ...

He managed to get another job. But figured out he wanted to work with actual software development, and it also seems to be a shortage of software developers. But it was virtually impossible to get a job without a degree or experience. So he's now at age 45 enrolling a five year university program to become an engineer on paper ...


This is so unfortunate, but I'm not surprised. What kind of poor management, when met with an efficiency that could double an employee's output by automating their current job, limits it back to the 50% efficiency? I've met some managers like that...


Pandoc can bring you quite far here.


I got a STEM degree in the early 1990s, and my usual note taking style was in the same vein: I used four colours of pen, a straightedge for lines, and tried to make nicely presentable notes that I would not have to make alterations to after the lecture.

In retrospect I think this was completely insane. I was so preoccupied with the mundane details of layout and presentation that many of the important technical details the professors were talking about went right by me. I'm amazed I managed to get by with this style.

One of the courses I did best in was one for which the blackboard presentation was drawn from the textbook, and in that one I did not bother with the elaborate note taking, just relied on the textbook. For some reason I never made the connection between me doing unusually well in that course and the fact that I wasn't distracted by note taking.

If I were to do it all over again I would make my notes merely capture the information (and if I knew the information was in my text, just capture enough to identify where), and if I really wanted beautifully laid out notes I would rewrite them after class, with the added benefit that the rewriting would be an implicit review.


I now use org-mode to do my notes it pretty much removes the need to write non math latex and when you have to write math you just inline the latex. And because I also write my assignments in the same file I can generate a nice latex file with everything I have written doing the course.


Org-mode is awesome, but the points about snippets still apply. AFAIR yasnippet should support most, if not all, capabilities presented in this article.


As a 30-year latex user and a 10-year newbie to vim, I am impressed by the author's skills, and will likely copy some of his macros. However, as someone who has taught mathematically-inclined material for those three decades, I cannot recommend using a computer to take notes in class, for I have simply never seen a student who found that effective.

Although some students try to take notes on a computer during the first day of my classes, I have never seen one who tried to do that after the second or third lecture. The paper method (or, equivalently, using a stylus to hand-write on a screen) is simply better suited to the dynamic of a class. An effective class is not a linear presentation of material, a sort of recitation of a book by a professor. And effective notes are not transcriptions of the class material. An effective class weaves around through a topic, building on interactions with the students. This often involves departures from a simple path that, transcribed in real-time, would be footnotes within footnotes within footnotes, "Inception" style. And of course mathematical material tends to involve a lot of diagrams. Hand-written notes, with lots of arrows between ideas and boxes with sketches, are not just a good way of making a record of a class, but they are a great way of understanding what's going on in real time.

The only place I could see this detailed note-taking method working would be in a class where the teacher essentially reproduced a book in class. But is that the kind of class that justifies the cost of tuition?

I have two anecdotes I'd like to share.

1. A student came to me to ask a question about something that came up in class. I asked to see her notes, to get a clearer idea of what was confusing her. The notes were amazingly insightful and clear. I asked how she took those notes, which contained some things I had said and others I had not said. She replied "I don't write down what you say, I write down what I think you mean." This student will likely be a professor in a few years, and I envy the students who will take her classes.

2. Last term, I recommended that my students try the Cornell note-taking method. (See http://lsc.cornell.edu/notes.html for an example, although there are many treatments of the method online, including videos.) The students who tried it seemed to enjoy it, and it may be no accident that the class leader was one of them.


I have a similar but simpler setup. The crucial difference in my setup is that instead of using full blown LaTeX, I use TeXMe -- https://github.com/susam/texme -- which supports Markdown and LaTeX.

So I write plain text files with Markdown + LaTeX, slap a single line of TeXMe JavaScript either at the top or bottom, and open the file with browser to see the rendered math.

Like the OP I use Vim too with some customization with :ino and :ab. Nothing beats the editing productivity and convenience of Vim!


An alternate approach: Somewhere in the middle of my first math degree I basically stopped taking notes in lectures (maybe 1/2 page, or a few lines per lecture, just any "aha" moment, really). Best change I ever made.

This way I could focus on the lecture itself - and as you can't learn this stuff without doing it my "real" notes were made later while doing exercises.


Interestingly he uses pretty much the same techniques that I relied on when typing lecture notes with Word:

- Formula auto-buildup with automatic replacements of \stuff with Unicode keeps the mess of backslashes and braces more readable (and it also allowed me to immediately spot where I mistyped something)

- I used snippet-like things for parts I had to type a few times, such as a formula that's revisited a handful of times alter.

- Some things are simply easier to type in Word (with UnicodeMath) than LaTeX, such as a^12 being automatically what a^{12} is in LaTeX or fractions being written as a/b, thus requiring fewer braces. Also, as a user of a non-US keyboard layout back then, UnicodeMath's use of () instead of {} for invisible grouping and automatically resizing parentheses meant a lot less typing in general and less syntax to inadvertently break the layout.

The only thing I could not do in real-time was figures where I often did a quick sketch on paper and in the evening converted that into a nice drawing. But text and math was (at least for me) easily writable in real-time and generally required no post-processing or prettification. Assigning certain styles to keyboard shortcuts was also something the author probably used snippets for, but the end result for the typing experience is pretty much the same.

I did write notes by hand the preceding year, averaging about 7 pages of notes per lecture. Others have mentioned it too, the very act of writing notes helps remembering. For the handwritten notes I could just as well have bought the book by the professor, but I didn't do that on purpose. For me, there was no difference in being able to remember my notes between handwriting and typing. And generally I did spend most of the lecture writing and understanding came later when solving the assignments.


This is how I took notes in college as well. TeX people may scoff but word is way better for taking math notes quickly. Just learn the key combos and you can do almost anything rapidly. The only thing I found tedious was matrix/vector stuff.


I used to do this, but I switched to just using a Jupyter Notebook. It’s nice to be able to move between multiple computers, with no need to set up a LaTeX install.

A couple of things I love about this setup:

I can write in Markdown and drop to LaTeX when I need to forumalate any equations.

For homework, I can implement a quick Python script inline to build intuition behind a topic.

I can use Sympy to simplify and solve for more complex derivations. This outputs LaTeX which I can paste into the requisite Markdown cell.

With Plotly, I can quickly create a nice 2D or 3D visualization.


Hi, what sort of complex derivations can you solve for with Sympy?


Tons of different things: https://www.sympy.org/en/features.html. Try it for yourself: https://live.sympy.org/

E.g. find critical points on a surface:

  e = (x-y+2)*(x**2+y**2-9)
  solve([e.diff(x), e.diff(y)], [x, y])
Note that this online demo runs at a restricted speed; locally (e.g. install Anaconda and use Jupyter Notebook or QtConsole) it's much faster.


Impressive! For anyone looking to do something similar, but in Sublime, I can recommend the LatexTools[0] plugin, which gives similar live previews of math mode. I'd never considered embedding figures from Inkscape though.

I also decided that I wanted to keep lecture notes in LaTeX, and the best advice I have for anyone is to just practice. Start from LyX if it helps, but just make sure that you grind down the rough edges. It takes a long time, but like many skills that are worth learning, it takes lots of effort but the payoff is worth it.

[0]: https://github.com/SublimeText/LaTeXTools


Start from LyX if it helps, but just make sure that you grind down the rough edges.

Fully enough, I would have exactly the opposite recommendation: Start by writing LaTeX out manually, then move on to LyX when you have a good understanding.

This is due to a combination of (1) needing to already know about LaTeX features before you can know to look for them in LyX (buried in menus or whatever) and (2) although LaTeX errors are much rarer when you're using LyX, when you do get them they're often really confusing ones. I'd say that using LyX requires greater knowledge of LaTeX than using LaTeX directly, just applied less often.

The benefit of LyX is not that you avoid needing to know about LaTeX. It's that you don't have to see it when you're editing your content. Equations with a lot of subscripts and superscripts come to mind; anyone who claims that it is easier to find and fix mistakes in a nested superscript in the raw LaTeX rather than just clicking directly in rendered representation and fixing it in place is, frankly, lying, if only to themselves.


I'm surprised to see not enough mentions of Emacs's Orgmode which clearly dominates Vim when it comes to note-taking with or without Latex. Not to start another Vim vs Emacs war, I've been using both of them for quite some years now for each of their specialties. But when it comes to Notetaking, Orgmode is hands-down far superior with it's rich plugin ecosystem & minor modes within. Some plugins I use to do Latexy stuffs on Emacs is (ofc) Auctex, latex-preview-pane, PDFTools. Finally, OxHugo to export my Latexy org as a blog post to my Hugo blog.


See https://github.com/jceb/vim-orgmode for Orgmode in Vim.


1700 pages? You've just rewritten the textbook. That doesn't seem like a good use of time.


Hey, for note taking using markdown and mathjax, I also like Typora (https://typora.io) a lot.

Easy to install, wysiwym, works out-of-the-box!


I do the same thing (markdown and mathjax) but I use TeXMe (https://github.com/susam/texme). I like TeXMe a lot because it turns any Markdown and LaTeX notes into a self-rendering file. Just open your Markdown+LaTeX notes in any browser and it renders itself beautifully, almost looks like a paper.

It is not wysiwyg though. But for me the convenience of distributing my Markdown+LaTeX source itself that can render in any browser without a separate compilation/processing step is a huge win!

See https://github.com/susam/texme#get-started if you are curious how it works.


I did the same thing when I was in uni. Couple of my profs asked for my notes so they can make class notes for next year. I also did all of my math assignments this way and it was so easy copying stuff from the notes and working with it without erasing and compromising on space. I could break down every algebraic step for maximum clarity.


I did this during college (but with emacs).

It was fine. I was in the habit of TeXing up my homework anyway so was fairly practiced, and I have shit handwriting and know I'll never reference anything I write on paper, or have it to look at in a few years. I also don't get that much out of lectures.

YMMV

It's nice to have it to reference now though.


I used to do this too, but I took pics of the figures or drew on paper them instead. The only times you don't feel like the silliest student in the room when live texing is when you have one of those professors that edits each equation in place for 5 mins and quickly instead of rewriting the equations in edited form.

There are some lectures where every week something truly unique happens that is not available in any one book in the whole world, AND you have to know it well for your area or bc of a hard test.

But in all other cases, where the information can be found in some textbook or it is some well studied subject, my opinion is it's not worth it. Texing can turn into an escape from actually learning the stuff


I took notes using emacs and LaTeX in similar fashion. But I started by doing all of my assignments with it until I became proficient enough. I can type much faster than I write. I didn’t use any Elisp to help — though I probably should have in retrospect. I did have some common LaTeX macros/commands. It was nice to have the notes to study from in the end.

This helped most in doing assignments and is what I’d recommend to others. I would write by pencil and paper then type as LaTeX. This forced me to review my solutions and fix mistakes or improve them.

I didn’t attempt to get too fancy with plots in real-time (I kept a notebook for those courses) but I did do graph theory and commutative diagrams (category theory) with tikz.


Why would you torture yourself like this? In mathematics understanding is everything, and using the time to listen carefully and understand is more important than having perfect notes, handwritten notes are quite enough.


Beautiful tricks for writing efficiently in LaTeX. But I just hate to take notes during lectures. I prefer if the professor gives the printed notes and then you need just to add small annotations, if anything.



Dropping a bombshell: https://github.com/brennier/quicktex


While this is certainly impressive, writing math formulas by hand commits them to memory way more effectively than typing latex commands/snippets. Although, an argument could be made that writing formulas in lecture is negligible compared to the amount of practice required outside of lecture for any mathematics course.


Why don't universities just videotape the lectures as they are happening and make them available for reference to the students. Then the students can just pay full attention to listening the lecture while it is happening, then the students can use the tapes later to make notes later if required.


When I see a Math lecture written in LaTeX, I immediately know that I will probably be too dumb to follow it. It's almost always a deep exposition on what the writer want to show he/she knows or how many complicated formulas they can apply rather than really try to teach me something.


Not necessarily true. If you take the score of e.g. Chopin's Ballade N.3 you'd be inclined to think sheet music is all just show off. Abstract notation takes time to parse and understand when you see it for the first time, no matter how well versed you are.


A template expander is indispensable for productivity. I have a perl script that expands text based on matching regular expressions. In this way I'm not tied to any particular editors: I wrap it in an AppleScript for a text service, and I wrap it in a shell script for working in Acme.


Of course that doesn't get you niceties like jumping to different parts of the template and mirroring edits. But having it universally available might be worth the trade-offs. How do you invoke it in Acme? Tag item mouse-click for every expansion?


Just option click the script name. The script look at the current window body, RE match dot or RE match texts right before the dot. The first match executes the associated action. It's basically an extended version of plumber.


Good ol' Live-TeXing. Googling "LiveTeXing" will show you other examples of this, if you are curious to see more.

For those who aren't already familiar with Vim, Kile 3.0 beta is a fine substitute. It does most of what's described in the post in a GUI environment.


I really like this, but it would be very hard to learn all the macros. There were no real portable computers when I did undergrad. When I much later went to law school I transcribed about 90% of what the professors said on a latptop and then later went back though it to make outlines and then outlines of outlines. I took some premed classes after that but because of the drawings I had to handwrite the notes. I still transcribed as much as possible of what the professors said and later went back and outlined from it. I've never been able to learn from the textbook and if I ever missed a class I did poorly if tested on that material.


Very impressive. The first displayed text page contains a typo at the bottom : CHAUCHY iso CAUCHY. As others have said physically rewriting is part of comprehension (as is rewriting new words learned in a new language) As the lecture notes are drafts from the black board I suggest using a font that does not make it look like perfectly printed. You can fool yourself believing what you wrote because it looks so pretty.

If you are writing a considerable amount of latex his setup is really cool. I will you these ideas but using emacs in stead of vim. Wonderful job!!


This is really neat. But for me, if typing on a keyboard becomes just as functional as writing, I would still choose paper and pencil for two reasons: no power is required and it effortlessly autosaves.


That's interesting, I don't use vim snippets but seems like there is a few of them (mainly snipMate/UltiSnips)

https://vi.stackexchange.com/questions/7466/what-is-the-diff...

And there is a community-maintained repository of snippets: https://github.com/honza/vim-snippets


Neat. I'm a self-taught developer, and I learned a lot by watching MIT computer science lectures on youtube while taking notes in a markdown file. But I definitely hit a wall when I tried to follow the Mathematics for Computer Science course. I didn't have a good way to handle the notation. Ultimately though I think if I ever decide to follow through with that I'll probably just write in a notebook and scan the documents so I can easily reference them. But I love the dedication to figuring this out!


Hi. From: Emacs org-mode users who export to latex/pdf.


The real value I see here, is being able to write anything, such as a publication-quality scientific document - in Vim. I have yet to see a comprehensive overview of what this would entail in Vim. I think Orgmode [1] in Vim makes progress towards this.

[1] https://github.com/jceb/vim-orgmode


Something different, but I use this

https://remarkable.com/

Think of a big Kindle, good battery, and really good writing experience (much like paper). I can note on pdfs, it has handwriting recognition, exports well and is otherwise a joy to use. I used to have a top of the line Samsung tablet before, and was never really happy with it for taking notes and reading.


How does this compare to taking notes on a Surface or iPad, color aside?

It looks really cool, but pricey for what it can do.


That looks really nice, a bit expensive though.


Samsung Galaxy Note 10.1 (the tab) had a feature in cooperation with WolframAlpha a few years back that translated your handwritten formula into a nice digital formula. It was like 90% there. Unfortunately fixing interpretation errors was a pain in the ass, which made it basically useless.

I wonder if there was any meaningful improvement on this approach. Even just adding a nice UI to fix errors would've made it really useful.


That's quite remarkable that you were able to do so many things so effortless in real-time.

And all the notes look so beautiful.


Very cool & beautiful notes!

I'm looking forward to seeing how the author live-TeX's figures - I'd love to get better at creating figures in TeX even in a slower, more offline context.

Having to drop to Python in some cases seems non-ideal though. If only there were some editor with good, customisable scripting built-in.....


I want to ask about the converse of this article. I teach at a college. I make presentations using LaTeX. I like to imagine that one advantage is that students can suck them off the intranet and work from them.

I want to ask if this is common. Do students not find that other people do it?


So what I see here is a very impressive, hand built tab completion system for a specific task. Makes lots of things much faster. Now all you need to do is speed it up some more by using less keystrokes and a stenotype machine.

But really the takeaway is the auto-completion. Incredibly useful.


Didn't believe that this is really possible. Certainly interesting to see what is possible with macros and workflow optimizations. However, why is this extensive note taking necessary? Shouldn't the course materials provide a digital copy of the script?


Now that 'Escape' is not a real hardware key in the new Macbook Pro anymore and even otherwise 'Escape' has always been one of the hard to reach keys, what is workaround for avoiding the 'Escape' key in Vim?


some people use Shift Lock (which is barely used, and closer to pinky), and a colleague of mine use the sequence 'ii'


Did you mean Caps Lock? Which tool do you use? I found https://github.com/susam/uncap but it does not have a MacOS binary.


You don't need any external program. Open System Preferences, go to Keyboard and click on "Modifiers Keys...", then you can map Caps Lock to Esc.


Caps Lock is the original placement of the Esc key. It's much more useful having Esc on your home row.


i map <tab> <esc>, which is much easier to reach. Thanks to autoindent the TAB key is useless inside vim.


people often map `jk` or `jj`, or the key to the left of `1` to Esc. I use `jk`.


I tried the idea of using `jk` in the past and found that it surely cannot be a perfect replacement of Escape.

Say I perform these mappings:

  :noremap jk <Esc>
  :inoremap jk <Esc>
Now granted, pressing `jk` in insert mode escapes me to normal mode. But many use cases that work with the Escape key do not work with `jk` anymore.

For example, try:

  :ab hn Hacker News
Now type `hn` in insert mode and press Escape, it would expand to `Hacker News` like it should. But then type `hn` in insert mode and press `jk`, it does not expand to `Hacker News`.


I use ctrl+[ myself.


Nice setup. Good explanation and seemingly gets the job done.

Just one grievance: if you are concerned with parsing your latex (even if that's only possible while you restrict yourself), you should use the parentheses as math delimiters: `\( x + z\)`


This is impressive.

There is no way I would be able to take these notes, live, and learn the mathematics simultaneously. So this approach wouldn't be a good idea for me, and perhaps most people.

But if you're able to do that, then it's doubly impressive.


The techniques in the article definitely are useful to improve efficiency of typing math. I have used vi/vim and latex for many years (over 20). And this still impressed me a lot. Can’t wait to see how he does the figures.



This is pretty amazing. I regularly use LaTeX for typesetting homework at school but have never been able to keep up during lectures. I'll have to look into including this in my workflow.


Beautiful notes! But I don't believe those figures are made using LaTeX and Vim... I can't see how you convert keyboard strokes to nice figures shown in the example.


From the original post:

> There, I ex­plained my work­flow of tak­ing lec­ture notes in LaTeX using Vim and how I draw fig­ures in Inkscape.

Looks like the author was using Inkscape earlier but may have switched to something else recently. You can draw impressively beautiful diagrams in LaTeX with TikZ although it can be a lot of work to do so with TikZ which would make it difficult for live note taking.


Probably it's "compose key" feature available on linux, allowing one to type alternative characters via key mnemonics, rather than numeric key codes like on windows.

https://en.wikipedia.org/wiki/Compose_key


I'm not following. What is it exactly that you don't believe? Those figures are exactly the type of figures one gets using LaTeX.


I have to make a plug for the project I'm working on as it seems like you guys are the target market:

https://getpolarized.io/

Polar allows students and researchers to keep all their research in one place, take notes, highlights, annotations, etc.

You can tag your books and suspend resume reading without losing your place.

It also supports sync with Anki which is rather nice.

The one caveat is that I don't (yet) support math as well as I would like.

Latex is supported by summernote but I haven't enabled the module yet. I usually wait for enough people to complain but math is definitely something I want to support.


While I don't plan on doing this during lectures, I will be taking some of these tips to help when composing assignments and papers, thanks for posting!


I use libre office writer, it has a very good math formula editor. (Unlike MS word that keeps crashing when you try to write a math formula)


I've got the usefulness of Ultisnip in this article at least. I couldn't understand everything else... mathematics?


I guess if you have high wpm, this might be feasible. I unfortunately don't, even after constant practice.


Anyone know what theme/font he's using?


Oh look it's the daily 'look how inadequate you are for not doing this unnecessary leet thing' post.


This is godly.


i use onenote to import the pdf of the textbook and then annotate that. this process seems like someone who doesn't know what to use their programming skills for in order to over engineer a solution to a vaguely defined problem(take pretty notes using software)

what is the point of recreating everything in the textbook again?




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