For the majority of people, it is difficult to properly absorb large quantities of information without some form of note taking.
Mathematics notes are perhaps more condensed and less personalised (needing to copy out theorems and proofs) than notes one might expect from an English student, but should remain a vital step in your learning process. On one level, challenging yourself to clarify and organise the abstract ideas you might attain from a reading or lecture allows you go on to the exercises that will cement your understanding of a topic without having to refer back to the source material constantly. Additionally, diagramming adds another level of interaction with the material, and helps establish a more concrete relationship with it.
For your note taking, I would consider the following factors
Organisation - If you take notes in this way, will you be able to find them years in the future or will they be chucked in the paper bin in a week?
Drawing - Can I draw quick effective diagrams, with clear labels and accurate shapes?
Symbols - Are my numbers and symbols distinct and clear? Would I be able to even read them in a few years?
Generally, people opt for one of the following methods
Typing Note Taking
This includes using a special platform and some kind of coding language such as LaTeX which allows you to use written shortcuts to display equations and numbers.
Advantages:
- Looks beautiful
- Easy to organise
- You can't lose them
Disadvantages:
- Takes a bit of time to learn how to use LaTeX, and even then it is rather slow
Would recommend:
Notion (App)
Gitbook
Drawing On a Tablet
This normally entails a special pen and tablet, and is a very popular option for many mathematicians.
Advantages:
- Can easily use many different colours and decorations
- Easy to organise
- You can't lose them
Disadvantages:
- Takes a bit of time to learn how to draw and even then if your normal handwriting is bad, your notes will still look messy!
- Expensive Equipment
Would recommend:
Goodnotes
Notability
Handwritten
What can I say, I'm old fashioned.
Advantages:
- Quick and easy
- Don't have to carry around electric devices
- No charging needed
Disadvantages:
- Soooooo easy to lose
- Will often be messy
Would recommend:
Getting a notebook or a solid filing system
Colour coding your notes by stickers so you can find topics easily
I will write more on each of the recommended platforms later, but try some preliminary research of your own! I personally use a combo of written and typed notes (typed for the more formal proofs, and written for personal notes) because I lose things very easily.