i will now write all my texts and articles with the following notation: :) signifies the end of a proof :/ signifies a question :( signifies a limitation in the experiment edit: :o signifies a theorem or lemma
@yurigouveawagner94323 жыл бұрын
god dang it I edited and lost the heart
@nealcarpenter30933 жыл бұрын
I really like your notation - will be suggesting it to my students for their notes. Thanks.
@thedoublehelix56613 жыл бұрын
I like to draw a smiley on the inside of the end of proof square
@yurigouveawagner94323 жыл бұрын
@@nealcarpenter3093 thank you! are you a professor? It's cool to imagine this idea influencing a class somewhere in the world
@nealcarpenter30933 жыл бұрын
@@yurigouveawagner9432 Hey, good or humorous (if there's a diff.) ideas spread. I teach math, grades 6-8, though that does include some Calculus.
@joaqbadillo46733 жыл бұрын
This guy also speaks Chinese, Grant has everything covered.
@ilickcatnip3 жыл бұрын
I'm absolutely blown away by this man!
@gasun12743 жыл бұрын
his tones are off though, but i never spoke mandarin in a colloquial setting so maybe there's something about when it's ok to change tones in certain contexts.
@alsatusmd1A133 жыл бұрын
@@donsanderson Mandarin is what people commonly mean by the language “Chinese”.
@seeker44303 жыл бұрын
@@donsanderson Really where did you find this information? I really want to hear him speak chinese
@user-zu1ix3yq2w3 жыл бұрын
This is the advantage of a powerful memory.
@durian75513 жыл бұрын
To any of you wondering, the outro (下次一定) is a common Chinese phrase/meme to say "maybe next time" or "take a rain check".
@mrnarason3 жыл бұрын
Basically never lol
@dqrksun3 жыл бұрын
下次亿定
@blue-whitestar25983 жыл бұрын
Yes, great pun, wasn’t expecting that!
@esepecesito3 жыл бұрын
Like the mexican "Ahorita!" ?
@superlugiaultra3 жыл бұрын
'next time for sure'
@markkennedy97673 жыл бұрын
12:00 this is why Grant is among the best maths educators out there. He talks about the emotion in maths, about stressing what's important vs the detail. It explains why the first time I properly intuited linear independence was after looking at his Linear algebra series. Some people will argue you can't visualise all maths but I think there's a happy medium between slavishly following symbols on a page and characterising what they represent more fully. This is why Grant is a bit of a hero for me.
@MathTutor13 жыл бұрын
Agree.
@Notsosarcastic_025 ай бұрын
Well just to tell as a fact , here in India , textbooks do have these kind of emojis , more like characters as whole in textbooks interacting with children and trying to tell them the concepts like a story or something through the textbook . I remember here in my state board textbook (local educational board's published textbook ) , there was a Rubik's cube interacting with us asking us questions or giving us a recap of the previous chapter at the start of a new chapter and also giving us some tips , they put him into corners and it was interesting.
@almoni1273 жыл бұрын
I would recommend Jiří Matoušek's "Thirty-three miniatures". It's about 33 beautiful applications of linear algebra. Also, all textbooks by him that I checked out are gold.
@GrantSanderson3 жыл бұрын
Sounds amazing, I’ll check it out!
@VarunRamanathan280319993 жыл бұрын
+inf Matousek's books are incredible!
@user-zx6os1fy6w3 жыл бұрын
Thank you, sir! I come from China, and I learned quite a lot from your teachings. They are very insightful! Thank you very much! 感谢!
@Benderhino2 жыл бұрын
is china fun?
@user-zx6os1fy6w2 жыл бұрын
@@Benderhino Why don't you come to China and get the answer by yourself?
@Benderhino2 жыл бұрын
@@user-zx6os1fy6w nah man busy with poverty stuff, this is embarrassing I wish everyone was dead, anyways, have a nice day.
@OrigamiMarie3 жыл бұрын
When talking about natural talent, I think about crafting. When I have just started teaching someone to knit or crochet, at some point, after they've gotten just good enough to reliably make stitches, they'll watch me do the same craft and say something like "gosh you're so fast and I'm so slow, I wish I was fast". And when it's about crafting, the response to this is actually really intuitive. I say "well, I've been doing this about two decades longer than you have, so I should be faster; if I wasn't, there would be something going rather wrong".
@kreek223 жыл бұрын
But, bio-communism isn't real.
@mixti15623 жыл бұрын
that question about not being gifted enough was hard to hear. coming from a competition math background, i often felt that the community could be very toxic and make me feel like i was not "gifted" enough
@HAL--vf6cg3 жыл бұрын
@@markv785 this is just my opinion, but SATs are a terrible mode of evaluation, especially for college admissions.
@rollingsnowball90953 жыл бұрын
Competition math can be really discouraging for students who want to get into math but can’t “keep up” with everyone else. I never even thought that I could ponder problems for a day or more. Everything was kinda fast-paced. It’s funny that continuity can work perfectly fine only using rational numbers. Talk about lifting up your pencil! Oh and that room problem, I didn’t find that easy at all lol. Although, convex functions ARE quite interesting *cough* *cough* Legendre transform. Love your content! Can’t wait for more on diff eqs and probability
@xXDarQXx3 жыл бұрын
the room problem really isn't that hard. click read more if you want a hint (to find the solution I came up with) think about the room with the smallest number of people.
@kreek223 жыл бұрын
The agon is all.
@Umarology883 жыл бұрын
Being a practicing engineer, I'm really interested in theory of nonlinear dynamics and mathematics behind. The Nonlinear Dynamics Book will be a real help. Thanks very much, Grant! ❤
@jaredlichtman10213 жыл бұрын
For the room problem: a "physical/intuitive" interpretation of the sum-of-squares is as a weighted count of the population, where each person is weighted by the number of their roommates.
@__koaaa_96193 жыл бұрын
Can’t help but mention that it can also be viewed as the variance of a distribution + the mean squared, where in this case the mean is constant, so it basically reflects the variance.
@DS-qg9cd3 жыл бұрын
I like to think that it is because of the fact that (x + a)^n > x^n + a^n, you can always choose x^n with n > 1 and you'll get the same proof
@mincraftfrontiersman3 жыл бұрын
6:47 Regarding the concept of being gifted vs. not: I've always held to the belief that there *are* people who are better in a given field by their nature, but *anyone* can become skilled through effort. Anyone can become skilled, but some people have a head start. Regarding math specifically, yes. There are individuals who are naturally good at it; their brains are wired in a way that makes learning mathematics natural. These are the individuals we'd typically call "gifted." For others, learning math is harder. The ""not gifted"" individuals. It's very easy to see someone breeze through things that you struggle with and come to the conclusion that you're just not gifted enough to progress, but that's categorically untrue. Just because it takes more effort for you to learn something doesn't mean you can't. If you're willing to put your head down and push through, you can learn any skill you want. Whether you're gifted or not determines where you start, not where you end up.
@geraldsnodd3 жыл бұрын
Agreed, I think the same.
@NoriMori19922 жыл бұрын
I'm not sure it's true that _anyone_ can become skilled at math just by putting in more effort. Frankly, I don't think that's true of _anything._ But I agree that there are most likely many people in the world who could become skilled at math, but are never given a chance or a reason to put in enough work.
@Adhjie11 ай бұрын
Given a chance: ramanujan. Or has the chance Richard Feynman said hard works he didn't want honors.
@Adhjie11 ай бұрын
Tho yes genes is a factor. Eg cofactor factor constanta etc iirc l'hospital rule
@omarbourhani92653 жыл бұрын
Please do not stop making those videos 🙏🙏 You are changing my life 🙂
@TheAcer46663 жыл бұрын
I bet whoever came up with that sum of squares solution had some connection to Cambridge. They used to grade their exams by taking the sum of squares of the scores to each question, to encourage people to prioritise answering fewer questions more completely rather than doing a lot of questions partially. As you say, problem solving is a lot about your experience....
@wallacealbert23653 жыл бұрын
Dude, you're a legend. Thank you for the hard work you put into your videos to make things clearer. Seriously, thank you!!
@GurpreetSingh-en3gx3 жыл бұрын
5:00 Yes yes yes yes, I am obsessed with Valadmir Arnold's writings, I have been collecting his works in English but most of his writings are in Russian. Currently learning a lot from his book on Catastrophe Theory. I feel VI Arnold changed my life, his essays on mathematical pedagogy are revolutionary and I feel you are the one who will make his dream come true of unifying maths of physics which were divorced by the Evil Bourbaki's.
@maalikserebryakov2 жыл бұрын
Lol don’t let arnold brainwash you with his nonsensical opinions the bourbaki’s did a great job and the existence of Pure mathematics is super convenient and useful
@josemesquita_3 жыл бұрын
You are an extremely talented communicator, for real.
@JoelRosenfeld3 жыл бұрын
I am really enjoying these videos on this second channel. Great to hear conversations and interviews that give more depth behind the characters in mathematics. On the nature vs nurture aspect. I really do feel that there is an in-built ability to engage with mathematics in some people. I know that I saw friends with whom I performed on level with in undergrad really outpace me in graduate courses. It really showed me there was a difference in ability. There is a spectrum of human ability and Tao and Von Neumann are really at the peak of this. If there are people at the top and the bottom, there are going to be people at every point in between. Of course, this is really hard to quantify, and I don’t think there is value in approaching education this way. I think most topics taught in school should be approachable to everyone, but after a point, you see real differentiation between students.
@GrantSanderson3 жыл бұрын
What’s hard to tell is if this is actually innate, or based on instincts learned so young that it might as well be innate.
@JoelRosenfeld3 жыл бұрын
@@GrantSanderson yeah, it really is hard to characterize and identify. Though it is undeniable with people like Gauss, where they comprehended arithmetic at 3 years old. But that may be apocryphal too.
@CalBruin3 жыл бұрын
The Hubbard text is rather good for all the topics covered. I think the book is especially great for those who have studied already Linear Algebra, Real Analysis, and Multivariable Calculus and are in need of a more in depth review. We used that book for Math 23a & b with Paul Bamberg at Harvard. When I took the class, we used that very same 4th edition.
@akshaysriram85593 жыл бұрын
I have been following and looking up to this guy for years, and never would have expected him to speak Chinese so fluently.
@nealcarpenter30933 жыл бұрын
This is full of valuable suggestions. Just "the convexity of x squared" at 21:20 led me to an answer to a question that's bothered me for years, namely: "Why do we nearly always use & teach Standard Deviation, rather than MAD or AAD?" Not bad for a 5 second toss off remark!
@columbus8myhw3 жыл бұрын
It seems to me that you can add up other functions and it will still work, for example adding 2^x where x is the number of people for each room
@caiollvllal3 жыл бұрын
@@columbus8myhw i think we just need to use a strictly convex function
@skilz80982 жыл бұрын
I've always enjoyed math and physics. The one thing I have learned over time is that numbers, math and all that follows they are nothing more than a product of the mind as they are all conceptual ideas. At the end of the day, math is nothing more than a model and it is what you make of it! I enjoy hearing all different kinds of perspectives and approaches. 3Blue1Brown is one of my favorites along with Mathologer and a few others... I love their presentations and visualization methods. It's almost like comparing or listening to a monotone college professor who'd soon enough put you to sleep on trying to explain the phenomenons of the Mandelbrot Set as opposed to writing a simple computer program to graph it visually being able to see and interact with the infinite patterns and levels of details that a simple equation produces. Grant and others like him allow mathematics to be fun and engaging instead of being monotonous, drab and dreary... Keep up the great work!
@akshaysriram85593 жыл бұрын
22:13 Being a majorly doubtful visual learner of mathematics, I've been dying to know this. Thank you so much Grant .
@AwesomeMinecraftTNT3 жыл бұрын
Hubbard’s book is fantastic! It was the textbook for my first proof-based class, and it made me switch to the math major
@justastrangerx7 ай бұрын
Fastest 25 mins of my life. Love listening to you Grant, always a pleasure.
@guest_informant3 жыл бұрын
I would say that as long as you've done a reasonable amount of preparation then the fault pretty much always lies with the textbook. One of many examples of this is I once supported ten different students through the exact same maths course. 7 had textbook A - Topic X was impenetrable, only ever to be understood by the best and the brightest. Topic Y was completely straightforward and I was never asked about it. 3 had textbook B - Topic X was completely straightforward and I was never asked about it. Topic Y was impenetrable, only ever to be understood by the best and the brightest. I taught Topic X to those with textbook A, and Topic Y to those with textbook B, made those topics seem completely straightforward and everyone thought I was a genius.
@UCFc1XDsWoHaZmXom2KVxvuA3 жыл бұрын
18:31 Grant tries to remember a mathematical puzzle, his platonic brainworks appears to screen.
@dPaziS6 ай бұрын
Heard the lil intro theme phrase and couldn't help but to think on 3Blew1Blown
@kck95423 жыл бұрын
Imagine Next time grant come up with "Namaste, To kese hen aap log" I hope someone from India will sponsor you for making some series.
@shrey3773 жыл бұрын
@@quirtt HM orz 🛐
@srikrishna2503 жыл бұрын
😂
@juliorosas-cortes4243 жыл бұрын
is it weird that i almost cried at ( 6:47 - Not being "gifted" enough ) ?
@particleonazock22463 жыл бұрын
Why you no doctor??
@franciscomorais72833 жыл бұрын
Great video! Really hope you keep posting on this channel. (The podcast is also fantastic!)
@Umbra4513 жыл бұрын
Being frustrated by my math textbooks is how I found this channel in the first place. 😛
@scanerang3 жыл бұрын
I was moving stuff around and now my computer screen sits closer to me. Finally understand why your channel is called 3 Blue 1 Brown! :D
@Gameboygenius3 жыл бұрын
It's always amazing the first time you notice!
@jonathanlevy96353 жыл бұрын
2:09 actually during my third year in university I had a course which was dedicated only to proofs from this book. Thank you prof. Yuval roichman!
@eterty8335 Жыл бұрын
It's amazing that the first couple minutes of this are the reason I now know where the name "3Blue1Brown" comes from. Genuinely so damn cool.
2:25 woah! Grant, in your interview with Steven Strogatz, he mentioned teaching at a math program at Hampshire College (HCSSiM). I just realized today that turns out this quote from Erdos was actually in 1985 when he visited HCSSiM and was giving a talk. "yellow pig camp" :)
@skilz80982 жыл бұрын
As for the continuity example. I think the most discrete answer would be a function is continuous at a given input when both of its limits exist and are equal or converge to the same value. Take sin(t) for example, no matter what input you use within this function both the left and right hand limits exist and are equal. Now, take the tangent function and examine its left and right hand limits at tan(PI/2) or tan(45) and other multiples of them. Both limits exist, yet they are not equal. The limit approach towards the right tends to +infinity and the limit approach towards the left tends to -infinity. Here we can see that the sine and cosine functions are both continuous where the tangent, cotangent, secant and cosecant are not continuous for all of their domains. The challenging thing here is that we are typically taught about continuity with respect to functions and graphs before we are ever introduced to the concepts of limits. Yet I think the best proof and representation of continuity lies within the properties of a functions limits across all of its domain.
@kindlez983 жыл бұрын
That intro woke me up!
@cookiecan103 жыл бұрын
I only just now noticed how one of your eyes is 3/4 blue and 1/4 brown. Guess that's where the name comes from xD
@Derpuwolf3 жыл бұрын
And the logo design too, it’s an iris!
@berryzhang72633 жыл бұрын
when he spoke chinese in the intro i SCREAMED he did so well i love my bilingual king
@berryzhang72633 жыл бұрын
@@donsanderson yeah!! his pronunciation was so good and he even added some tones which is super impressive
@santilasdor3 жыл бұрын
the intro got me shook
@GlowingMpd Жыл бұрын
Wow, what a beautiful narrative voice! So glad you didn’t dumb this one down by putting music over this fascinating Information 😇👍
@DD-rl7xo3 жыл бұрын
Dear Grant, The one-third of Linear Algebra of the Hubbard and Hubbard book is a great resource of LA but is rather short. And the longer, more elaborate textbooks of Linear Algebra that I could find were unintuitive(Like Axler, Strang, etc). Books like Hoffman Kunze and Halmos seem to be at a higher level than what I currently am at. Are there other detailed textbooks of Linear Algebra that teach the subject primarily as the study of *linear transformations* rather than the study of mathematical objects consisting of a bunch of numbers arranged in an array and weird operations on those objects like multiplication whose rules kind of seem arbitrary, pointless and unmotivated.
@simply423 жыл бұрын
I just took a college course called "abstract linear algebra" and we used the first 4 chapters of a book called "linear algebra done wrong." Rather than just starting with the algorthims on vectors and matricies, the book starts from the most abstract definition of a vector space, then looks at transformations between vector spaces, then shows exactly why matricies characterize linear transformations. The book then uses that as a jumping off point to learn the algorthims and stuff like row reduction, rank, and eigenvalues. Based on your description, it sounds like it's what you are looking for
@martinepstein98263 жыл бұрын
I'd recommend Axler but it sounds like you already tried him. He's all about emphasizing linear transformations over matrices. What did you find unintuitive about his book?
@DD-rl7xo3 жыл бұрын
@@simply42 Oh that sounds good, I would surely like to try that.
@DD-rl7xo3 жыл бұрын
@@martinepstein9826 I like that Axler's book tells us abstract definitions rather than focusing on computations. But my problem with the book is that it feels less motivated. Throughout the book, all sorts of operations and mathematical objects with their different properties are introduced. However, we are never told once why mathematicians invented that concept (I am not so concerned with real life applications but I really want to know why mathematicians defined things in one way rather than the other. Surely, all of the definitions in the book were later formalizations of intuitive ideas of mathematicians. Those ideas that motivated them to define those objects with those properties in *that specific way and not any other* is what I want to know so that I can appreciate what the definition actually stands for). And Axler's book while being abstract, is not intuitive or motivated (atleast to me).
@nicholasandrzejkiewicz3 жыл бұрын
Axler's book is not abstract lol
@middleearthhills97793 жыл бұрын
Judging over gifted thing can sure demotivate you, but practising and learning perquisite can sure bring surprising change to learn math. Also, I guess visualisation really helps to understand what it meant instead mere wandering in head, though it will not always the case as context , reality and drawing are critical to relate all the time as so many known and unknown parameters we have to dealt with.
@ulissemini54923 жыл бұрын
the intro!, does grant know Chinese or did he just learn the greeting?
@GrantSanderson3 жыл бұрын
I took some Chinese back in high school, and spent a couple weeks in Beijing. Sadly I've forgotten most. This was a greeting a translator handed to me, likewise for the outro.
@le0nz3 жыл бұрын
@@GrantSanderson you are so gangster that I just assume you knew mandarin.
@microhoarray3 жыл бұрын
@@le0nz ahahhahahahaha samee
@unplannedsyntaxАй бұрын
Besides everything good about Grant Sanderson, he's also got the best diction/ voice on the internet.. or anywhere! I can listen to him for hours on end.
@michaelhunter80063 жыл бұрын
Great video. Agreed on visualization as a gateway to help. I have some stuff on symmetry and computation. Have a great day and keep up the great work.
@berylliosis52503 жыл бұрын
Hey! I thought of the sum of squares solution almost instantly. That feels pretty neat
@shahidanowar16143 жыл бұрын
You got me scared af at the beginning..lol
@garrisonsnow77768 ай бұрын
Got some books for Christmas this year tbh -- pretty excited thanks for the recommendations
@Sourjya_Mukherjee Жыл бұрын
I've just realized the reason why the channel is called 3b1b - Grant's right eye has a mix of brown and blue. It's amazing how this detail only struck me today!
@salomao19893 жыл бұрын
Dude, your eye IS the 3b1b logo! Never noticed it before! Mind = blown
@BryanLeeWilliams3 жыл бұрын
I find it interesting that your channel reached 1M subscribers just after Steve Mould's and ahead of Matt Parker's (which hasn't happened yet, he's still around 900K). But all in all it's a great win for STEM.
@yonatanbeer34753 жыл бұрын
3blue1brown hit 1 million subs in 2018, I'm pretty sure that's well before Steve Mould
@1ogic9483 жыл бұрын
His main KZfaq is at 3.85M right now, this video celebrates the Chinese channel (on BiliBili) reaching 1M! The rest of the translated channels have between a few hundred and a tens of thousands subs each.
@dandelincheng99023 жыл бұрын
Ahhhhh! Didn’t expect this at all lol. Love your contents!
@santiagoarce5672 Жыл бұрын
Recently read Mathematical Methods of Classical Mechanics by Vladimir Arnold and it's probably my favourite book. Super cool topics and ingeneous presentation, just a beautiful textbook.
@johnchessant30123 жыл бұрын
probability series when? 下次一定! 下次一定!
@Maria-yx4se Жыл бұрын
your right eye really is 3blue1brown
@writethatdown100 Жыл бұрын
wait what? that's crazy!
@prometeus65643 жыл бұрын
So, you created Manim!... you are the best!
@user-pw4gt3xr1dАй бұрын
Besides about everything good about Grant Sanderson, the best diction on the internet.. or anywhere! I can listen to him for hours on end.
@ferraneb3 жыл бұрын
A different way to think about the room problem: for each person, count how many people they share a room with (including themselves) and add all of those numbers up. It's easy to see that the result is the sum of squares of the people in each room. But the number increases for the person moving rooms, it increases by 1 in the people of the room they're moving into and decreases by 1 for the people in the room they're moving out of. By the fact that there are more people in the former, the result is a net increase in the total.
@davesreb2 ай бұрын
You mentioned that it would be great if there were emojis in the margins of textbooks to help with understanding. In the Park City Math Institute (PCMI) problem sets used in their math teacher seminars, there are those sorts of comments (sadly, no emojis) in the margins. Sometimes they’re there for humor, but other comments are informative. I really like them!
@pahularora96423 жыл бұрын
Love your work Grant ❤❤❤
@samirelzein19783 жыл бұрын
waiting for your next videos, just the old good 3b1b
@nass88993 жыл бұрын
did anyone else just realize the 3blue1brown comes from his right eye? thats insane!
@12vak3 жыл бұрын
I don't believe in the philosophy that frustration is apart of your interest. The reason is that I have found plenty of scenarios where reading a book has been less or not at all frustrating compared to jumping blindly into a project. I enjoyed the not at all frustrating approach and I learned more from that.
@williamch992 жыл бұрын
The question with the room made me think about the Herfindahl-Hirschmann that measures market concentration.
@gabrielaangelinabernaliban25783 жыл бұрын
I love your Chanel 💕💕 You are the best!!
@newsshorts7158 Жыл бұрын
1) John H. Hubbard ( Vector Calculus, Linear Algebra, and Differential forms ) 2) Steven H. Strongatz ( Non-Linear Dynamics and Chaos ) 3) Martin Aigner Gûnter M Ziegler ( Proofs from The Book ) 4) J. Michael Steele ( The Cauchy - Schwarz Master Class )
@petersage515711 ай бұрын
"...because Pi has legs." I was not expecting this; I always assumed it was related to the circular nature of the 3blue1brown logo. At any rate, the Pi creatures are a great lure to catch the eye of casual KZfaq viewers who might not realize they have an interest in math. "Come for the cute critters; stay for the learning."
@N74923 жыл бұрын
"it's a curve you can draw without lifting your pencil" -- Euler, as reported by Ian Stewart.
@Aesthetycs Жыл бұрын
Incredible
@BOBMAN19803 жыл бұрын
This video came up in my feed at EXACTLY the right moment. Just a couple of hours ago, I finally decided that the vexation of a pop-math book I was trying to learn from was too much for me to deal with, and it's time for me to move on, so as not stymie my progress. (I've always struggled with math since my algebra days, but aced logic, and have managed to teach myself enough of the relevant math for my physics to not fall too far behind.) I'm not going to say the book was 'bad'. Just that it's way of presenting the information--some stuff about a family of 6 boys, 6 girls, a mom and dad, and trying to see how many dance pairs the siblings can make--was not helpful at all. But at least I learned what FACTORIAL is!
@sacalius_papalagius2 жыл бұрын
I think I have a problem. I dig all the axioms and definitions when I start reading about a branch of mathematics but I don't really like the how all this is usefull part that comes after.
@venkatbabu17223 жыл бұрын
You can easily add one plus one is two. But real mechanical trace for that is a different story. There are so many ways but there is no proof that there is only one way to solve a problem. Though the idea is the same result. Because source and destination are same for every problem. Visualisation is the different forms of how human brains work. Almost 90% of mathematical solutions lie on filling the gaps. For example a random numbers sequence to an orderly is filling the gaps to regular.
@cogitoergosum28463 жыл бұрын
Nonlinear dynamics was phenomenal
@nexovec3 жыл бұрын
7:45 You don't understand mathematics, you get used to it. And apparently, so does van Neuman, because that's his quote.
@EulersBasement3 жыл бұрын
Freshman year we used Hubbard and most of my friends made fun of me for liking the book. At last, someone else likes it.
@SweatySockGaming3 жыл бұрын
Alot of people like that book
@alexpehers30333 жыл бұрын
Thank you soooo much, I love your videos!
@dunebrowning98293 жыл бұрын
The problem at 19:00 really looks like some sort of inverse of entropy since entropy is a time dependent phenomina I think this is a very interesting problem.
@noonesperfect3 жыл бұрын
好的 3蓝色的1棕色的 .... I almost thought entire video will be in Chinese lol
@ahmadsalameh79593 жыл бұрын
Hey Grant, can you in your next podcast interviews interview a famous math lecturer on youtube like Gilbert Strang or Tom Leighton?
@knightwik3 жыл бұрын
@@markv785 He is one of my professors for mathematics at my university!
@sumitgupta69053 жыл бұрын
Yes , bring prof. Strang
@Handelsbilanzdefizit3 жыл бұрын
My recommendation: "Elements" from Euklid. First learn the basics and learn to think mathematically, then the rest is easy. It's like jumping in a pool. First, the water is just cold. After a while, it makes really fun.
@raptorzz8571 Жыл бұрын
Do you mean Euclid?
@imranq92413 жыл бұрын
What's crazy is that i recently picked up each of the books Grant mentions except for the Cauchy schwarz master class
@im44852 жыл бұрын
Hello Grant. I am immensely benefiting from your videos. Can you please make a video where you could maybe show a roadman for self learners of mathematics? Your favorite books?
@edellavalle3 жыл бұрын
I need a version of this video but every time he says "The Book" the volume goes way up
@arnav2573 жыл бұрын
3:30 Thought provoking, indeed: why not mainstreamise masterclasses in mathematics?
@sceKernelDestroy3 жыл бұрын
We definitely should!
@thedarkknight18653 жыл бұрын
Calculus is brain of Maths and Alzebra its heart
@Maniclout3 жыл бұрын
This dude is amazing
@shawon2653 жыл бұрын
Hi Grant, what's your thoughts on Nathan Carter’s book "Visual Group Theory"? I like all the visualizations, applications and even warnings against misconceptions. Is there any better book recommendation for Group Theory?
@shawon2653 жыл бұрын
I should probably mention I am currently learning Group Theory from this book. I have gone to an introductory class, but everything was just too abstract. I understood them, like Cosets for example. But those definitions didn't stick with me. But here, they use Cayley diagrams and point out Cosets with a few examples which creates a clear mental image for me. I worry if this book is not "Complete and concrete enough". But personally I am open to reading other books after this.
@adityakhanna1133 жыл бұрын
19:30 The problem of rooms is very closely related to the Raising Operator on integer partitions
@cherrymarriedindiscord1404 Жыл бұрын
... the things I missed in my education dude... The things I missed...
@akashsudhanshu5420 Жыл бұрын
Honestly, I feel sad that I have learnt math in a way that I can write proofs, solve problems but not yet learnt the way that I can recite proofs in a poetic way (like your videos), in a simple- sleak, clear way., like a story. I am inspiredby your videos, 2 days from now, I have to give a seminar on Fourier series. And I will try my best to make it motivating, that will make audience interested in its maths. I was going to lecture like dumping the theory infront of them, but then I saw your video and I clearly see what's smelly, unattractive and whats has a nice fragrance, makes us wonder. Your videos have opened a closed gate that only allowed theory to pass, now I am interested in simple exxplanation. I know this leap will be difficult for me, to be patient, read and write in my own words, but I want to promise that I beleive its going to be rewarding, I would love it. I wont give up. Thankyou so much.
@simongee75793 жыл бұрын
😳😳😳the language was unexpected...
@gromgromeson3 жыл бұрын
Geometric/Clifford algebra when? :)
@TranquilSeaOfMath10 ай бұрын
12:12 The book, _Cryptological Mathematics_ by Robert Edward Lewand, has a few characters in it that react, and "interact" with the information.
@stemstudentph92463 жыл бұрын
Thank you for this video.
@khaled46353 жыл бұрын
Grant giving a student friendly perspective on Mathematics, is probably on of the best things on KZfaq. What I am missing in the book recommendations list is a discrete mathematics book, is there any good textbook about the subject for autodidacts?
@fakhrimahendra41713 жыл бұрын
I dont know you have that many fans in mainland china
@andyl.59983 жыл бұрын
Well, math is the universal language of STEM.
@GrantSanderson3 жыл бұрын
It's largely thanks to a vibrant set of translators who have kept that page well-loved and running.