In other words, I know what to do in order to solve the types of questions we're going to have to solve in an exam, but I don't have a real, longer-term understanding of the concepts (or even much of an understanding at all when it's possible to follow steps to solve certain types of problems).
This is coming from a CS degree that teaches a lot of theoretical math concepts. Even for questions where you have to prove something, I often just understand what the proof should look like and what it should include, but I sometimes don't truly 'get' it.
It's also hard to find time to do deeper investigations into concepts when that time spent isn't going to increase my grade and will take away from understanding how to solve problems for other courses.
Does anyone have suggestions for learning things on a deeper level as opposed to just enough to complete an assignment/exam?
In one sense you have a lot of time now, but you are being drowned in new concepts and ideas. Too many to properly digest.
Goal 1 is to pass, and get your degree. Goal 2 is to set aside some time to explore and dig. You can't assimilate everything, but you can take this opportunity to see what excites you, what interests you.
Cast a broad net. I took a few electives that were "interest only" (unrelated to my major). I sat in a few random classes of random subjects. I connected with others doing the same major and we spent time going down rabbit holes together.
Mostly though, you'll have a lifetime of life. Sometimes you'll have no time (baby in the house) at other times you'll have gaps to fill. Without the pressure of an exam you'll be able to take all the time you need.
Turns out, I never really needed or cared about the math. So I don't spend a lot of time on that. Other things did grab my fancy, and I've gone down those roads along the way.
Most of all remember that learning doesn't stop when you leave. It's just getting started.
One is to try to come up with a project or experiment or use case where you're actually implementing some of what you're learning. (That'd also be a good question for a professor or teaching assistant: how do they use this stuff in the real world?)
One of the best career-building skills (for when you leave academia) is "information interviewing." That is, find someone who has the job you want, and ask them to meet you/have lunch, just so you can pick their brain about the industry. Yes, sometimes they'll know of a job opening that you can apply for -- but also, their perspective really helps you focus on what's important about what you've learned, and where to go next.
Also, I had a friend who started a study group teaching others the things he'd just learned the day before. He said it was great for him, because it made him restate everything he was learning, and be ready to field questions and give examples.
Yes, a life time of learning. After all, it took us at least a hundred years to come up with most of that stuff you’re cramming.
If you cannot find a social nerd club to talk it out, try an LLM! Or strap promptfoo on ollama and make your own nerd social club! (https://ollama.ai/library)
to give an example from my own experience...if you were to learn electronics at university or even school VS learning yourself...how low would the standard corpus go??
would students sit and play with magnets, build electro magnets, build a levitating system, wind their own coils and inductors? make an electrolytic capacitor with salt and metal plates? make a loud speaker from scratch (that barely works? but gives you a huge AHA moment??)
i think university in general is just not run to allow the free spirit of roaming and play based learning to happen....of course you feel like you're not learning, you're quite literally just jumping through hoops to get a certificate...imo.
the gist of what im trying to get at - and particularly why i started this comment, is dont fool yourself into thinking you "get the basics". I have been an audio nerd for 30 years, and i just watched a video the other day which showed how to make a loudspeaker with a piece of paper and some foil and magnets....only then did i REALLY get what was going on. Same with maths...can you calculate in your head? all manners of things?? your basics probably suck - get better at them.
- Build a CPU from scratch
- Design electronics (PCB)
- Create a programming language
- Build a website
- Create an Operating System
- Build open source software
The method of action is the most effective way to learn something.
You don't learn for the sake of it, you learn exactly to be able to solve problems.
If it's too easy - find harder assignments. They will give you "deep" understanging eventually.
Can always take a comparative semiotics approach to Western academics (based in classical logic). aka enumerated point forms/abstractions/rules in CS vs. enumerated point forms/abstractions/rules in construction science/art (not just the 'geometry'/color schemes).
Perhaps at end of semester, use above to envision how related forms/abstractions/rules of classes taken get used/interpreted in different discipline contexts (say relative to CS degree -- autocad vs. lisp vs. lisp for linguistics). aka a disciplines context for lambda/iota/epsion calculus.
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bit advance starter example idea (with 1st,2nd and 3rd order classic logic):
'concept of pixelated art' per different disciplines[0]:
So, picking on calculus formulat that's easy to integrate once know the 'trick':
integrate e raised to the floor (b/2 - a/2) --> gives spread sheet grid with anti-lambda diagonal.
For this exercise, the grid, less diagonals is the conceptual initial state of spreadsheet.
Keeping things simple, dark square is "1", colorless square is "0"
1) Using 'art' on the above formula, can create a picture with the bounds of b & a via flipping squares dark.
2) Using physics on the above formulat board, "qubits', can flip the diagonal slop to indicate dark square used in picture. (or 'baud' the modem constellation for something less b/w)
3) So, how to speed things up with CS.
* Awk with regular expressions to generate delimited file (of size within range of (b,a) ). import each delimited field to (1:1) corresponding spreadsheet cell.
OR dump the phyiscs angles and 'sed' angles to cell color and reimport.
Read in the (b,a) grid into tree. Break tree up into regions of contiguous groupings with start of tree in grouping as index in an array.
Test with [1]. Perhaps auto generate things like [2][3] and/or create a compile to python/javascript/awk gcc extension.
[0] : https://www.youtube.com/watch?v=CG5UAwnaBoI
[1] : https://www.kevs3d.co.uk/dev/lsystems/
[2] : http://www.ioccc.org/2012/tromp/hint.html / http://tromp.github.io/cl/cl.html
[3] : https://www.media.mit.edu/projects/2d-an-exploration-of-draw...