Take Sparse notes:
Here's how I take notes when reading from a textbook
Section title and page number
Brief summary of what the section is trying to accomplish
Theorem/axiom names, brief summary, and page number
Any other significant subsection with brief summary and page number
For video lectures that have no accompanying textbook to go off of its trickier but still keep notes sparse. Write down video times where the professor goes over the topics, main point of topic, and the timestamp they do.
If ever you truly don’t understand a section in the textbook or the video when writing down that topic put a question mark by it. Go through the rest of the lecture / chapter and then come back after and look up that topic and make sure you at least understand what it's trying to do even if you don’t understand it mechanically.
Just don’t waste too much time taking notes, you have the textbook and lecture to refer back to at any time, you just need to point to where the important stuff is.
Always put some hours per day/week/(whatever study period you have) into doing your own projects. School projects are nice but there is nothing like actually making things yourself, starting from scratch and going through the whole design process, it can be little functions all the way through whole programs but I can not emphasize enough how you should make stuff. It will solidify what you are learning and force you to understand it on a practical level. It's easy to intuitively get how something should work, but you might find it a lot more complex to get it working when you actually start the project.
Alongside that, implementing things is a great way to check if you actually understand something, this is the whole point of homework and projects but sometimes it’s easy to forget that. There have been many times I think I get the concept a research paper is going for, start trying to implement it and find out I didn’t really understand it. At least not on the level of creating it, which is its own skillset to be fair.
It’s okay to not fully understand something the first time you go over it. If you are reading something in the textbook before the lecture, and the lecture doesn’t mention it and the homework doesn’t bring it up either you might be okay with letting that topic go half understood. The honest truth is you're not going to remember everything. I probably have forgotten a good chunk of what I learned in calculus at this point but I remember the important stuff because it keeps getting brought up over and over again down the line. Its like survival of the fittest for ideas, what ideas you need to succeed will be reinforced over time as you study and learn, what ideas you don’t will slowly die off. But you will be surprised at some of the random topics that come back out of nowhere in math, those seemingly unlikely connections are why math is so interesting.
Do use AI tools (ChatGPT, Claude) to help you reflect on homework problem solutions or clear up conceptual issues. Don’t use AI tools to tell you the answer to homework problems. Homework is trying to train your brain to work on hard problems and to think logically through them, that isn’t a skill you should outsource to AI or homework solvers. Plus you shouldn't really trust the AI’s answers yet on pure math problems as they still make some incorrect jumps in logic. But they are pretty good for helpful explanations.
When working on personal projects do use AI tools like Cursor, it will help speed up development by a lot and you should always be using the best tools you have available to you. Unless for some reason you wish to not use the best tools for some personal challenge but that is up to you.
The pomodoro technique is a great way to study. I usually do 50-10, doing 50 minutes at a time then a 10 minute break. Don’t adhere to this religiously, if you are deep in a problem and really focused on it, keep working on it and take a longer break when needed. It’s more important to follow your train of thought than to take a break in that instance.
That being said if you really are stuck on a problem take an early break and walk around, do something for a while and then when you come back to it you will probably do better on the problem or notice something you missed. brains are weird like this and get stuck in some weird suboptimal way of thinking about the problem that taking breaks can help reset.
Some days you wont be able to focus, your brain wont work, etc. That’s just something you have to live with and not beat yourself up over. Just try to rest and come back ready to start again the next day. Something you can do during this down days is explore, just look up random things you are curious about or ideas you have. Browse around HuggingFace or Github. You will be surprised how many ideas exploration will give you and new things you can follow up on in the future. Some of the best things I have found that I have really helped me stay motivated have been from these days where I wasn't able to study. Of course if you are spending a week or so not able to study, maybe that should motivate some greater self reflection.
Don’t rush. Through courses, or homework, or programming assignments. Don’t rush. You should be trying to do these problems right the first time. Take the time these problems need and really try to crack them, it will make you better. If you’re rushing and half-assing the answers to get to the answer key there is just no point in doing this. Remember this isn’t school, you are not accredited for this, you get no degree. If you cheat yourself here there really is no point to doing it in the first place. This applies to projects too. Big programs are not built in a day, making things takes time. Don’t get too anxious about a slow pace and then give up on the project before it is done, see things through. One time I was stuck on a problem for a few days and the solution honest to god came to me in a dream. Just keep trying and be patient.
Pull from many different sources to solve confusion, other textbooks, Youtube videos, AI chatbots. The more ways you can conceptually understand a topic the better off you will be.
Lastly just hang in there, learning is hard and math is one of if not the hardest things to learn, it’s okay if you don’t get it just keep trying. The only truly not okay thing to do is give up.