Thinking......

You delve through the insanities of what you learn to remove the shield on the classic yield of your efforts in learning the needful and then fly in the sky instead of staying dry. One thing I observed so far is that starting looks simple, just like the ending for the audience and the journey you go through, the one that makes you cram and apply balm to your palm like damn is when you’d feel the heat for real….pencil, eraser, sharpener, and plain papers. Its a whole another level of assessing your morale, zeal, tranquillity, ability, agility, and whole mindset, the ubiquity of which is unignorable. Be it reel-life or real-life scenarios, the bottom is the autumn for experiential learning, so joyous. So, to un-paralyze by shielding the inside function being an outside function, which engineered the field, I’d want to be in, gets to the point where, well, all this is diesel for me.

You can't generalize these curvy integrals without knowing what they mean, not being sure of the "w.r.t" and the ability to express in different forms to deduce it well. No, no, they ain't your questions yet. At least that sounded believable. Say, e^13ix is a part of an integral expression with some numerator, denominator, constants, and so forth. Ah, don't bug yourself with some cis theta, e^i*theta, and clearly, what not? Just pause, please. It's time for integration by substitution, so you chose t = e^ix; Firstly, think of another way of writing e^13ix. Keep aside the curvy friend, the e, the i, and everything. It could be written as (eAix)^13 ? Hmm. Ain't bad? Just very kind of you to acknowledge that. Even if you've been delving into completely different stuff before this, it don't matter. One should come this far to go ahead. Say, what if this is rotated at an angle? Laterally thoughtful. I like that. On the 30th page of your research work, if I ask you about the 12th equation, you won't be able to say, and you don't need to, except how you think it can be visualized to be like. You can't "remember" and go with questions that need self-check in the first place. Almost nothing may happen until you sit under that tree, stop the fan, sit in that room, play that instrumental, and have that accompanying environment. I don't think even I'm fit to ask you any if I haven't been a part of your work, with you in your process in some damn way and nothing like that.

Coming back, amid everything, the reason for outcry, as I've always felt, is that the "continuity" was dangerously inexistent. That is utterly wrong—a chosen laziness. Chill out, ease yourself and tone down the unhealthy vibes around but if it's a choice conscious enough since you are not sufficiently "moved" by anything so far and you got it now, move now, you know that. Take the call in a nutshell. On the other hand, you have vague, unclear, "brushing-aside," and random teaching. Worse than Brownian motion. Hmm, way worse. The epitome of clear-cut escapism and lack of justice.

If a humongous vehicle is required for certain needs, that's alright. Needs can range from efficient transportation of materials to the passion for cars, especially in the case of their technicalities (and not just mileage). However, think again if it's to show off success through this immenseness and technicality. If it's something you crave because of your childlike view towards it and childlike zeal to ride it, it's all right. The childlike fascination to go places instead of choosing to spoil it is best. The thing is about intention. The same applies to houses, provided you sometimes find the homeliness of this choice. It’s about time.

Inquisitiveness in how engineering expresses structures and equipment is worth considering. Not everyone can (and would) design and build anything as such if not for the stability and trust placed into how it won't collapse. The thing is, why do you want to remove it all and then, again, put it off when the expenditure you're wobbling about would be optimal if you'd focus on the materials and equipment you're unfortunately using? It's about optimizing. When you design, collect and build, you actually have a powerful and wholesome lens for looking at things. And "space management" is extremely important.

Be it the optimal dimensions of the system of a heavy-built and capable overhead tank, the angle at and perfection with which one should deal with welding, drilling, jargoning fittings in the system(s), and typical mechanical equipment(JCB, crane, other mechanical equipment and myriad of materials to construct stuff and larger structures and all), these involve notable mastery of technique and some real thinking. Safety is assessable—the vulnerability of airplane wings? Designing, with its miniature details, was already theorized. Well, isn't it about the detailing that you carefully do and observe with perfection?

Intentionally facing opportunity costs and Marginal Private Costs (due to significant others' inefficiencies) by living in nCr and nPr (no rushing towards Calculus for time-being outcomes, please! so chose to go through the time-taking leaps and bounds), when many ran sprints thinking they were marathons instead of the high count of the completion before even the actual theme starts and what could dy/dx of tan(theta) be (i.e., 0) (example) when Calculus already came to a dearly near end yields the final and real victory (P3) while experiencing the ‘thesis,’ health constraint, efforts of one-way traffic, diluted consumption of 19/24 hours, new, old marking way and step-by-step thing. I think that the purpose of literacy and education was to be around the lines of “ I want to join out here to envision and further experience those that create educationalists and, most importantly, self-contained learners filled with an abundance of gravitation towards ethics, traditional research and questions driven by inquisitiveness, all of which are intrinsic of an entity that lets the fundamental thought processes integral to research-based concepts flourish.” All this avoids the flattening of passion's curve as the one that of perseverance does, time after time, which can further disallow the students to overthink missed content/learning by frictionlessly learning from the very beginning, i.e., the main driving force.

We're good if the degree to which memorizing and understanding work out converges well by not just being a product of a sole bandwagon, i.e., merely inputting the substance. Going through the process of memory storage, which could be considered at a later stage in deeper dimensions, is fine. These divergent distinctions startle the mind to think about the nature of math and physics. The truth is that at least a few of us are intrinsically agog about what we have chosen amongst these STEM fields, which are engrossing, but we need the virtuous and unimpeachable or at least, scrupulous guidance, sources of learning, zeal, and perseverance (preferably at insane levels relative to you and not to some uncommon individual) to begin our genesis in here, the absence of which is making many (including those who have heard it and haven’t really experienced directly at any level) develop a whole new level of magnitude of aversion. This universal language, ‘Mathematics,’ has a definitive power to initiate lateral thinking, visualization, and design-based thinking and craft the purely proof-based or traditional engineering sector by shaping the mindset(s) to do so, particularly when it's considered the language of our miscellaneous ideas.

Again, some serious nostalgia, out of many years back

P.S.

By the way, I used to watch the "Let's solve math problems" YT channel. You can look into that.

Just not anything that'd complicate how this beautiful language is taught and mastered. You get habituated to a language and explore it to simplify and ease one another's problems. And it's also about describing beauty.

Those who constructed the baselines and reference frames didn’t drift with the fantasies and jargon that keep aside the substance when there is a chance not to. We're not doing hypergeometric stuff at all, so for things so way before it, you don't want to murmur and run over. Just one basic scenario and sub-titles for those that need to give out more lateral cases would be sad. Nature itself drove them, followed by the mere mortals. Imagine the insane quandary or even precariousness when they were starting and/or creating, but first, they’ve done what they are known for and then ended up specializing in the gravitating and/or intimidating areas. I mean, ఎంత చెట్టుకి అంత గాలి . As we go up and come down, it's to go ahead of what has been passed down to us by our universal ancestors.

I believe there is nothing to insignify but prioritize, and it's really about that certain instant in life(which would be many).

Let's start with this majorly babyish stuff. Though boring, they are quite adoring. As a kid, you may have thought so much, reasoned the best way, and wanted to know more, so all that was in your mind is what you'd like to feel again as you grow older. The thing is, put the continuum at the top of the game.

The indirectness resulting from what looks arbitrary to the core can be amazingly astounding.

"Engineering is 90% common sense," or at least a larger part of it is definitely so, and the question is how common this sense actually is.

It's fine if, say, this Cauchy theorem is not doing it for you. Consider it as it is and move on. Later, you can patternize all you've been through and create some linkage.

Ground strength, visualization, lateral thinking, common sense, knowledge, and then wisdom are definitely the paralyzed dynamics of the present human life. They're those that can absolutely help exercise the nature of Math, taking you to great places, provided how beautiful those mazes have always been. Perhaps, it's a matter of patience crisis (and I believe it sure is), so if it's better a bit(well, actually, a lot), math gets so "real" in no time.

Continuity, asymptotes, and lateral thinking are a few good traits of this insanely daunting language called Math.