I'm not whether I said passion is "pass + ion," so I'm taking this moment to say it out loud!
Here's one detailed advice/journal-esque write-up!
An irreconcilable gap between the prerequisites, the actual course content, and the fundamental knowledge required to succeed. No relevant prerequisites, just a system moving faster than you can keep up with, and learning materials riddled with errors and loopholes. If it's a high-credit class and there's limited timeframe, the journey becomes incessantly problematic and undermines confidence and comprehension. The one standing on 88 and the one on 78 will echo the same "That one? Too much of a project to meet milestones rather than actually useful". Regardless of whatever you are doing apart from the study, you feel the sentient through and through.
TL:DR
I've always done that "self learning", taking my own time doing thorough thinking, close and deep reads & giving it my own spin. Essentially, I preferred the reverse learning process very early in that level of a serious time crunch. Has it's own merits and demerits to be fair. What is eye-opening is the fact that unlearning happens to most of us, so we relearn better.
Passively consuming (as it is typically meant) over a solid amount of time adds to the “activity” and feels bigger than ever to your mind. This is organic for those who happily lean into analyzing and questioning what they encounter. It may be running in the background, there’s a subconscious ear working towards that, and we really care about how we tap into it. Our ears are taking it all in, and we are getting the work done at the forefront. What is passive is actually active in that sense. It's all in the mental time you feel you have and what your minds seems to be taking in.
Material should not just be learned but owned. But really, how much do we retain? And if we don’t retain it, do we ever actually attain it? Passive delivery has its value, though the more you rely on it, the harder active creation feels and that can scare you off entirely.
I’ve been writing for ages, whether it’s in emails { yeap, those personal drafts that still aren't out fgs. The interface feels good ;) } or in the MS Word app on my phone during a car ride (not here on this long-forgotten site cause the interface here is glaring for my eyes :o }, not even realizing it's something that can be out there. Philosophizing life to make it make sense is interesting for all I know. Reasonable? Considerate of instincts and emotions? It's in the sensing :) A wide variety of views and outlooks growing with the life that moves and grounded in a sense of responsibility.
Always wrote about what I consume passively, and that process of writing converts passive consumption into active engagement. When I write, I’m doing something with the material. That’s how I internalize it and make it mine.
What we’re able to reproduce is active learning, even if it happens subconsciously. At the same time, the sheer volume of information we absorb passively is equally important. Repeated passive reception is valuable because it keeps filling us. Unless I'm literally inactive, passive and active distinction doesn't worry me much, to an extent that I'm happy to have it the passive way.
I think learning is a process so multifaceted that you can't really sort out much. Let’s say you’re trying to explain a formula you just read. Suddenly, you’re stuck. Why? Because your understanding isn’t as complete as you thought it was. It’s humbling but necessary, and this process of creation exposes where the holes are.
Expose yourself to the material and try to use it. You'll be fine. Make certain knowledge and skills habitual first cause deeper understanding can come later. Sure, you may be having helluva time and could spend all your time deriving/investigating each and everything, but it depends on where you stand or you can just set differently spaced time slots to spend time however you like, so that the bigger picture is still around and the flow isn't breaking every now and then. Also don't negate the indirect and direct skills you gain out of this cool language called Math.
You're trying to learn how to cook, but every time you crack an egg, you stop to Google how eggs are formed and the chemical structure of proteins. By the time you’re done researching, the batter’s gone cold, and you’ve forgotten what you were even making in the first place. And this is what we fear, i.e. wasted time/discontinuity, lost interest and all guilty about it.
This. Why?
The deeper understanding can (and should) come later. Consider it is what it is (for now) and the Page 30 is waiting for you but you're still on Page 10, so you need to move forward to return soon.
Math is not a black-and-white box.
Math isn’t just the difference in thought between two people solving a problem but also the difference in your own thought when you approach the same problem again. Because, in reality, there’s a whole world in between.
You can have a checklist of the properties (of shape, build, etc) to verify. Sometimes, you can have an overwhelming proposition, but then another voice from me simplifies it, trimming it down to its elegant core. Then there are the ones you don’t know (at least, not yet), but under certain assumptions, they suddenly work. Before I know it, the room becomes a space of collaboration. Let the ideas spring up out of nowhere...something you didn’t even see yourself at first. Math needs to stop being something they're scared of and start being something they live.
Details, details, details. Neglecting them invites trouble.
Start before the official start. Yeap! There will be those pals with amazing experience who, after installation or quick revision, just need a few minutes to get back into the swing of things. There will be those who wrap up a PCB in …30ish minutes ? Be it software packages or the learning content itself, already start sipping a bit of that and whatever liquid you complement that with.
Life follows a non-linear path – it's a journey. It goes on and on and on. It needs your thoroughness.
Prolonged concentration is a plus.
Tune into your independence. Peek into nothing and see how it goes.
Regarding lateral thinking and imagination: try to approach problems like reverse engineering and "connect" different topics/dots you encounter. Please do so for your own sake! Imagination and intuition both are important. Generalizing and finding governing equations is great.
Better understanding comes from visualizing and it gets better day by day. Maths can be downright baffling at first glance. Over time and active involvement, you start to "see" things in ways that weren't accessible before.
Breaking things down to basics and pure doing help. Befriend common sense, build your own thought process and start before the official start, you’ll soon get the cushion you deserve.
Teaching is the way but not with half-knowledge...but honestly, do we know what's full knowledge? we're either unexplored, too rushed, or not thinking critically enough. Just brainstorm whatever you do know and start teaching everything around you..walls, trees, screens, humans, animals, whatever! This and my 'writing' does it for me.
Reasoning is a minefield of fallacies, exploding left, right, and center. Few think logically at all. The odds during the first time you try to piece together a coherent argument or derive a concept is that it’s a hot mess. Talk about reasoning so flawed it practically trips over itself, i.e. incoherent ideas, hole-filled and conclusions that hit dead ends faster than one can utter self-contradictory.
If you want to derive something, do it without looking at the derivation. I mean it. You might as well find other ways.
I recently entered Linear Algebra btw. Love the snake-looking integrals. Differentiate easy before them haha. I mean, Calculus and Algebra are little oases of logic and creativity things you'd love. I really would have preferred vector calculus (some Lin Alg helps FYI...welp, always ig...you can do without this if you're ok with vectors). For some, it’s just some manageable extension of high school math and for others, they might not have dabbled into Linear algebra or Discrete math yet. Say, row elementary operations are not as ‘elementary’ as they are called.
A 3×3 matrix multiplication could take you 8 minutes and a week later, you could end up doing so well in applying row elementary operations to different types of matrices. Row elementary operations was never a thing for me. It was a very blurry experience to begin with. Of course, eigenvalues and eigenvectors will only make sense if you proceed from here. Solving differential equations this way interested me. The determinants were cool, though. Their relation to areas, volumes, and linear transformations was fun. Dot product, cross product, and norms and inner products was a little bit more fun , especially when visualizing vectors in different dimensions. Linear independence felt like a stretch by that point,.. cause it was a mishmash of everything math excluding Calculus (came later). Learning to determine when sets of vectors are linearly independent and how they span a space was a bonus.
Start with a sane piece of mind. Keep it that way. Expect asymmetric distribution of time intervals spent in these myriads of sub-topics and umbrellas of finely spread chapters.
Pinpoint the exact constraints that are pulling you back and resolve 'em soon. We don't necessarily "love" it at every point in time. It really comes down to how you feel love, which imo is the good, the bad and the ugly.
Try earning good practices before the not-so-good practices get habitually ingrained in you.
Good practices…you’ll need them. Practice is for problems and scenarios that aren’t necessarily designed to make you think laterally, critically, and creatively. So don’t stigmatize practice itself by saying it isn’t enough. It’s a journey, and it’s important to do it across a proper variety of situations. You’ll psychologically ingrain these practices, shaping how you think and perceive things. It’s the muscle. Jiu-jitsu. It’s the thought that you want to feel all the feelings….yes, you should!
Funny thing is, I’ve always loved the so-called “boring” stuff. What’s typically labeled as non-boring has rarely amused me. For those who know me, I’m definitely not a boring person. I just find and add value to the most unobvious things, not the superfluous gibberish. And oh, if you’re very down (not the ‘I wanna be down’), I put in the extra, silly or sweet, effort to observe if its worth our time.
And wait, there is resource scarcity, in the sense that the pages you choose shouldn’t disrupt your peace or throw off your pace. Choose the "right" oneS. That book which narrates clumsily, drowns you in verbose descriptions, or uses uneasy notation/presentation doesn't need to be in your bag. The book needs to speak to you. Find your own way to the facts, and the book leads you to it. And hey, write those matrices BIGGGGG with plenty of space between the entries. Good space management is a lifesaver!
The safe balance amid high expectations and pressure.
Our eyes are like invaluable gems, our windows to the world; the only means to witness the world in a way that other parts of our body can't let us do, isn't it? With everything around us, maintaining their health feels like a Herculean task. Life has its way of hurling curveballs, testing our limits. You're here, you're fighting the fight, and that speaks volumes. One day at a time, alright? Above all, pets and plants are the best healing sources.
Identity in Academic Performance. This does not mean you amplify a sense of paranoia in you weigh you down. Let the work speak for itself.
Time Management and Prioritization.
The multiplicity of solutions to a problem.
To actually understand nearly anything, one language is indispensable – math. Advanced math is gold in Machine learning, too. Anything that sounds fancy is pain and pleasure both. Time to use this universal language, especially as we see it make our linguistics edgier! Embrace careful thought, lateral thinking and precise execution. Be weirdly driven about stuff that typically won’t ‘seem’ to pay off just yet.
It’s not a communication issue, because some of us reach a point where we forget words because math has flooded our brains a little too immaculately.
If you find the pacing of lectures too slow, jot down points or questions that pique your interest, then dive into them during your personal study time. If they're too fast, it's the classic case of "Um, what just happened?". A well-thought advice for you - Have a thorough look at what "will" be taught ; not what "was" taught.
Observe what you (thought you) knew in action. Bring in that momentum. Do that action. Pick up that pencil and paper. We always come with some familiarity, but when you are actively interacting with the happenings, you'll realize you just probably overheard the words or titles too often without actually caring to know what's up.
At some point, you can't find a "convincing" "answer" to "how." Better just begin now. You may not be early, but don't be late either. Start before the official start (a millionth time!).
Abstraction lets you cut through the clutter and hone in on the heart of the problem. But hey, Abstract math is pretty eerie :) The abstract world is, by definition, abstract. It can be tiresome ; sometimes a dessert, other times a desert. It's either a good thing cause the crux will be on your own way or it's too alienating to go through.
Proof? The real treasure, the goldmine, is in these problematic proofs. That’s where the real grind happens, the sweat, the mental gymnastics. It's rigorous, not rigid. It is actually a creative and expansive discipline that embraces limitless freedom of thought and approach, leading to the exploration of infinite possibilities and structures.
Quality of Resources, both human and non-human. Good resources and, by extension, STEM educators, can either greatly contribute to or detract from the learning experience.
Hard work is essential.. merely counting hours won't suffice. There's a difference between overall duration and effective duration.
It's not exactly about laying down concrete timetables, "getting" everything right and having a rosy paper of numbers. That's a whole other situation. Imagine you only need 2 hours for a task in one area (realm P) because you've already spent 5 hours in another related area (realm Q). This kind of interconnectedness is absolutely ok and better.
I know the "time frames" we have are pretty narrowed down and we are always on the run but dust yourself up and try again, i.e. you need to let yourself realize that there is dust on you and then, do something about it.
The alternate universe kicks in nearly every time. Don't perceive it as an issue and worry about "eradicating" it. Just put in the time, effort. It’s more of an action and an experience worth having, not the emotional and preconceived reactions we bottle up. Eventually, you’ll ‘get’ it - the things working their way into your awareness on a subliminal level. This process is like developing a "sixth sense", letting you connect the dots naturally as your experience grows.
Know where you stand atm and then, proceed. Without the bigger picture or because you don't get the problem context and the concept application just yet, you can't expect to rectify yourself earlier.
It’s particularly worse if you have been introduced to anything in the worst way.
"...They are more like alphabets. You want your memory to make up a word out of any set of alphabets." There are times when certain topics feel and are like that.
Often, we're conditioned to “get” "effortlessness" in understanding, especially when there is not a lot of time and when you think you know something too well (came across it so often that you’re barely familiar). It will be "effortless" and it can only be possible if you train it like a muscle and push through the irritating problems. Continue, don't abruptly stop. Lack of continuity often leads to forgetfulness. "Continuity" is what many miss, and as they pursue it perfectly, it's a new day every day, which is not necessarily a good thing…not in this case. You can't always go back to square one duh! So, yes, as you continue, the core essence emerges, and it's time to handle the heat. If you take a beat cause it's hard to handle, you should. You’ll inevitably return, drawn by the gravity of your passion, while maintaining your sanity. It’s like jiu-jitsu. And I get your temple aches and the sheer stress and strain. All in all, whoever is the effortless kind will up the game.
The urge to "understand it all" is insanely prevalent. Let that not put you down. You genuinely need to acknowledge the time it takes to feel confident and empowered. Familiarize yourself with the outline of what's expected and " with all that laid-back attitude " (familiarize like the breeze), proceed looking at them and working them out everyday. I mean, with a mountain on your neck, you've got to find ways to stick around.
Look around, try and reassess. But try not to go too far back to a point of no return, ok?
Imagine you're swimming. If you keep thrashing around trying to stay afloat, you’ll exhaust yourself. You’ve got to relax and let the water support you.
Take a beat and you’ll return with a fresh lens. This goes for when the fan has not only been hit but also yeeted into oblivion, i.e. you haven’t even partially accessed your math sense yet, and continuity is out the window.
Learning is not literally DIY to a point where hell breaks loose and you're holding onto no one. If something takes you so long to get through it, reach out, seek help.At the back of the mind, seeking help isn't usually that normalized. Again, learning isn’t literally DIY :)
You pick up some, you can't pick up others. I might as well say it’s worse with electronics, machine design and all things “engineering”.
So, you move forward to look back and then make it make sense for yourself. Don’t feel guilty. You're always engaged and thinking about it. And honestly, we don’t expose ourselves to as much as we think we do. If you haven’t had much exposure to engineering, you’re probably floundering instead of feeling the “flow.” That flow comes with cumulative experience.
Math, as a language, lets you rest more often than, say, Machine Design. Relatively speaking, it’s cumulative. Electronics, being a language too (but also an application….so beware of explosions!), isn’t any kinder if you’re a noob. Forget about programming hardware by cobbling together code examples, cause this will only lead to feelings of guilt and, for sure, disinterest.
'Relative' is the key..to a few words I have for you. Some have high bouncing back speeds leaving no stone unturned and others slog through the brightest mornings cause it's so dim inside of them. So I get what it means when I tell ya to know where you stand atm. You may need one more "concentrated" hour than a person ahead of you but that is all. You'll reach there soon.
Given the overview, ask all sorts of questions: what, why, how, when, and where. Define, describe, explain, exemplify, analyze, and evaluate characteristics, behaviour, functions, and applications and a variety of aspects you can think of. Trigonometry, Elementary Algebra & Functions (especially analyzing those various graphs, curve sketching & understanding domain, codomain and range, etc....) for sure. Get that foundation right. Your forte in algebra shows up when you pick up on Integration.
Maintaining Continuity, Clarity & Concentration - We are like asymptotes to our paintings; point discontinuities are common because we can regain momentum. The closer we get to our painting, the better we feel. See I searched the sky high and low (a song ref 😊) and I better keep track of the local minima and global maxima on my way.
What will creep in, will creep in. Music? Yes. Buddies? Yes. Think about what stimulates you. What is your stimulus? Observe.
Treat the process like a treat. Here's to what young scholars can achieve when they're given a problem, crystal-clear constraints/expectations, the tools, and the liberty to create.✨
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