Thank you. I was explaining to my friend why in "order of operations" that multiplication and division were interchangeable same with addition and subtraction. And when i said "because basically theyre the same thing" she looked at me as if i was crazy 😂
@@savazeroa try solving 5+2*6 solely going left to right without using order of operations. That's how many eggs I collected from the chooks over the past 3 days, so there is a correct answer: 17
A future original 3B1B in the making, keep up the great work and amazing videos. Would love to see longer videos if it meant minimizing holes and gaps. Thank you for your work!
I always find it so odd that people struggle so much with algebra. Probably a result of it being taught way too late, as substitution is so basic that it really should just be taught around the same time as multiplication (and should be followed within a year or two by parentheses and factorisation, as they're another one people tend to struggle with due to how late they're taught.)
I see people struggling with Fractions, it's so easy, it's literally just division and people struggle with it, in my opinion they should only teach fractions and avoid pure division as much as possible, because in the future(High school) these people won't use "÷" anymore and will only use fraction.
@@reclaimer2019 you could probably teach ÷ when teaching other alternative notations like *, ^, and ↑↑↑ and just teach them like you would alternative characters in English like @, &, etc. Though you can always just teach both division and fraction notation simultaneously as different was of writing it, as ÷ is really important for factorisation, as 1/x(2+3) [2*(1/x)+3*(1/x)] and 1÷x(2+3) [1÷(2x+3x)] aren't the same thing [x=1, 1/1(2+3)=5, 1÷(2*1+3*1)=1/5]. You Can get around this with 1/(x(2+3)) or a long fraction sign that I don't feel like looking for the unicode for, but a division sign does the job just fine too.
@@reclaimer2019they should be taught that these are equal, also, the notation for a single line equation can get very messy, but it makes absurd sense. Like how 1/1+1 is different than 1/(1+1), but some people seem to not be able to recognize this.
People struggle with algebra due to the fact it makes no sense. This is because algebra in Western countries isn't taught systematically but with an adhoc approach. When we were going over equations we never went over what operations you can do to them. Also parentheses aren't explained well usually. For example something like this 5+(5-4) would be "incorrect" to solve as 5+5-4=6 even though the parenthesis in this case do nothing.
Got to hand it to you mate, although i knew these concepts beforehand, the visualization and most importantly your explanations were amazing, very underrated video, amazingly put
@@SbF6H the thing with these equations is that, if you dont know what it represents, its very difficult to reverse engineer what it represents even if you know the notation unlike some simpler equations. i personally didnt know it but its pretty easy to understand.
As a maths enjoyer, I have no Idea what a normal person would think watching this... But for me, I absolutely love this content! You display it very well.
16:04 well not quite. Because there is no way to get back constants that were lost in the derivative. So we add a constant labeled C to represent them. WARNING‼️:NEVER forget to add constant C!!
Not exactly... In math we cant but If It is a real scenario we can, for exemple imagine a car standing still starts moving we know It acelerating at 4m/s^2 so the intregal in relation to time would be 4t + c = v but the c is the initial velocity wich is 0 so we we know v = 4t (in m/s) so we figured c.
@@everyting9240 well, look at that, you DID add a "c" there. Yes, its 0, but that's the point. You did add it. And also, in all the situations of integration, THAT IS HOW "c" IS FOUND!!! By using constraints, (and pay attention here @everything9240) not just in physics, but in maths too!!!
@@thekiwiflarethey're right though. You often have to solve for the constant using known conditions, and that's a known condition for that case so it's easy to just plug in.
@@FunctionallyLiteratePerson yeah but that completely throws out the point of the original comment - you can't know the initial conditions if all you have is the final result
Not exactly sure why I watched the entire video, considering I've done all that in depth throughout my academic journey, but damn, that's an easy to grasp and extremely quick explanation to lots of interchanging mathematical concepts that I was taught through years of math classes. Honestly well done. Had this existed half a decade ago, it would have made my life way more "understandable" (definitely not easier - applying everything mentioned here to actual use is why proper education takes years, not 30 minutes).
I love why math works and I’m glad more people are covering it in depth. You should do mechanics next, it’s pretty easy to explain how we get the laws of motion and why things like energy are useful
This was… incredible!! I absolutely love your videos and how you build up concepts. Your visuals are spectacular and your explanations show an amazing and unique ability to communicate concepts in a way that is absolutely perfect for anyone who just feels like “they don’t get it” to have that “aha!” moment.
Quick note at 16:00, dy/dx is actually the derivative f’(x) Whereas if we want to do the action of taking the derivative of f(x), We gotta write out d/dx f(x). Think of d/dx as the derivative operator, Just like how x tells us to multiply, d/dx tells us to take the derivative While dy/dx = f’(x)
This is AMAZING. Thank you for making it. I've just finished an AP math course (basic 1st year math in hs ) and this went through and beyond all my knowledge 😅
I've messed with all of these functions and haven't felt like I've ever had a better understanding then right now after watching this video. I'm sure the average person will need more so please keep up the incredible work that you're doing!
if I were a creationist after watching this video I would have prayed for your good health tonight. But since I’m not, all I can say is stay away from the drugs because honestly, we need more of this. You never disappoint 🔥🔥🔥🔥🔥 oh wait i just realized that this is the result of frying your alkaloid receptors with caffeine , forget what i said earlier do more of them 🔥🔥🔥🔥🔥🔥
4:47 Just a minor suggestion. Perhaps avoid the combination of untextured red-green colors in your presentation so they are more color blind friendly. Suggestions: 1. Substituting one with blue or any other color combinations that are color blind friendly 2. Using differentiating textured graphics if you want to keep the red and green. (like the textured bar, columns charts in excel) Hope that helps.
16:04 There seems to be a lot wrong with this slide. There's no constant term in the integration. The differentiation also has the differential of y multiplied by f(x) giving the f'(x), instead of differentiation being an operator applied to f(x). Correction: The constant term is explained later in the video, so that is an understandable omission.
If I had a nickel for every time MAKiT made a video about the progression of maths I would have four nickels Which is certainly a lot more than the two that Dr Doof had
You are amazing! Edit: Also, mathematicians are not asking "why is that useful?", because that's for engineers and physicists or computer scientists to figure out. For mathematicians it is entirely enough to say "because we can".
This was just a lovely piece of art. I mean the graphics were just unbelievable. Picky question. How long did it take you to create this masterpiece? (And if it has not been obvious, you've gained another subscriber👍)
Thanks for real though I had some misunderstanding in calculus and trigonometry, and you clearly explained them while not making a big deal out of things that can be explained simply. Thank you again and hope you do well. Good luck with your channel and your future works. Peace!
Nice work! It unsurprisingly doesn't cover a number of underrated subjects because they aren't perceived to have enough use (different numeral systems, hyperbolic space, modular arithmetic, etc.)
Great video, very satisfying ending, still hate the fact that you wrote sqrt(-1) which is technically undefined and -1^2 = 1^2 forgetting the parenthesis. Love from Brazil 🇫🇷
30:43 thank you man. i feel so validated. i tried explaining to everyone i could that sines and cosines just don't feel usable. un-graspable and undefined. but here they are. in their true form. beautiful.
another way to write sin and cos: sin(z) = (e^(iz) - e^(-iz))/(2i) cos(z) = (e^(iz) + e^(-iz))/2 This format makes them easier to use with complex inputs z, can help you prove derivative and integral trig properties, as well as shows the connection to the hyperbolic trig functions sinh and cosh.
This didn't sit right with me and i kept mentioning it during the stream this was being made I personally would define sin and cos by their infinite taylor series, of course, the formula for the taylor series requires the derivatives of sin and cos respectively, but in the case of sin and cos they're nice infinite sums (for the maclauren series) technically, i think maybe this is a circular definition as the motivation behind taylor series involves the derivatives of sin and cos, and we're using that to define sin and cos, but i can't think of anything better- Defining them in terms of complex exponentiation would require a definition of complex exponentiation If you define complex exponentiation by plugging i into the taylor series of e^x, and then proving e^ix is equal to cos(x)+isin(x), (using the taylor series of cos(x) and sin(x)) you're still using the taylor series. if you don't want to use the taylor series, and just define complex exponentiation by euler's formula, you still have cos and sin in eulers formula! it's a circular definition! Please tell me where i'm wrong- i think i'm probably wrong
@@savazeroa @savazeroa no you're 100% correct, i noticed that in the vid as well that it seemed self-referntial and kinda reduntant but i guess he didn't wanna go on a tangent to explain series but yh defining them with their series expansion would be more correct than what is shown
I suggest you watch brain nourishment There's a guy making brainrot videos that talk about math, I don't remember the name, but he's really funny. You can look up one of his videos though (Jenna Ortega teaches u substitution or Taylor Swift explains the Taylor series)
already attending university for mathematics, but this video really makes me fall in love again with the subject. Thank you for sharing the beauties of mathematics with the world ❤
I’ve never learnt what sin actually was before, this was the best explanation possible presented at the maximum speed I could comprehend perfectly, thank you so much
8:48 minor correction - if the slope is negative, then increasing delta x increases slope. Similarly, at 8:33, if delta x is negative, increasing delta y decreases slope.
I can't say I followed everything about complex numbers. Mostly because you clearly rushed them over (and made that did) But jesus christ I did not see the transform twist coming that was genuinely best explanation of it I have ever seen. I watched multiple videos on the topic and as you can guess, none of them remained in my head at all but this, while incomplete, is such a good starting point I feel like I could go and write code for whole scheme right now. Would probably fail but still!
Great video :P, I was expecting a section for exponentials and logarithms but not really necessary for the last equation i guess, maybe just to understand what the euler's constant means
23:45 we very briefly talked about basic sohcahtoa last year in geometry class but this is my first time learning about trig with it being explained really well :D
If you break any field down to it's most basic parts, they're all "simple", but the complexity is derived from the amount and interactions of those basic parts
Hey dude! Great video, but I think you’re wrong about the rectangle. Unless the side lengths are irrational numbers, then you can still do repeated addition. Move the decimal place over three times in that case and you can still represent the problem as repeated addition. The only caveat is if you’re dealing with infinitely small or short lengths or irrational numbers.
Makit my man you did scare me 2 times during this video (i was sleepy/tired) But yeah I love the video you literally condensed all this into a sub 40 min video, that is big
Excellent animations MAKiT! Small tip right here- Just make your videos and titles more predictable. The transitions from topic to topic feel a bit without context or logic.
What about nonlinear differential equations? Even an equation with just a few commonly used operators can create a feedback system with extremely complex solutions. Some even cannot be solved at all using any known method. How about computational complexity theory? There is an entire group of problems where there is no known algorithm that can efficiently solve them, but if we were to somehow find an efficient algorithm for one, we can solve any of them efficiently. And it is impossible to create a computer that can decide whether any given program will eventually halt.
Interesting video. Few things to add: 1) Please don't write -1^2 when you mean (-1)^2... 2) Regarding the Euler formula e^(it)=cos(t)+i*sin(t), it doesn't just tell you that the point moves along a circle, but it also moves a long a circle in a constant speed. So the very weird behavior of the sine and cosine in one dimension is just the "shadow" of a very simple movement in 2 dimensions. For example, it is not that clear why the integral of sine over a period of 2pi is zero, and you need to do some calculus for that, but it is very simple once we think of it as one coordinate of a rotation at constant speed around the origin. Also, this behavior implies the important exponent property of e^(t+s)=e^t*e^s which stands at the heart of Fourier transforms. This is why, while you can do Fourier transforms using sines and cosines, the theory becomes so much simpler once you go to the complex numbers. 3) Finally, the Fourier transform is not an equation (as you said at the end), but a notation. Afterwards, we usually show that it has several interesting properties, and in particular the inverse transform, but it is still a notation (or more generally, a function)
