The 7 Levels of Math
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- čas přidán 15. 06. 2024
- Discussing the 7 levels of Math.
What was your favorite and least favorite level of math?
00:00 - Intro
00:50 - Counting
01:42 - Mental math
03:02 - Speedy math
03:51 - Adding letters
04:54 - Triangle
06:09 - Calculus
07:25 - Quit or Finish - Krátké a kreslené filmy
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I love how calculus is seen as an end or a final boss, but if you actually get to study Maths in an University it's literally just the beginning, and realize it's just an specific case of some really, really abstract topics.
All the math simps are coming out of the woodwork smh 🤦♀️
Edit: Just in case it wasn’t obvious this is sarcastic and I have a great appreciation for people who are good at programming and maths because it means I don’t have to do it. I’ll stick to music and graphic design.
I mean I think calculus being the beginning of uni math is bad. I'm from Jamaica and we do logic and proofs discrete math stuff that calculus
And then uni math is really the analysis stuff and the algebraic stuff unless your school has like undergrad topology or something and half of them don't need Calc at all
@Average man if so, why did he even bother with his level 7, “quit or finish”? It’s so nonsensical that he’s asserting there’s absolutely nothing after calculus
It's not that specific, calculus is about any rate of change. Simply talking about the speed of something is a derivative
@@Tisamenfeu He means calculus can be extended into more abstract objects that are analysis type things
Hate to break it to you, but calculus is the start of math, not the end. Also, an understanding of math allows you to learn science much faster. There's too much science to learn and you'll never learn fast enough without math. If you hate it, you likely just didn't have good enough teachers and so you warped your frustration into anger so you didn't have to feel bad about yourself even though it probably wasn't your fault anyway. Nevertheless, if you see something like calculus as inapplicable to everyday life, that simply means you don't understand it well enough to apply it.
As an engineer and a scientist I vow for this. That's so true. All the math you have learned before calculus are just the basics for preparing you to the beginning of the real math world, that starts with limits, derivatives and integrals, but expands to many things such as differential equations, linear algebra, calculus with complex numbers, alternative systems of coordinates such as polar and so one.
nerd
@@ralph7605 ofc, but hes still right.
So true!!
Hate to break it to you, but he is rating it by difficulty and the order he learned it in
Bro really said "Calculus is the final boss of maths 😭😭".
calculus is nothing compared to what is *actually* hard
Calculus is the start 😢(based on other comment)
@moh6410 the true final boss is algebraic topology 🥱
@@christophersoonah for me its Differential Geometry. Algebraic topology is rather difficult too.
HAHAHAHAHAHAHA. That's the best way to know a person knows NOTHING about Mathematics.
As a senior math major I have to say: Calculus is only the beginning of your brain being forcibly re-wired. Calculus is still relatively computational (i.e. you can still learn an algorithm or equation and just run some values through it), just wait until you get into Abstract Algebra (Group Theory really) or Proofs and Analysis, THAT'S when the training wheels come off and you have to actually learn on your own how to derive and understand the world of concepts and logic that Mathematics is comprised of.
is doing proofs in high school not common or is this a different type of proof? we did a lot of the trigonometric identities and also theyd give integrals that we wouldnt be able to solve on our own and you just had to use a bunch of trig to get it to look somewhat like the answer and then you could go from there.
@@jonathanodude6660 Proofs are normally something you do in undergraduate math courses.
Yeah.. I'd say too much of current math focus is on computation (let computers do that!), and too little on modeling and applying it to the world around us. So students can go as high as calculus and not understand what it's for.
Some fields of computer science are good for teaching you what things are for like: CG, and like AI.
Idk basic abstract algebra seems easier to me than calculus, though I am not sure if my course corresponds to calculus or real analysis bc it's not english
@@jonathanodude6660yeah, same I had trig identities but i just memorized them because my teacher reused them.
I once heard someone say that once a kid in his class asked the teacher "Where will we use these in real life"
The teacher said "You won't but one of the smart kids might"
That's harsh to say
But it is the truth
The violation.
Savage. But still, that's not really an answer
Math teaches students to think logically and solve problems. Many people don’t understand the utility of math classes because they never tried to.
Grade 1-8 math is used everywhere whenever numbers are needed (measurement, construction, etc)
Then high school math is in the iffy region
Some are still necessary such as interest and statistics
Calculus and beyond becomes a matter of solving diff eq that models a lot of things in the real world, being able to describe patterns via group theory, being able to linearize and preserve as much information by linear algebra and lastly be able to criticize existence, uniqueness and properties of answers via analysis
Logic and topology are also useful to think about what’s important and how to loosen some restrictions
Geometry is too rigid that it’s impossible to construct a Torus with geometry
Additionally certain ideas tie math together such as the Euler identity and how the fundamental group of the circle is really just integers
Here are the actual 7 levels of math:
1) Arithmetic: counting, adding, subtracting, multiplying and dividing, up to and including multiplying and dividing multi-digit numbers.
2) Basic Algebra: solving basic linear equations, solving systems of linear equations, basic algebraic manupilation including applying the distributive law, fractions, negative numbers, square roots and exponents, along with appropriate topics in other areas such as Pythagora's theorem and basic divisibility
3) High School Algebra: basic polynomials, quadratic equations, trigonometry, congruences, functions, linear algebra, basic group theory, basic combinatorics: permutation, variation and combination
4) Basic Calculus: limits, single and multivariable calculus, basic differential equations, basic topology, more advanced group theory.
5) Advanced Calculus: Fourier and other transforms, Green's functions, Stoke's theorem, manifolds, Lie groups, tangent spaces. Most scientists outside of math and physics will stop here.
6) Advanced Undergrad Math: Noether's theorem, gauge theory, Galois theory, vector bundles, differential forms, de Rham coholomogy, Dynkin diagrams and a bunch of other stuff that is already extremely esoteric. This is usually where physicists, except certain types of mathematical phycisists, jump ship.
7) Graduate and Research Math: Incredibly technical to the point where only specialists in that particular field can read and understand papers. The jump from Level 6 to Level 7 is probably the biggest jump of them all as it requires a lot of adjustment. The concepts are incredibly difficult, to the point of being barely understandable, due to them incorporating a ridiculous amount of mathematical ideas inside.
7) honestly impractical but highly specialized and theoretical topics like: combinatorics, number theory, mathematical notation-based concepts like set theory
almost like a jump from math to philosophy
I’m about to dive into levels 4 and 5 at University next year with my Civil Engineering curriculum! I’ve loved math so far, especially Algebra and Trig. Looking forward to diving into Calculus and it’s applications in my science and engineering classes.
I liked reading this, thanks for writing this.
I’m still at my first year physics undergrad and I’m already the level 5, can’t wait for the level 6 bruv
@@bringbackthedislikecount6767 the maths tends to calm down after first year tbh and stays around roughly that level but a bit higher, look into linear algebra if youre going to study quantum though
As a scientist, all of my frustrations and blunders had one single source: I didn’t know enough math.
Yep. Half of the frustration is "I don't know how to properly deal with this" and the other half is "I know I once knew how to deal with this, why can't I remember now?", with a tiny slice being "I know exactly what I'm doing but the calculations are extremely long and tedious".
@@Anankin12 wtf bro you really described my brain during an exam or solving practice questions
5:33 Fun fact: sine, cosine, and tangent are actually way more relevant in circles than triangles 👀. After all, when you're measuring the sine of an angle, what you're really measuring is the value on the y-axis of the point at the intersection of the circle's circumference and a linear function going through the origin, where the origin is the point of the angle. The cosine is that point's value on the x-axis. This is used *way more often* especially in physics.
Wait fr?
@LannieBaby Yeah this concept is called Unit Circle
Memorizing the unit circle makes trigonometric problems much easier to deal with. 11th grade me fell in love with it.
@@LannieBaby yessirr. Using a right angled triangle, you can only find trigonometric ratios of acute angles. Using a unit cirlce makes so much more sense. All sorts of angles fit in
@@CoolCatDoingAKickflipim in grade 8 and i dont have to use it but its very cool
I have taken over 40 mathematics courses past calculus 3, and what you described as level 7 is where real math starts.
Exactly he has no idea what he’s talking about
40 MATHEMATIC COURSES WTF HOW OLD R U
He is talking about the average person!Not everyone studies maths in university!GOT IT?
Elo guys I'm a kid in middle school. I'm here because I want to ask you(my seniors) a question
As you can see this is simple math which I clearly fail to understand (╥﹏╥)
Example 8: Two persons take steps of 80 cm and 90 cm respectively. If they start in step, how far will they walk before they are in step again?
Please can you help me in understanding the question. I am weak in English and cognitive ability as well. I'm so sorry for the trouble😰
@@klaou9154 In the grand scheme of things though, calculus is truly only the start.
Math isn't just about numbers and that's the reason why so many people hate it, instead it is all about logical reasoning, results that conduct to other results and if we keep teaching kids only to multiply or divide faster instead of making them actually think, they are bounded to hate math.
You see the problem is in soceity we value illogical insults to the human mind more than rational thinking and this is reflected in soceity, and school mirrors soceity thats where actual problem lies
In Math, I view the number side of things as the main base line of math. The full letter formulas I view as rules and thinking processes not in numbers, but just like an instruction manual. I then view any mix in between as a regular math problem… as for geometry, I can solve that in my brain, and I don’t view it as numbers, variables, or anything else! I use my imagination to construct real life results of figures. That’s why I used to get solid A’s until Algebra 2, it was because they are trying to to the find the answer thing instead of jumping to the rules symbolized. Because I can visualize symbols better than numbers.
I would strongly suggest that people try to view mathematical numbers as a real world scenario type of thing. And symbolic math as a more imaginative type design. Instead of using mathematical to solve them. I say this because by knowing what the symbols mean and do, you can better figure out a problem faster and better than wasting time constructing the answer as if the symbols were numbers or representations of numbers!
I HATED math when it was about calculating and speed. Calculus is a lovely thing though.
That's why math reforms were introduced I guess which the trad math tribes hated it and waged a war that divided the algorithm ritual religion and hereforth created two different religion.
Yes, I realized this and a lot of things suddenly clicked.
Unfortunately, I don’t think anyone fully immersed in Tik Tok Funny Dance Land is going to be well equipped to deal with math’s logical side, or really any sort of problem that demands analyzing more than 10 things at once for any reason.
The funny thing is that everything prior to calculus is just one large toolbox of random information that is needed to get started into mathematics (or any real depth of any natural science subject). Then after you get through the tool box, you can then start really doing fluidly connected topics like the series of calculus classes used. With this you can branch out into all sorts of topics (linear algebra, modern algebra, matrix algebra, graph theory, etc etc etc). Calculus is the beginning not the end. The saddest part is that the school system makes people hate math at the tutorial levels and so no one ever gets a chance to enjoy the real game.
One very important tool is proofs, but those are not taught in high school.
I mean to be fair the concepts taught in school are reasonable, you don't really need to teach proofs and anything pure in highschool. Although I do think more emphasis on probability and statistics is more important than calculus if I'm being honest. Reason being the relevancy to a wider range of majors (Other than STEM)
I loved math so much as a kid, then for years after my Adhd got bad I thought I was bad at it and thought my passion left, and only in the last year since I've been diagnosed and treated for it I found out that I do still have that passion and love for it, and I'm now retaking my precal and statistic 1st year course and building up my skills to where they were meant to be, and I must say, I think that the love of math is something that can be deep in us and present itself as long as you're under the right circumstances.
I agree
this sounds a lot like a "school made me hate math" problem, once you start to study math alone it's much much more easy and fulfilling
School def makes u think that maybe I should take things into my own hands and study for myself. The pain of school ed is that it makes u suffer because of its irrationality.
exactly, being forced to do something just takes the fun out of it.
I thought I hated math in highschool. I was able to stop taking math classes in my sophomore year of high school since I could transfer my middle school credit for Algebra and Geometry, and I only took the bare minimum for my first couple years in college. Being exposed to math at the college level and especially stuff at and above the level or calculus made it significantly more interesting to study.
Yeah, agreed. Engineering major here. As you figured, I need the math. That said, I was sitting in the summer just before I started and touched Calculus for the 1st time. To prep though, I had to make sure I at least could do all of college algebra (I knew it would contain trig stuff, but I thought it'd be a mostly casual dabble in it being a 1st class). I began to love it, because what made me love math was filling in all the weak points I had in my understanding. It was that feeling of allowing myself to be empowered that made the suffering through feel worth it, because I could see the applications. It also helped that my father's college algebra book, the one I used, had many examples where each given section had a real world circumstance for about half of any problem set. Today I was trying to figure out how based on relative altitude you can figure out where your horizon line lays if you are of course viewing the world as a perfect sphere. This also helped me realize that because of the way that works, you'll never be able to see 100% of a hemisphere of a sphere at any given time. All from the geometry I've been refreshed on periodically throughout the years and some vague intuition with vectors and limits. When you decide to push out to try to solve some of your own problems, that's when the truly interesting stuff begins.
Exactly
We've known the 'why' for millennia, and we've used math to advance our society to where it is today. Every single topic you learn in math, especially calculus, has hundreds of applications used in a variety of fields. If schools stop teaching math society will eventually crumble, which is why nations strive to teach it to everyone.
Yes, calculus was literally a consequence of asking questions like:
-How many meters did I travel, if I walked at 2m/s for 10 seconds and then I started to speed up to 5m/s in 3 seconds and maintained that speed for another 5 seconds?
-How much water can this bottle hold?
That's the why, it's something necessary to explain the world, but we never get a teacher in highschool to tell us something like that, because most teach without any passion.
Then tell me ... Why are humans driving themselves to extinction? What's the point of advancing forward if many are falling backwards
tbh I believe that math/science subjects overall improves general intelligence (critical thinking skills, etc) and that therefore this is why we're doing math, not because it has some direct advantage, more of due to the indirect advantage of not having generations of dummies who can't come up to rational conclusion on their own (+ also develop an interest for the subject in some students so they can get involved in whatever math related job later on)
Yeah calculus should be taught in high school!
In my country, math lessons have been gradually replaced with more humanities, such as the official language of the country, when the majority doesn’t speak it, but you have to know it. As a result, during the final high school exams, probably only 200-300 people from the capital choose maths, and the whole city was at the same examination center.
In my sophomore year of college, I took differential equations, my teacher told us that the stuff we were learning that year was where the applications of everything we had learned before would finally make sense and she couldn't have been more right. Everything in algebra and calculus is theory, built on the fundamentals, that once you master, you can apply to real life situations. I definitely agree though that it has to do with the teacher more than the student. My first 3 years of high school I hated math and barely understood it, but my senior year I moved to a different school and the teacher there did everything in her power to motivate us and make sure we understood what we were learning. That was when I decided to be an engineer and when I really started to fall in love with math
Ironically, I think the best part of math is when it gets abstracted from actual calculations and is more of a hypothetical collection of thoughts than anything instantly applicable (e.g. multiplying numbers). I wasn't very good at doing the simple stuff, when it was all about learning and practice and in my personal opinion, thinking really about abstract logic and going deeply into the "why and how?" made it interesting in the first place.
The thinking stuff makes it more a puzzle and definitely more fun than mind numbing series of multiplication questions.
The weird thing for me is that the exact opposite thing happened for me! I wasn't a big fan of math from grade 1 to 5. I started to really like it from the second part of grade 7, when I stopped getting lessons that required rigorous arithmetic. My love for mathematics only grew *exponentially* from then on. I loved trigonometry, co-ordinate geometry, complex numbers and other things that didn't require rigorous arithmetic, but more of your brain. I also started learning Calculus in grade 8 through videos. I can now do integration with basic techniques like trigonometric substitution, u-substitution and integration by parts. I love and I mean, LOVE calculus. It's so fun and perfect for my brain. So, I guess it's really different for different people.
Edit: 343 likes and 21 comments, Wow! I love numbers in the form x^3 and 3x!
well, author's love for mathematic was also growing exponentially... but with imaginary rate...
@@dimastus Yeah, started growing with a factor of i from grade 6.
Holy fuck exactly the same here. By 8th grade I had finished Calc 2 and 1 and in now working from a university Calc book instead the regular school books. I’m almost finished with it and can’t wait to move on to differential equations!!
Me too!
bro saaaaaaame, math gets so interesting once you get to the higher level math. Its a new lens to view the world.
I think the why is to let a few people into highly mathematical subjects, in the first grades of school I struggled alot with math, then I gradually became better, this led me to choose a stem university. If it wasn't for the initial pain, I would have never taken this path
the why is actually to teach people how to calculate things instead of going with their gut.
@@dablob4491 in the same way, people never pick up conceptual math and therefore struggle
I used to really hate math in the first 13-14 years of life.. it always brought my scores down. And then I stopped giving a fuck about my scores and tried to understand how stuff worked out, it really made me feel good about the subject itself. It's beautiful
Okay now I finally understand why school required me to do astrology on words, like seriously I was great at math but that shit prevented me from getting into a stem uni and now I am in engineering
@arougueburrito7111 We should blend the two learning methods
Level 1: High school math and calculus
Level 2: Undergrad degree
Level 3: Masters degree/Early grad school
Level 4: Phd
Level 5: Postdoc/industry researcher
Level 6: Associate professor, established researcher
Level 7: Full professor
Level 9: Terrance Tao and co. (The elites of math)
Level 8:Have a break,have a KitKat
@@CZcamsUser-yl9ys level 8: hyper AI. Writting billions of pages that proves Goldbach conjecture, can be verified by computer based automatic logic check, but none of human beings can understand it.
Level 7.1: Quaternions and advanced analytic continuation Level 7.2: Octonions, Sedenions and Triginitaduonions Level 7.3: Cayley-Dickson Construction, Cardinals, Ordinals, Surreal and Surcomplex Numbers, Number system creation, Modified Cayley-Dickson Construction
Level 8:
Applying all of this to physics: Wave-particles, string theory, quarks, gravitons, preons, multiverse, omniverse, complex probability and statistics
It's kinda funny cause in reality the math you learn up to high school is just prerequisite. Math pretty much begins at calc 1 and linear algebra. My partial differential equations professor used to joke that whenever we had a problem that would simplify down to something with just vector calculus or below that the rest of the problem was just "stuff you learned in kindergarten." The truth is that it takes a lot of math to understand what math is really useful for.
Something that I think would help with the "why am I learning this" problem is making linear algebra the first university math class rather than calculus. I use linear algebra sooooo much more compared to how much I use calculus. Calculus is largely a tool for dealing with physics; the most use I've gotten out of calculus so far is fourier analysis and the sturm-liouville problem.
Also, I believe people have a fundamental misunderstanding of what math really is--math is logical reasoning. Numbers are a small part of math, and the ability to do calculations fast is just "technical ability." Being good at math is being able to craft logical arguments and perform logical reasoning. I've had a few proof-based math classes, and it's essentially like writing essays.
In fact, guidelines for writing proofs (that I remember) are the following:
1. Use words when possible and not symbols
2. Never start a sentence with a symbol
3. End each thought with a "."
4. Be clear
In other words, its a formal argument.
Should I learn logic statements?
The people who often ask the question: "when will math be useful" are usually also the people who get 0 benefit from their math indeed. Its a self-fulfilling proficy.
I constantly use math and loved learning it. Need geometry all the time. Integrals and derivations not that often but it happens. Just using formulas and switching units mostly. Its crazy how much you can estimate with some basic math and knowledge.
The things you are talking about can skilled easily in minutes on google rather then grinding your brains for months in school
@@blckcosmos you cannot learn math "in minutes" on google. You only think so because you spent a decade in school learning, and then look back and think it was easy.
The process of schooling is long and grueling for a reason. You cannot teach calculus to a child if you do not teach them adding, subtracting, multiplication, division, ect.
People are mistaken when they say Calculus is the end of math, in fact, it is the beginning. Everything you have done was the setup, it was giving you the tools.
@@CMT_Crabbles i agree with you but also disagree on part of cannot learning from google cuz if you try once rather then seeing the comples wording of books a person on internet can explain you that sentence in seconds rather then try to understand that specific thing take hours
@@blckcosmos You may "learn" something from google, but School repeats what you're learning and makes you fully understand and master a certain topic. If you do a few problems on Google, get them right, and then go to bed, you will probably wake up the next morning without a clue of what you did yesterday.
In daily life, maybe higher level maths aren't going to be used, optimization if you really want to be efficient with something.
But, if you are going to build an embedded system, graphics engine, anything that's cool, oh boy, you're about to use a hell lot of math, and there is not such thing as rewarding as solving a hard problem in paper and then see it working in real life.
There is always one purpose of mathematical education: the training of the mind!
Additionally, math is like Dark Souls, hard to get into but once you're in, you start to see the fun, practicality and magic of it.
So Brain day = mathematics classes 💪💪💪
fun? bro you high
Greatest analogy I've ever seen
To get to your Plin Plin Plon, you may learn all basics and practice them well enough.
bro u on drugs
I'm the other way around. I never liked maths between ages 3-12 but then trigonometry got me interested and when I was 15/16 I had decided to learn the entire A-level course before I'd even taken it because I was so fascinated. I'm now studying it in university and it gets more interesting every day
Now that i have passed my secondary education, and am learning maths and proceding towards calculus.
The thing i want to talk about is that ,now i am learning how to solve logarithms,advance exponents problems ,sets
And it feels pretty amazing that now i am practicing how to solve them and later on i will use them as a tool for getting my work done. Its a incredible feeling for me
Currently in Calculus 2 struggling with different methods of integration... BUT I am having the time of my life because I have people around me and good professors that have taught me to not give up. I wanna be a civil engineer one day and hopefully I'll apply this stuff in my future job
You got this man
I feel you brotha, hope you achieve it
Four words: black pen red pen
Integration is only important for the concepts and to develop understanding of what it is
You never actually have to compute an actual integral (especially since it’s always approximated by some form of Riemann sum)
I personally found Calc III way harder than II. It requires a lot more visualization and conceptualization which Calc II has a lot more pattern recognition. Seems like most people find one pretty easy and the other crazy hard.
Imagine if this man takes a proof based math course
He already has
is doing proofs in high school not common or is this a different type of proof? we did a lot of the trigonometric identities and also theyd give integrals that we wouldnt be able to solve on our own and you just had to use a bunch of trig or substitutions to get it to look somewhat like the answer and then you could go from there.
well i have a course and 90% of the content is: theorem => proof => theorem => proof => ...@@jonathanodude6660
@@jonathanodude6660 Completely, utterly different.
A proper proof will incorporate quantifiers, negated statements and use equivalent forms in order to prove or disprove certain statements. They will typically cover at least 1-2 blackboards for basic proofs (eg proving why pytaghoras' theorem works) or several depending on whatever it is you're trying to prove.
It's like having to learn an entirely new language.
This right here isn't even a proof. It's a statement.
∼ (∀x ∈ S, R(x)) ≡ ∃x ∈ S, ∼ R(x),
This reads something like:
Not all possible x values that are a part of the set of S or the function R
then there is one x value in the set of S which is not portrayed by the function R
It's quite frightening at first because this looks nothing like school math anymore.
Proofs in general get rid of the whole x²+2x+1=2 logic you might know from school.
@@Anon-io3nw ah ok. Our proofs were 1 or 2 pages at most and I don’t think they were from first principles, we always assumed most high level identities and such unless that was the identity we were proving. We only did proof by induction and contradiction I think and maybe one more and I remember learning about the converse, inverse and contrapositive of a statement in order to be able to determine if something is proved or not but I don’t know most of those symbols other than for all and element of. I probably knew the triple bar one at some point but I did that course 7 years ago and my current course hasn’t used it. Unless it’s as simple as “is equivalent to” or something.
I would say though I loved doing proofs in high school. I wasn’t frightened by them or anything. I enjoyed being able to use things I knew to work out other things. Like this year I was assumed to know the identity: sin^2(x) + cos^2(x) = 1 and I didn’t know it bc it’s been 6 years since I’ve used any identities at all, so I had a look at what sin and cos meant and I got (O/H)^2 + (A/H)^2 which I rewrote as (O^2 + A^2)/ H^2, then I immediately recognised Pythagoras and so I could put H^2 /H^2 = 1 and the feeling from doing high school proofs came back again. I think maths can be beautiful when those kinds of things pop out of nowhere. I understand geometric interpretations a lot but I really struggle I think when you use a drawing as proof like the (x->0)lim((sinx)/x) proof with the tanx line and everything my mind just shuts down lol.
Something I want to drop here is that there is more to math class than just numbers and calculations. An import skill that you are also taught, but no one tells you about is 'problem solving'. Something everyone needs almost every day in his life. imo
So you can word it better in the future:
Mathematics is a numerical representation of logic - something any human uses daily hundreds of times. It's simply a way of training different logical and problemsolving skills. "Adding letters" as this guy in the video ignorantly put it, is the mathematical way of being able to structure logic without full knowledge, and using said logic to then arrive at the full knowledge.
as a physicist i love maths and i don't understand why people hate it. It has so many applications in careers: physics, engineering, science, computer science, finance, business, IT etc.
To me the more abstract math becomes the more I love it. That's probably why algebra is so easy for me.
me too
@@NotChinmayi same, currently in topology and knot theory
Algebra isn’t abstract at all
@@your_-_mom linear and discrete are both branches of abstract algebra, so yes algebra can be abstract
@@your_-_mom show me what a variable looks like
This is so funny yet sad to watch as a mathematician. It's sad for me to think most math teachers (and even myself) are unable to teach math by motivating enough or helping understand it easily.
Math has always been about solving scientific problems. From finding the distance to something using angles (trigonometry) to the unsolved problems of today that relate to physics or cryptography (which one can only try to solve after landing on a PhD in Math)
If I may ask, just generally, what was your dissertation on?
@@MercurySlugger The Banach-Mazur Theorem and other isometric embeddings of metric and normed spaces. Basically a theory of classifying those spaces by proving you can put them inside a particular one, like C([0,1]).
You're describing applied math, but when we say "math", it is assumed we are talking about pure math.
@@junerichardson3377I was talking about both, as big results in pure math keep finding some application these days. Also, the math in this video is not very deep. It's surface-level enough to have been developed before there was a distinction between pure and applied, if that's what you mean
Math isn't for everyone, get over it
I'm still is high school and I'm loving learning math, I find myself searching through CZcams about math topics because I find it so interesting and just beautiful to understand.
If we really want to ask ourselves "why do we learn math" we should ask "why" to basically everything else in life, we don't need to know how to write, how to draw or how stuff works to survive but we still learn it because it is just beautiful to know.
Mathematics is a numerical representation of logic - something any human uses daily hundreds of times. It's simply a way of training different logical and problemsolving skills. "Adding letters" as the guy in the video states, out of pure ignorance, is the mathematical way of being able to structure logic without full knowledge, and using said logic to then arrive at the full knowledge.
I personally only started even liking math when the letters were introduced. Arithmetic is a slog, algebra is fun. The highest math class I've taken is Calc 1, which I found quite intuitive. Hopefully I'll be able to grasp any future classes I take.
Arithmetic is a slog, like cutting the lawn with a pair of nail clippers.
3:43 same vibe as "what color is your Bugatti?"
True it may be hard for teachers to include real life application in math lesson but it would definitely increase the curiosity students would have towards mathematics
What do you mean? Were I am from like 95% of the time was them throwing real world applications at you when we did trig they were like why bother only the smart kids will have a use for it and for the rest that will be harder to imagine
Honestly yeah.
It’s why I love science so much. We get to do labs and instead of just being told “write down this equation and blah,” we actually get to know what it does in person or at least see an example. Math is fun when expirmenting, not when it’s done in a boring classroom where all you hear is “x. find the limit. Blah.”
calculus is everywhere, from a simple pendulum to an electron in a box and then they say mathematics barely have any practical significance huh
I study math and i Can say, that your method of counting with your fingers has helped me a lot
What the heck 😅
My math class feels like a bad sitcom where I'm the punchline every episode. The teacher's explanations are like trying to decipher ancient hieroglyphs, and every equation feels like a slap in the face. I sit here in rage, wondering if I accidentally signed up for a torture chamber instead of a classroom. Each problem is like a personal insult, laughing about my intelligence with its absurdity. Every class is a battle, and I'm ready to throw in the towel and declare war on numbers altogether.
Math starts getting so much more fun after you start doing calculus in n-dimensions and you generalize all of high school algebra, (abstract algebra) and you deal with weird spaces and stuff, it's insanely entertaining
3:35 bro really pulled a “what color is your bugatti?” on his classmate
When I was probably in 1st or 2nd grade, I discovered series and summation. Not like the proper way to do it, I just stumbled upon the concept of it. I would always punch into the calculator, 1 + 2 + 3... and so on, and wondered if there was a way to write the sum of so many numbers, like add every number 1-40, but my little brain had a tough time comprehending. It went to the back of my mind until years later in math we came upon summation, arithmetic and geometric series and I loved them.
thats oddly cute
And then little jimmy discovered that the sum of all natural numbers up to infinity is -1/12 😧
Calculus absolutely has its uses. Im currently 16 second to last year in Dutch highschool and even i can see there are many applications for it. In economics class for example you can calculate the total surplus of a market using integral calculus. This is because the total surplus is just the difference between supply and demand so you use integral calculus to calculate the area underneath the formula for both and subtract them from eachother. Because the formulas we use in economics are linear we were taught to just calculate the area of the triangle with basic maths. But this is only possible because the formulas were linear. You cannot use it on an exponential function which more accurately reflect real markets.
learning Calculus without Physics is the problem. Calculus was invented for Physics. Learn them together!
I’ve had a very different experience, for some reason I had a lot of trouble with basic arithmetic in grade school. I had to stay after school to practice because I was so far behind the other students. But when they introduced algebra I loved it. I spent a lot of time by myself learning math. I became fascinated by what it can do and how it can answer deep questions about the nature of reality. I taught myself “calculus,” or at least how to differentiate polynomials and such. I loved the beauty of the equations in calculus, they look elegant to me, as if they are a mathematical poem. It can be hard to figure out the meaning at first but when you look deeper sometimes there is a world underneath it all. Especially infinite series, those are just sick. But I can definitely understand how the mathematics that is taught at higher levels feels arbitrary and uninteresting, the things that are commonly taught in the classroom can be pretty vapid. I doodled a lot in class rather than paying attention, I learned a lot of the subject by playing with it on my own.
I have dyscalculia, so I hated math with a passion! When we had those multiplication tests, I failed. I never learned my multiplication tables because I mentally cannot do numbers. I cried from physical pain while doing my math homework! But then, they started adding letters and I was allowed to use a calculator!! And from that point, I fell in love with math! When my calculus teacher took away the calculators, I loved math enough that I made up tips for myself - instead of just knowing 8 * 8, I would draw little trees and then do long addition (with my fingers :P)
I actually had fun doing my ex's math homework, but I was bribed with ube ice cream.
I salute thee.
So cool to see someone with discalculia be good at math!
Sure, you remember that the derivative of 5x^3 = 15x^2, but you can't do 8*8.
We don’t believe your story
@@hmwh4t who's "we"
Tysm for this video it was somewhat helpful
For me I didn’t really like math until a couple years ago. Now I’m a freshman in college doing mechanical engineering because I love calculus and other math so much. It’s a pain in the ass to learn it sometimes, but it’s awesome to learn math, apply it to a real situation, and get the results you expected from your calculations.
You missed the groovy 7th level! Matrix math (Linear Algebra) and Differential Equations! These and previous topics like calculus apply very directly to engineering, so the math has all been very real for me. Unfortunately it's not this way for many others...
there's also theory math like sets, graphs, etc, matrixs, differentials, and null space vectors are all cool, topographic math and the other sorts is also pretty crazy. Calculus is definitely the start to where math gets very interesting for me, and honestly gets very very cool
@@quack3891 I believe the correct plural form of a matrix is matrices.
Sorry.
It really gets fun when you get into real a complex analysis
Diff Eq is pretty cool, Linear kicked my ass though
Series.......
I really liked calculus. Mostly because after highschool I went on to study History and regretted it. The next year I start a new degree in Chemical Engineering (which is just Chemistry + a lot of physics and math) and I really like that I can solve things that are impossible to do without calculus. (example: knowing things such as heat transfer / mass transfer in reactors allows you to know if you need a bigger/smaller reactor and also what the costs are of running it, quite important on an industrial scale)
i respectfully disagree. i feel the same thing about english, and I struggle hard in terms of comprehension (specifically MCQ), but I never say english is a bad subject. just because teachers I've had haven't taught anything doesn't tell me anything about the actual subject. they shouldn't teach it in 2 different ways, they should teach it in the best way they can. you have to motivate kids to be curious, and I'm lucky because I had that type of teacher. you may not have, and that's completely fine. but just one thing: check out some videos by Veritasium and the series "The Essence of Calculus" by 3Blue1Brown. It shows how beautiful math can really be. for my future job, math will be vital (data science), and I love learning it. "I quit the idea of going into STEM at calculus" - please, don't, unless you know that you never want to do a STEM job in your life even after learning mathematics.
as dumb as this sounds, have an ego. prove to yourself that you can do mathematics, and it will come to you. and start off small, whether that may be algebra 1 or pre-calculus, start off where you feel comfortable, and work your way up. self-learning, math especially, is a great experience, and I hope you will one day share my sentiment :)
This is very interesting from the point of view of someone who’s just starting Physics at a university. Just like a lot of other commenters said, Calculus really is the very first university math course for many students of science and engineering. As for the point about practical applications: Calculus already makes up like 70% of the math I have to use in Thermodynamics, which is my very first Physics course.
Calculus and the theory of sequence-number are so hard. But, they're so interesting, and something is miracle, like the complexity of calculus, the abstraction of sequence-number, and the relationship between them.
"calculus is the final boss"
who gon tell him
Homie hasn't even seen
- General Topology
- Algebraic Topology
- Set Theory
- Linear Algebra
- Category Theory
- Real Analysis
- Complex Analysis
- Functional Analysis
- Differential Geometry
- Graph Theory
4:10
this is a variation of Cauchy's equation
the general solution to f(x) is e^cx where c is a real number
no one asked 💀
@@cslvttvghtsBRO CURED CANCER-Teacher
I know you were sharing your personal experience with math and you have a lot of questions. Now, I am not sure what higher studies you pursued, if any, but from my experience, what i will say is that school math and MATH are very very different. One is a factory churned brain, trained to solve few generic types of problems with a syllabus vomited over the world while the other is a beautiful understand of worlds beyond our comprehension. Actual mathematics (which in all honesty begins when you start 'real analysis' in university, everything before that is application mathematics, where one has to remember a formula and solve problems based on it) is about finding ways to prove things that we observe in a cold, emotionless way. In a way, where even an ant or aliens - if they develop the same symbols - will agree. I believe that to be the real heart of mathematics, modelling -> Proving -> Abstracting to n dimensions.
I only took two years of calculus in college, and that was the end of my math studies. I found that knowing calculus was pretty much absolutely necessary to understand physics, which in turn was necessary to understand chemistry, which in turn was necessary to understand biochemistry, which was my major. After college, I used calculus to derive the formulas for loan amortization. (This was in the dinosaur age before business calculators and the Internet.) And that was the last time I ever used calculus for anything. However I have a long-deceased distant cousin named Oswald Veblen who advanced the mathematical field of topology. And tell ya wut: If you think calculus is arcane, try looking at topology. I'm not sure that even topologists can even define what topology IS. Certainly not in any way that makes the slightest bit of sense to ME.
I think maths crewed itself by never telling students why you needed to know it, and because that, people dropped it and hated on it because they didn't see a use in it
Yeah. You could say that. But it's more of a problem that all subjects face.
Maths is an abstract concept. Meaning, it was never meant to be direct. You have to fix your problems into the equations and
change those equations as suited to your needs. It all comes down to Imagination.
yeah lets do physics with counting on our fingers, who needs more math than that
@@AdelAdel-pn1bq Couldn't have said it better by myself.
🤣
The only way i made myself love math is by making daily life math. I would countlessly collect useless data from daily lives, such as how many rotations of a tire to travel a certain distance, and etc, and it would make math seem less alien to me. Everybody's got their own ways. I remember being completely fascinated by pi and trigonometry when i first learnt them. I've always wanted to figure out the hypotenuse but now I do!
As a math teacher, I hated to have to show why they needed to know it. For most, arithmetic is enough. No other subject needs to do this. Nobody asks this of history or literature teachers. Once, when the lesson was on complex numbers, I told the students I was now going to teach something that has no use to them so do not ask. Now electrical engineers will say they use them all the time. If I said that, my students would say they are not going to be engineers. I wish students would just have fun with math and think of it as a game or puzzle.
"Calculus is the final boss of math"
Real Analysis: ALLOW ME TO INTRODUCE MYSELF
De Rham Cohomology: hello there
Honestly I love calculus. Derivatives showed me a whole new way to understand the world around me and see relationships between concepts. I am currently pursueing my undergrad in chemistry and hey, many people may not use math, but ive found it helpful for understanding chemistry and the orbitals of electrons
Ah the good old "I liked math until they added letters to it". A clear sign that someone doesn't fully understand what math is all about.
For me, math is fun for me because of competition math. Competition problems are so different from your standard "haha plug it in to a formula": You need to figure out what steps you need to take, often adding many different techniques and formulas together, meaning its hard to just chuck things at a wall, and the process behind figuring things out can be really fun, and when you find those juicy key steps and everything clicks together, it is the best feeling in the world (or maybe its sex, haven't tried it)
Some official exams, like pearson IGCSE do this, when the bulk of questions are easy plug in formula and thats it, but then there are some questions of these type, where you really have to figure out what to do to separate the smarter students.
Anyone who is good with puzzles and is able to develop tricks and methodologies to handle them in general will be mentally well-equipped to handle these sorts of problems.
It separates the test-conquerers from the problem-solvers.
comp math is amazing i did it in middle school
@@codspreedrun But competitive math IS usually proof writing. There are plenty of olympiads for high schoolers, and for undergrad students like myself, there is the Putnam
Bruh!! Don't be obbssesed into maths
For me it's actually exactly the opposite, I disliked math pretty much all throughout school, but now that I'm in university I've mostly enjoyed my algebra and discrete mathematics course that I took last semester. i don't know why but Algebraic Structures just fascinate me.
f you mean "algebraic structures"?
@@bene2451 You need to do Discrete Math to learn about algebraic structures. Algebraic structures are basically sets of numbers where you can perform addition, subtraction, multiplication and division...basically operations.
@@bene2451monoids, groups, rings, fields, vector spaces, affine spaces, etc
@@bene2451 Taking what you have been taught about algebra (like a+b=b+a) and generalizing it to other algebras, many times where those axioms do not hold. Why does multiplying any number by zero return zero? Those sorts of things
I was the same way! I'm in graduate school for math now but abstract algebra and its different objects were so fascinating to me as a young undergraduate.
It took me a bit to understand calculus. I honestly didn’t even know I was doing calculus for a while but that just goes to show just how smoothly my teacher was able to transition into it. After I wrapped my brain around it, I was doing pretty good. But then Covid hit. In Australia there was A LOT of time spent in lockdowns. And every moment I spent on online classes was another moment of lost sanity. I couldn’t understand my teacher, I didn’t have my classmates (who were much smarter then me) to explain things I didn’t understand, I didn’t have the teacher there able to be on the board drawing things out… and most of all, the atmosphere of the class was lost making it VERY hard to pay attention. Year 11 I fell behind. Then in year 12 I gave up. I was able to study enough to get a decent score for my finals but it was no where near as much as I could have had. I think many people will understand the feeling that I went through when I went into that exam. You KNOW you don’t know a chunk of the topics enough to be tested on it. Only things that got me through were the topics that I did know enough of. But, I had accepted defeat before hand. So I was able to go through it slightly happy.
as someone who studies engineering. math is literally the only thing keeping you in. almost if not everything revolves around math. and calculous is just the start of it
I quit math at calculus. In fact, I quit the idea of going into STEM at calculus. I was starting to have trouble before that point, but I thought it would just be a little hurdle. When it became clear to me it wasn't, I knew I had to quit.
The thing with math is, either you love it for what it is, or it's just a tool to help you with other things you love. When it's neither of those and it just feels forced upon you, it's terrible. I never loved math for what it was, but at first, it was easy for me, and I thought it was pretty useful most of the time. When it stopped feeling useful and it started being hard for me is when everything fell apart.
Now that I'm thinking about this, I genuinely think there should be two ways to teach math. One for those who love it for what it is, and one for those who want to use it as a tool. The current state of things in education is good for the former, but not for the latter. I would have preferred learning the math as I learned where and when to use it in more concrete applications (and by that, I don't mean day-to-day application, I mean like science and stuff). The reason I lost all motivation to put actual effort into math when it got hard isn't because it got hard, but because I just didn't see the point. After a certain point, all the math I was learning felt completely disconnected from anything else I was learning, and that wasn't fun. When I was learning calculus, my science classes didn't use more than basic algebra. I think there should be an option for those who want the two to be better integrated with each other.
Edit :
I'd like to point out that it isn't the only reason I quit STEM, but it is a major reason nonetheless. I am very happy with my new choice, much happier in fact than I ever was in STEM. I have little to no interest in taking math classes again. I would like people to stop trying to convince me to give it another go, I have absolutely zero interest in doing so. I've already moved on with other things, and I'm having a blast.
I understand that for some of you, even when it was difficult and not enjoyable, you managed to get through it and you were rewarded for your efforts, but understand that people don't always have the motivation and interest to manage to get through it.
To make it extra clear, my problem with math isn't that it's difficult, I think some people didn't understand my point here. My point is that I didn't have an end goal in sight. I was just putting in effort for the sake of effort, or putting in effort just for some number on my report, and I didn't enjoy that. The fact that MAYBE it would be POSSIBLY useful AT SOME POINT in the future, probably a few years down the line, just wasn't enough to motivate me. I needed something more concrete, more applicable in the short term, and that's what was lacking. And I genuinely believe it's in no way math's fault, but rather the way it's taught, and I think there are ways it could be improved. Not for my sake, it's way too late for that, but for our children's sake.
Did you take a physics class, everything is basically calculus. The reason they only have you use algebra in high school science typically is because not everyone is strong enough at calculus by that point to apply it.
If you want to pursue anything in computer, science, or engineering, I'm sorry to say that you will need to confront the full math content head-on. It's just not possible to get through those 3 subjects without good foundations in calculus, linear algebra, geometry/trig, and complex analysis.
Additionally, more and more subjects are getting mathematized each year. Chemistry is nearly there, and biology is well underway. Finance and marketing are also going that way.
Our world is increasingly data driven, too, so math is now encroaching onto even the softer sciences via advanced statistics.
The only space where "practical math" remains are the trades, Medicine (though new tools means learning more math) management, and maybe some artistic endeavors (though art is getting more mathematized too via the introduction of computation).
Math powers the world now. It's a matter of finding a learning method that works. Math is the new degree that can take you anywhere. I suggest to all my students to consider minors in math or statistics. The upshot is that once you break through the calculus barrier, it is inevitable that you will find a branch of math that suits you. Math is diverse with lots of different topics for many different types of people. It's diverse because it can be used in all kinds of problems. Keep working at it. You are never too old to learn math!
@@racool911 I understand that, but it's a problem of focus. Math was always taught independently from anything else for me, and that's the issue. If someone sees math as a tool, but doesn't know what to use it for, it seems pointless to learn. Emphasis on "seems", of course, but you don't know what you don't know when you're in the thick of it and everything just sucks. That's why I say math teaching should be better integrated with science in schools for those who don't like math for math's sake. By that I mean : When you learn something in math, we should be able to immediately use it in science, or when we learn science, the teacher should be clear that "We can't go further here because you haven't learned the math yet". It's about better working with the student's motivation to learn math.
@@CrownedFalcon00 It's not a matter of being too old to learn math. It's a matter of hating learning it. I'm not saying math is not important, I'm saying that I want to have a damn good reason to learn anything math-related because it is an absolute torture to go through for me. Maybe I'll have to learn advanced statistics in my new field, but I'll learn it when I need it.
To be clear, I'm not saying math is the problem. Having a topic you don't enjoy learning is normal. For some, it's math, for others, it's grammar, etc. The problem is, math is a powerful tool, but the way it's taught oftentimes only works for those who like math for math's sake, and those who see it as a tool may have trouble seeing the benefits at the moment they learn it. That's why I say math teaching should be better integrated with other topics, so that those who see it as a tool can better see the applications and be more motivated to learn.
Brother I’m not doing calculus, I can see that my brain is better suited to developing computers just like how Steve Jobs did then beating the Math bosses in a fight that will get me a high paying career in a single field. I see that as for me, that developing the brains behind my own computers and cars, are much much much more profitable than experiencing the battle of Mathematics. I can use simple mathematical equations to solve problems hundreds of times more complex than level one calculus, by developing the brains of a hand made devise which to a lot of people would be a feat equivalent to calculus, especially if it can grow to become a super giant like Apple or Microsoft. Not just in profits, but in complexity, and true engineering. Which even though engineers can do calculus. They often fail to reach the goal to develop something that would better develop humanity largely because they are the ones giving orders, not the ones doing them completely. We the workers, have on greater occasions, created feats that far surpass that of many of our greatest calculus mentalist on the planet.
Calculus actually restored my love of maths. Working with unknown angles killed it
with unknown angles? bro failed 9th grade geometry 💀
@@bene2451 F for respect.
@@bene2451c’mon man
@@bene2451yep. It was pretty arbitrary.
@@bene2451man I’m dyslexic and I hate working with unknown angles but love limits and derivatives
Considering all my current problems in life, I'm glad that math is a source of joy, not despair, personally.
There is no end for mathematics. As a well-known nerd of mathematics in my school(I am 7th grade and I learnt integration), I can safely say that there are a whole lot more than calculus. For example, abstract algebra. When you dig deep into each concepts, things quickly surpasses the difficulty of calculus. Even when you finished the entirety of mathematics, try to prove hypothesis and conjectures! The Poincare conjecture helps study the structure of the universe (It's a geometric conjecture).
Also calculus is extremely useful in Physics and Chemistry. Taking singular or multiple derivatives of a function gives us related information. For instance, let r(t) be the remains of a radioactive matter when time = t. Then r'(t) would be the decay speed of the radioactive matter. Applying the Newton's cooling function u(t) and after transformations, we can express r(t) in terms of r(0) and r(1).
I’m currently in undergrad as a freshman statistics major and calculus is very easy imo, and based on what I’ve seen so far, calculus 1 is the beginning of the real work. It’s the first class in your math progression at my university. I did my entire calc 1 textbook in a week on my own, and have been teaching myself other topics in math like some elements from calc 2 and elementary number theory in my free time. I really don’t understand why people think it’s this absurdly hard topic with zero applications.
Bro I did calc 1/2 as a sophomore In high school
did you ride the short bus or something?
@@bene2451 some times, there simply isn’t enough opportunities to take advanced classes in highschool. A kid I know was limited to taking multivariable in his senior year despite having studied far beyond it in his home country.
you really just need to go through the adventure of getting the hang of it until it becomes basic, in order for me to understand right now, i had to write 5 whole pages of calculus notes, but soon it will become regular
math is like, whatever how far you go, there is always something absurdly hard for you. if you think calculus is fine, then there are real analysis, functional analysis, etc... if you think number theory is fine, then there are elliptic curves, algebric geometry ahead.
@@bene2451 I never even got to take AP classes in high school because those idiots said it was necessary to spend half the day learning religion. So here I am acing calc being super proud of myself but also kind of resentful that I couldn't have done this in high school. That school wasted so much of my time.
I could have done so much more with my life. I could have gone to a better school than the little charity program that let me in. But at least I'm not one of those girls doing a rushed year so they can teach, half the classes they learn being religious classes, going to their fake college.
I was asked in high school why I wasn't going to this college that teaches linear algebra and calc 1, that's it for math. Cause regular college is inappropriate. I'm not here to party, I'm here to learn. So pissed. At least my younger brother is out of there and will get to go to a normal college and learn stuff.
From : How many stickers do you have?
To : What color is your Buccati?
He grew up
adding letters is from where maths became one of my favourite subject
I am studying Physics, and although the analyzes are made of real phenomena, the language I NEED to interpret it rigorously is math. Without it, I can only describe it with words that may not tell me or let me see all that I can get out of this phenomenon. And this applies to many fields of science.
Listening to people who say they hate mathematics always brings me to question how to improve the teaching of them.
Math is one of the most useful subjects thought in school. If you go to college and choose to go for any STEM related career, at least half of it will be math because thanks to it, we managed to get out society to where we are
i mean, true. even more than STEM its just that stuff is usually measured over time and when you have things changing its likely you'll want to use calculus to understand whats going on.
How many people really choose STEM careers though?
@@Fullmetalballsz a very very high amount
@@Fullmetalballsz 20%+ of graduates go to STEM
I was the opposite: I despised math until letters were added. I remember the moment that it all just *clicked* for me, and I absolutely loved it lol
you you explain your ways math has never made since I can't do it for my life.
Why does this make me think of someone losing it in a cramped classroom staring at their hands in disbelief as interstellar plays
@@firststriker5086LMFAO
1:13 - You can count up to 512 by counting on your hands in binary
1:05 there's actually a way to count to 1023 with your fingers called binary finger counting.
We need to let everyone know that maths is not just abt adding numbers and multiplying them 😂
maybe a "modeling" approach would be better from grade school.
En emphasis as math as precise communication:
- describe how many things you have
- describe a table
- describe a moving car
- describe some dynamic process
etc...
Not enough emphasis on math as communication and too much emphasis on obscure algorithms (like how to do long hand square root..). Let the computer run the algorithms, you focus on what to use to communicate what something is.
I think of everything you learn before calculus as just fundamental math. Like learning a language at school, you have to learn the rules of the language before speaking it. Calculus is speaking math. I am in engineering and just finished calc 3 and Differential. I love that I was able to continue to see math all the way through and recommended it to anyone.
Organic chemistry tutor helped me immensely with my precalc college course and brushing up on algebra.
For me, one of the ultimate benefits of learning math through an undergraduate level is that it trained my brain to think in different ways. These ways of thinking, is best as I can tell, can't happen without learning enough math. Especially important is seeing how much generalization can be achieved. Some other examples are becoming really good with ratios, layering of abstractions, being able to think about flows and changes.
Where I found my limit, no pun intended, was proofs. They require an amazing level a very careful thinking and creativity. Well, also I cannot handle too many layers of abstractions. And I depend too much on intuition.
My experience was the opposite
1. Why are we counting these fricking fingers?
2. Ooooo, so you do that in mind... That makes sense
3. Finally! I can count how many apples are in 1803400543 boxes when each box contains 543663 apples without using 2 tons of paper
4. You don't need numbers for math? That's interesting! I feel the power of simplification and generalization!
5. What a funny wave we see here! And It just describes every possible triangle with hypotenuse of 1!
6. So you can multiply a lot of things by very small numbers to get its area?
Or get a function that describes the area bellow the slope of given function?
I have seen it somewhere! It is from physics!
7. I haven't gotten to this level, yet
Well, I'm still actually learning trigonometry, and I only know the basics of basics of calculus
But hey! I'm still only 14 (technically 13)
Yea imo math only gets more interesting as you move through it. Calculus was my fav math course in high school. Applications are really cool and just the concept of working with infinity is really interesting.
terrance tao got his masters degree in math when he was 16, so "But hey! I'm still only 14 (technically 13)" isn't an excuse, so go work hard!
@@mastershooter64 I still have 2 years
So, yeah, that is an excuse
'till 2025 I will be at the level of modern Leonhard Euler but more lazy :P
But thanks for the words of encouragement
I really appreciate how you keep my motivation
> I feel the power of simplification and generalization!
Love that spirit! Keep it up! :D
so all of uni maths are in the area not covered in this video lol. where is my beloved differential geometry, algebraic topology or complex analysis
It's fun to see that most of math taught in school has nothing to do with actual math (meaning logic, proofs and abstraction)
Sounds as if you didn't like math, but you liked arithmetic. Math really starts around algebra, trig, and calculus, where you reach a point from which you can begin to apply your skills to interesting questions in the real world. Questions like finding the center of mass of a tapered rod, or locating the source of a gunshot based on the exact moment three different microphones detected the sound.
Thanks for sharing your experience honestly. The unfortunate thing about math is that it's often taught in a way that makes it look like it's worthwhile only when it's applicable. Math is done (and developed) just for the fun of it (I'm not trying to undermine the amazing applicability aspect by saying that). It's somewhat like cooking. Food is essential for survival, but we don't really need this many great cuisines and dishes from all over the world just for survival. Yet, we have them. But again, you are free to hate on any dish that you genuinely dislike. In fact, I strongly believe that math should not be forced. (BTW, there is calculus for complex numbers and complex functions too, which somehow is related to the distribution of prime numbers. More reasons to hate 😜)
Calculus is actually the part I most enjoyed, as i could finally derive formulas in physics and areas and volumes of shapes. They were no longer magic , and I felt that now I could understand everything
1:16: The thumb has only two sections, so you can only count to 28 this was. But there is way counting to 31 with just one hand using binary properties. The thumb counts as 1, the index finger as 2, the middle finger as 4, the ring finger as 8, and the pinky as 16. And now you combine these fingers for the number you want to represent.
You guys are making calculus sound interesting and Fun
i wasnt much of a math person (i have always steered more to art and writing) however i began to truly appreciate it once college started. i ended up majoring in computer science and taking programming and calculus at the same time really changed the way my brain thought - i feel like ive become much more mathematically inclined because of the overlap within the two classes. solving problems, trial and error, and abstract thinking is just a change of perspective and way of thinking and ive honestly found it really interesting. not to say that im now a genuis at math (really not, struggling to keep a B in calc), but ive enjoyed it a lot more.
Your ending could have saved the entire video just having calculus being the highest level by saying finish means you go on to take graduate-level classes in proofs, differential geometry, topology, analysis, and so on, and quit means you decide that all the time was wasted. You have the opinion you do about the applicability of higher-level math because you chose to quit.
Now we need the sequel for the 7 levels of post secondary math
@mr_think Honestly the best thing I've done, both while and after graduating as a math major, to actually utilize the theory aspect while also playing with the mechanical aspect of math was tinkering with graphing calculators. While ultimately you can't avoid either separately, playing with one can really give you practical intuition on the other. By turning it into a puzzle or challenge where you want to demonstrate or recreate the aspect of the other, you give it a tangible and in effect meaningful application that will surprise you as you'll start using that intuition in real life. You'll actually be more surprised by how much math you actually learned/remember, something that isn't inherently promoted in general education (public or private). You're mainly encouraged to develop a veneer of understanding/mastery but it's highly superficial until you spend intentful time to really experiment.
As a math major things you talked about are elementary level maths wait till you get to analysis, abstract algebra and non euclidean geometry
To be honest my love for math only got amplified when letters got added and when calculus started I truly started to love math
To know the "end" of maths for most people is the basis of the career I'm studying (Physics) makes me feel overwhelmed. Really love it tho
I’m pretty sure this video is satire, but in the case that it isn’t, I’ll agree with the other comments. If elementary calculus is the “final boss” of mathematics, then maybe you’re not the right person to be making this video
I know that my math journey is at the start (I'd like to be a mathematician and although I'm just sixteen and I know that lot of other people know about mathematics more then me I'm quite happy with opportunities to do mathematics university class as a special case and finishing my first theory) but calculus is absolutely base and start of mathematics and is applicable in everyday life, the difference is that people who don't know how to apply it say that it is an unsolvable question and therefore not important in life.
become an engineer instead because you can actually use the math you learn to help people rather than solve weird problems no one really cares about.
interesting :o this channel is surprisingly very underrated
Thank you so much, this video helped me get 84% in my test on trigonometric integration!
Im in calc 3 and i still have to take ordinary differential equations and partial differential equations before im done with math classes, and calc 3 is extremely easy compared to calc 2, calc 2 is the only hard calc class since it’s an exploration on many different techniques to solve more complicated types of equations
6:07 actually it is all because FFT(fast fourier transform),that make you see everything as circles,and a circle is best described as these triangle using thing.
could you elaborate on that, from an undergrad level of knowledge on fourier transform?
@@Fedethedangerous95 as you can see, Fourier transform assume all function be combination of sin and cos with different frquency and amplitude,and we know sin(x)*sin(x) is postive and cos(x)*cos(x) is also all positve and cos*sin is 0,so we just mutiplied the input values(maybe from a function)with sin and cos with different frquency and see their sum,that is fourier transformation.
@@Fedethedangerous95 in short,by mutiplied by sin(fx) and see its sum,we know how much the input to be like sin(fx),so does cos(fx)
and by the formula sin(fx+b)=sin(fx)*cos(b)+cos(fx)*sin(b)
and sin^2+cos^2=1
we cna know by squre sum the fourier transform,we can know the frquency of signal without need to know it is sin or cos or both with phase shift
@@Fedethedangerous95 and by using complex number as a tool to do two variable operation(in this case,linear transformation)you dont even need to metion cos and sin but comination of e^z which can be express as infinite series of polynomial,and being polynomial means there are tricks to do it faster,and the fact fourier transformation is linear transformation mean it can be done in reverse in almost same way...
@@user-nh6qi2zu1b ok, since I'm italian I probably am not familiar with this kind of terminology but I think I get it, you call "fourier transform" the expansion in series of sin,cos
and "fast fourier transform" the integral over |R , where the inverse of the transform becomes an integral multiplied by the exponential with opposite sign
thank you for the explanation, I was curious whether there was some other trick there :) where can I find more info on the correspondence between circles and triangles and its usage with fourier calculus?
skill issue
true
so damn true
Real man
Fax
Honestly correct
3:43 Nah that kid now walks around and ask people: “What color is your Bugatti?”😂
Guess that's one way to feel about the whole thing. I was one of those math lovers doodling equations on the edge of the paper. For me it was a logic problem like a crossword or maze but unlike those math could be used in real life. In that light each new operator was a whole new exciting world to understand. The day I learned variables was the coolest yet as it brought the idea of a balanced system into math! Now we could shuffle around some terms and calculate how far we traveled or solve the area of an odd shape. Onward and upward! Geometric Proofs brought a new way to think about mathematics as a whole and allow us to use compass constructions to split angles perfectly and up scale drawings. Along with that came Trigonometry, a complex and mysterious set of functions that allowed us to discover the hidden values on a triangle for craft projects. Then finally the crowning jewel! Calculus! A mind bending wonderland of possibility based on the rate of things and themselfs, calculus combines everything you've ever learned and shows you the why and the hows. As you crest the top of the hill into multivariable calculus and learn vectors, you can see everything... and soon realize you know nothing. Many may ask "what now?" There's too much to learn and none of it is relevant. Well my answer is go wild and learn to program! Life is full of random moments and situations and if you know math you can calculate the physics of water flowing through a funnel or light refracting through a glass on to a wall. They're not useful but it is nice to be able to say I know why that works! I've recently been thinking about fractals and how to control the shapes they make. I've made a lot of progress on my own and can almost start to make the fractals I envision :D
In conclusion math is a complex logic system for solving non-obvious questions. It is built up of layers of abstraction (meaning each system is relient on the last scope like arithmetic to algebra) which means becoming good at high level mathematics inherently make you better at the daily counting and allows you to break down extremely difficult problems into their complex abstract parts. You will probably never use all that math but the non-obvious answers it gives can be very entertaining.