Math Notes

How do you guys take notes in math? (or any subject).
I'm transitioning into a math major after taking a fair amount of math subjects but I have absolute trash tier notetaking. What are some good ways to lay out notes?
Do you write in caps like pic related?
Do you split the page vertically?
Do you use grid or lined paper?
Do you even take notes?

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My notes are a mess, but it just werks.

depends. I'm one of those people who thinks notes are a personal thing and it is something that's supposed to help me better understand later. I don't think there's some universal truth or rule to note taking.

with that being said, there are various suggestions and tips on the internet.

I don't write in all caps.
at some point i started flipping my notebooks sideways so it has a visual feeling of a writing board. I get the feeling I have more space for writing. in those cases I do sometimes split the page vertically.
I use grid paper with 1x1cm squares. standard math notebook in my country.
I use a ballpoint pen, usually blue. pencil work wears out after a short time.

use w/e paper and writing style you want. doesn't matter at all.

take notes in class
take notes from text

using your notes, re-write each section of each class in your own words

try practice problems

if you're stuck, refer to your re-write notes

if that doesn't work, go to a TA/Professor

>How do you guys take notes in math? (or any subject).

Chemistry Major

>I'm transitioning into a math major after taking a fair amount of math subjects but I have absolute trash tier note taking. What are some good ways to lay out notes?

I don't know about math, but I like to take a scarp piece of paper / scrap notebook and read the lecture slides / book before to get some background and overview. Also helps to "prime" the brain a bit. After that I go to class and take notes in a notebook or on lecture slides, but I don't care how organized it is. I also take notice of things that need addressing, a confusing step in a problem, something I want to add more details, a test hint, etc.

After class I will reread both my notes, and try to fill in those added things and combine both sets of notes into a master copy. I like to use engineering graph paper, because it is good quality and I tear it off the pad and put it into a three ring binder. OR I use a high quality lab notebook, but I found the binder method to be better.

When it gets close to the exam, if needed I will rewrite the notes to add more information to clarify things. I sometimes do this on paper, sometimes electronically using LaTeX, depending on my time.

>Do you write in caps like pic related?

No, too hard.

>Do you split the page vertically?

No, I just use the notebook as scrap.

>Do you use grid or lined paper?

I prefer grid for my good copy.

>Do you even take notes?

If you don't then you probably aren't doing too well.


This method worked for me. I went from a 3.0 to 4.0 in just one semester and since then. Organization is key, people who claim that organization doesn't matter are just memeing science as disorganized.


>Pic related. Physiology notes.

I print it myself atincompetech.com/graphpaper/plain/ and make it clean and hopefully compress each lecture in 1-3 pages.

>depends. I'm one of those people who thinks notes are a personal thing and it is something that's supposed to help me better understand later. I don't think there's some universal truth or rule to note taking.

This OP. There isn't really a one-size-fits-all method for note-taking. I know people who take notes that look disorganized and they have 4.0s and I know people with stellar notes you struggle to pass the course. Note-taking won't magically make you smarter, it will only put your retention of the material above what your baseline is, and everyone's baseline is different, so get to know yours first.

Think about understanding things like a set of skills.

You have some basic skills:

1. Retention/Recall ("I remember this much of the material")
2. Connection/Association/Relation ("this section is related to that section in these ways")
3. Deriving/Producing/Creating ("given all of this material, and all of these relations, I can create new material and relations which are also true")

If you can't remember the material, you won't have anything to make connections between, and if you have nothing to make connections between, you won't having any connections to derive from.

From those skills, you can then figure out where your personal weaknesses are. For me, even though I can derive pretty quickly (and associate even faster), I have a really shitty explicit memory, so while I could explain to your why something is true, the thing I'm talking about is either of no consequence, or too technical for anyone to care about.

Figure out what your weaknesses are, and work on them first. Remember, you'll always be good at the thing you're already good at "naturally". Always work on the things you aren't good at!

Like this.

Don't worry about super speshul or super sekret note taking techniques... this isn't an anime, so taking notes using some super technique isn't going to increase your grades, retention, or study habits.

Write down fucking everything the prof writes on the board. He will explain things, he will write and he will stop or slow down if you ask him. That's one thing people who don't do math don't know about math profs... math profs more than anyone know math is hard. They want you to learn.

Add little notes here and there if you need to along the way... things he says but doesn't write, things that you notice, whatever.

after class, review your notes IMMEDIATELY.
Write a 'good copy' of your notes. Go through your old notes line by fucking line and make sure you understand them. When you understand them, rewrite them (do not transcribe them) in a neat way so that you have them in a form that is CORRECT and that you UNDERSTAND for reviewing later.

Source: I'm a 4th year math major who spent years 1 to 3 not taking notes, then taking notes but never reviewing them, and then finally taking notes and reviewing them properly. Doing what I described up there is what I do and it really helps with understanding and retention.

tl;dr - do not transcribe; do not skim; do not read like a novel; math is about memorization; think of examples; try to make things intuitive; think of counter examples; ASK QUESTIONS RIGHT AWAY IF YOU DO NOT UNDERSTAND SOMETHING - IN CLASS AND IN OFFICE HOURS. THEY WILL BE MORE THAN HAPPY TO HELP YOU AND EXPLAIN.

>If you can't remember the material, you won't have anything to make connections between, and if you have nothing to make connections between, you won't having any connections to derive from.

How do you make connection when you have nothing to connect on?

Really like your method(s), was wondering if you could provide an approximation to how many hours per day you study per subject outside of class. And/Or a breakdown on your study habits, in time of however you work.
Your method sounds amazing, I doubt I have the patience for it though.

It does take a bit of time. I study a lot outside of class, to be honest, sometimes I don't even go to class because the book will do a better job of teaching you than the professor. I'm studying chemistry, but my focus is in physiology and pharmacology, since I want to go to medical school and I am interested in those things. I say I study maybe 40 - 50 hours a week, I treat it like a full-time job after fucking up a lot freshman year. I try to do 3 - 4 hours per credit hour, but of course some classes aren't going to require that much time, it depends on a lot of variables. I only really do the LaTeX notes if I have free time, but Word will do, even though I love the look of LaTeX more.

I didn't have the patience for it at first, but I kind of just made myself sit down with no distractions in a quiet isolated place and studied. I started with 25 minutes of pure focus and 5 minute break, but that wasn't enough time, so I changed over to 50 minutes on, 10 minutes off. I do it four times, and then take a 30 - 120 minute break, depending on how I feel. If you do that for a while, then you will get really, really good at focusing. I'm at the point where I can focus for hours without a break, but I still like to do the 50:10 ratio.

Depending on the class, in those 50 minutes I will either revise notes, do an "active recall" with my notes, or do practice problems. Active recall and active learning is really important. I try to organize my notes like I would be teaching a lecture on the class, and explain concepts and ideas to myself without looking at my notes, whiteboards / blackboards are good for this. It takes a while but is a really good way to learn. You should definitely look up active recall / learning, there is a lot on it that is good information.

>Cont.


There is one thing I forgot to mention in my original post, it is good to try to condense all those notes from those different sources. For example, my Human Physiology class assigned us like 4 different textbooks, thankfully medical books are cheap to rent, so it didn't cost much, but say the topic was on the Gastrointestinal System, I would read about it from the different books because sometimes different books stress different things, but it is often good to just find one good book to use, but I'm really into biomedical science so it doesn't feel like work to me. I will also supplement more information from different sources, as if I was writing a text, and then try to condense the notes to the most important points. I also look at the references that the professor uses, if they are journal I will skim it because 9 times out of 10 there will be a test question on it.

I'll give you a detailed process for say: Physiology - Lecture 22 - Class was recorded

>Look at syllabus to see reading required, see that it is chapter 9 - Heart Muscle; The Heart as a Pump and Function of the Heart Valves
>Look at titles in the glossary, those are gonna be the "big picture" ideas for the chapter
>I'll do a quick 5 to 10 min skim of pictures and graphs and then look over the lecture notes to see what the professor is stressing
>Then I'll get to work reading the book, I write down the headings and subheadings like you saw in the picture, those will serve as the main concepts, and then I will add details.
Example - Main heading: The Cardiac Cycle - Subheading: Diastole and Systole - Details from the text
>Look at lecture notes to see important details to see what the professor is stressing

>cont.

>It will take a little bit, but I will understand what the main concepts and add details and pictures if I don't understand something
>Revise with more information from other sources to strengthen the concept, if I understand it, and I can explain it, no need to add anymore information
>I will skim the lecture, but if I can predict and know what the professor is going to teach, and it seems like I already learned it, I won't go over it anymore. Same in lecture, I will just leave if it is a big lecture, but if it is small, then I have to suck it up and stay.

Then for active recall I will try to teach from those notes that I made or sometimes the professors notes. If I have time, then I will typeset it or add in other information from other sources until I feel comfortable.

I was able to get the highest score on all the exams in the Human Physiology class taken by undergraduates and graduates at my school, the average was in the 40's I would get 95's using this method. Using it in my classes has given me the fortune of getting A's and crushing the bell curve.

The thing is, the more qualitative the subject, the more time consuming it will be to do this method. Physiology has some equations, but a majority is qualitative. I've used this method for all types of classes, it is very useful for highly quantitative sciences or math. The only difference would be that I do a LOT more practice problems, and a lot less reading of different texts. I will explain the concept, example "What is a derivative?" then I will work through a variety of practice problems, but make sure you have a solutions manual that shows steps. Medicine is difficult because there is a lot of information in a short amount of time, whereas chemistry and math will not go over that much information in a short amount of time.

The amount of time spent on math is substantially lower than something like physiology.

Hope I helped! Let me know if you have anymore questions!

I'm interested in adopting a similar technique for notes to you. Binder size? Do you divide up a large binder for multiple related courses or prefer smaller binders? Do you use dividers? And least important, bar eraser? I've used a Pentel twist-erase for years, but heard some people suggest fancier bar erasers are very nice. Never wanted another thing to carry around and potentially forget.

I use a small binder for what we are learning that week and then transfer it to a large one for the whole course. 1 small and 1 large binder per class. I use dividers per chapter or topic. Also look into those paper punch protector stickers or else you will accidently tear out notes.

Thr bar erasers are real nice, but I prefer to write in pen. The uni-ball signo ultra micro .38 is one of my favorites, along with the pilot multi pen, and sharpie pens. For pencils, I use the kuru toga .3 mm edition. I also have a .5 mm. For cheap pens I like the paper mate write bro fine .8 mm or the Bic soft feel .8mm fine. Ad you can tell, I like the small mm pens and pencils.

I carry all of my writing utensils in a make up bag I got on amazon for like 2 dollars. Since those pens and pencils are kinda pricy you will take care of them more than some cheap pencil.

Loved your explanation, thank you so much!
One more question, do you jump around between subjects during one study session?

e.g. During a 4 hour study session with four 50 minute periods, say you have to study 1 chapter for two separate subjects, like Chemistry and Physiology, do you switch around between what to study during the periods in the same study session? Or, do just set to power through the full chapter(s) per session?

No notes, practice problems only

Anything else is pleb/brainlet tier.

Depends on the progress Ideally I like to do two of subject x and two of subject y.

You can sometimes even try to relate concepts from different classes. I took biochemistry, physical chemistry, and physiology in the same semester, and I could combine principles of those three to explain concepts. Which was pretty cool, but that was more in the revision of notes, not the initial reading of the chapter. But I would make side notes like "protein stability and interactions depend on thermodynamics, which we covered in physical chem" just a way to connect information.

Paper is a place for your mind to dump shortterm memory. It's not a journal of classroom activity. Because i'm cheap, i force myself to divide down the middle of the page, and use front and back.

Underrated.

>How do you guys take notes
I don't.

>dx is a second variable
>and consequently may be any real number

definitely triggered

either dx is a one-form and not a number at all
or you use nonstandard analysis and dx is literally LITERALLY defined by extending beyond the real numbers

jesus christ what the fuck kind of botched up version of calculus are you taking?

i'm guessing calc for business majors or some other specialized "for x" version

>one-form
Not him but wiki-ing this term out of curiosity lead me to differential geometry and multilinear algebra. I'm finishing up linear algebra right now. How does multilinear algebra differ from tensor algebra? Is this a standalone course (though I'm self-studying) or part of something else? I assumed I'm down to pretty much just needing tensor calculus before differential geometry. Would have taken this to SQT but I skimmed the catalog and it seems to be missing at the moment. Thanks.

Just b yourself

Physics grad student here. I hate graph paper and lined paper. Personally I just grab the printer paper from one of the libraries here (free). I just three-hole punch it and put it in a binder (not free). I don't know how people do math any other way. I have a friend who takes his notes in LaTeX. That's too hardcore for me. To be honest, I rarely look back at my notes. But it helps keep you engaged and if I were a professor I would be mad as hell if a student never took notes.

Use grid paper and a black pen.

I never took a formal class or anything on multilinear algebra, I just learned Grassmann algebra along the way. But I'm also a physics student so I learned what I needed of that + tensor calc + diff geometry + lie algebra bundled with my GR courses.

I think if you understand the ideas of linear algebra and what the actual point behind it all is (i.e. not just to solve linear equations and matrices and shit) then I think you'll do fine with the concepts.

This is from the internet. I typed in 'Math Notes'

Actually I change my mind, this is actually the best method.

>How 2 reference
>How 2 visualize