# Has anyone ever studied maths with RemNote?

I know the main purpose of Spaced Repetition tools is learning things by heart. Yet, the concept/descriptor frame is definitely made for understanding.

Therefore the question comes up, whether it makes sense to study maths with “spaced repetition”. If it does, what is the workflow like (LaTeX,…?)

I am looking forward to fresh ideas

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Definitely yes: To understand more complex ideas and make abstractions you have to firmly internalize the basic definitions and concepts first.

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I have used RemNote for studying statistics and the experience is superb. I basically used RN for making organised notes (example: https://www.remnote.io/a/stat7614-advanced-statistical-modelling-and-stat7609-research-methods-in-statistics-organised-notes/tw4AuLTJzfLcRiDrh) of random notes I jotted during lectures and tutorials. I think having good memory definitely helps excelling at maths (think of von Neumann!). But for mortals like me this fact does not mean using the cards function in RN for memorising proofs or definitions can help with improving my maths reasoning skills. Thus, I rely on RN in two ways:

1. Jot daily notes so that I have a perfect record, sorted by dates, of what I have gone through, and what I do not understand, and what I should pick up again in the next study session by making use of the “Edit Later” function. Such records I will complete after finishing a study session. This is the predominant way RN is used for studying mathematics.
2. Then, occasionally, when I feel there is a need of organising the cluttered handwritten notes, I will make organised notes to make my thinking more organised.

Making extremely organised notes every study session is just not feasible. For that you need a lot of time spent on latexing (even with the use of applications like mathpix that convert pictures to latex codes) and it is simply not feasible. I will make organised notes for particularly difficult theorem or particularlly appealing results, but not everything in my prof notes.

However, talking about this topic, I have the idea that one day maths students around the world can pool together their math notes to make a latex-searchable comprehensive mathematics notes database. While there exists math database with this comprehensiveness and searchability in mind (https://leanprover-community.github.io/), such database nonetheless is based on type theory and is completely written in machine-understandable symbols (but not un-trained humans). Remnote really seems to be an excellent platform to set up a comprehensive searchable maths database that is readable by humans, as it already has most of the bidirectional links features set up. Of coz, this would also mean a lot of efforts need to be used to put knowledge in maths textbooks on RN as latex, and the related copyrights issues.

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This reminds me of the quote by von Neumann: “Young man, in mathematics you don’t understand things. You just get used to them.”

I love the Q&A approach to writing proof adopted by the writer. This is another way of writing proof, and it is indeed a more natural way for humans to understand proof.

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Wow! The document is really impressing. At least for me (just finishing my A-levels) those LaTeX formulas look quite overwehlming haha thanks for showing what is possible with RemNote!

The last part that involves taking screenshots is the most work and for the recent exam, I didn’t even make it that far🙃 (I only got to practicing the majority of problems) The logic behind the last part is that you’ve already gone through all the problems so the only thing left for you is to do them again and RemNote seems best for that. You get the benefits of interleaving because of the random order and the spaced repetition is what allows you to do these problems again in the first place. Through spaced repetition you can avoid memorising an exercise and finding it way too easy because of it. It helps you forget the exercise so that you can actually revise. So yeah, I can definitely confirm that the first and second part of this workflow are highly effective and in the future I might also confirm the effectiveness of the third part.

I’m curious: why no clozes? Do you honestly remember every multiline card top to bottom each time?

I do use LaTex to learn Mathematics. But I don’t really use spaced repetition. Instead, I separate notes into three categories: permanent notes, fleeting notes, and literature notes. (Credit to Beau Haan) In a nutshell, I do spew text in fleeting notes on every theorem I encountered in math books. After done spew text, I summarize what I wrote into rem which forms the permanent notes. Then I organize these permanent notes under concept rem. Often, I get inspired there and write more permanent notes or fleeting notes.

Structure:
Literature notes: Theorems, formulas. Everything important from the Math book.
Fleeting notes: It’s basically my spew texts; It’s also where I breakdown theorems into pieces and linking back to previous theories; It’s also my random thoughts on the topic.
Permanent notes: well-articulated summarization of my fleeting notes. (I often keep the permanent notes in fleeting notes as well)

Benefit:
Messing around in fleeting notes makes you more daring to face difficult problems.
Fleeting notes to permanent notes allows different granularities of information to be presented.
Writing in fleeting notes, utilizing the indentation, will help you freely break down a complex problem into manageable pieces.

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No I don’t use the cards generated at all. I write the organised notes for review from top to down to refresh my memory of the structure of the course, and for later searching only. I want to keep the famous results so that when I hit [[ and search with latex I get immediately the relevant symbols. Hence here I use RN as a mini-database. Actually I discouraged copying results in notes and textbooks to the note since it’s not at all feasible nor effective. Mathematics-wise, I think RN is best for short record of what’s not understood day by day like a diary and secondarily used as a writing tool to organise one’s thoughts about difficult parts of the concepts acquired.

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This were some really interesting thoughts about this topic today. I didn’t really expect responses so fast. Nevermind, thanks!