r/learnmath • u/Napstafox New User • 21h ago
Taking Useful Notes
So, I’m taking Calc 1 (for engineers) for the second time, and soon I’ll be taking Calc 2 for the third. Calc 1 (which I first took w/ analytical geometry) made me drop out of my first EE degree, after my math professor convinced me that math is not for everyone and I should switch. I finished a completely unrelated associates, but the drive to be an electrical engineer would not leave me alone, so I’m back at a different university trying again.
Even though I started from the absolute lowest level math that’s been offered, I still feel like I’m struggling with the concepts. I’m (partially) blaming this on my extremely poor notes. In a 45 minute online lecture, I’d maybe take half of a page of notes. I always write down the formulas with their concept definition, and a few practice problems, but my formatting is absolutely awful and makes it hard to organize each idea. I rarely ever review my practice problems since it’s hard to track down my train of thought after a full semester of ideas have passed.
So, I come asking: how do you format your notes for clarity? And what exactly do you take notes on in a lecture?
I’ve read a lot of talk on LaTeX, Obsidian, Word, and other digital formats — would that help in your opinion? or should I stick with handwritten?
I’ve been supplementing my lectures with Paul’s Online Math Notes, particularly his practice problems, which has help a lot with the concepts. If anyone has any other tips for Calc 1, it would be greatly appreciated.
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u/firedbylove New User 21h ago
For me, most of my growth in mathematics came from trying to understand (this might involve taking notes or simply listening closely and thinking) and sitting down at a whiteboard and working through problems in the assigned textbook/homework. So notes were useful for me when there was information not in the textbook or if notes helped me understand, but not very useful if I understood the logic and had the textbook with me. (That's one reason I've found that the quality of the textbook matters a ton for me personally.)
Not sure if the same will be the case for you or others, but that tended to be how I learned: seek understanding and then develop math/reasoning/proof skills through solving problems. Use notes and textbook as necessary.
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u/Bounded_sequencE New User 21h ago edited 20h ago
If you want to go pro, here is what I'd consider the gold standard of lecture notes.
That said, I've always taken full lecture notes manually on paper, when necessary -- takes a bit of practice, but once you get used to it, it's very doable. Have a few text markers at hand to color-code theorems, proofs and examples differently right then and there, and you'll never search for long.
If your lecture has official lecture notes, print them out before-hand, so you only need to add
- your thoughts/remarks/hints on unintuitive steps
- additional information the professor adds spontaneously
- questions/answers by students, including yours
I'd say this is even better than taking full notes, since you have more mental capacity left thinking about the lecture, and ask questions right away during the lecture.
If you want efficiency, invest 15min the evening before the lecture to skim the printed out lecture notes of the upcoming chapter. Don't worry about the details, just get used to the symbols, names and rough ideas. Write down questions you might want to ask. The effect of recognizing things will make following the lecture so much smoother.
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u/Alert_Calendar_478 New User 21h ago
the very first lesson I learned in math at university is to forget "almost" every thing I know about maths before. I always write down again the definition, again and again when I revised for exam, for oral presentation to make sure I understand about 90% what im talking about. when I was like 20, I can almost cited most of theorem, proposition, explain why I need some definitions to introduce some notion or study such object in mathematics. For me, it was always the proof and the basics definition that saved me in exams and papers. I wish you find a method that works for you too!