You are setting the bar right now for the future of mathematics education, and you are setting it VERY high.

@allsparkwars2644

4 жыл бұрын

its approaching infinity

@Artaxerxes.

3 жыл бұрын

its over 9000

@christopherwright3586

3 жыл бұрын

It's more like -1/12

@praveensoni2245

3 жыл бұрын

@@Artaxerxes. best way to introduce

@commentor5479

3 жыл бұрын

@@christopherwright3586 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68...

0:34 9-Problem Solving Principles/Tip 1:15 Question 1 (Probability) 2:08 Who is Ben Eater? 4:25 Inscribed angle theorem, θL=2*θs 5:58 Tip-1 7:48 Tip-2 8:16 Question 2 9:34 Answer 2 10:29 Tip-3 15:17 Tip-4 22:48 Question 3 25:56 Answer 3 (Marked incorrectly, Answer: Option D) 26:31 Answer 1 27:28 Explanation for Q1, Floor function 30:38 Tip-5 32:53 Tip-6 33:36 Question 4 34:43 Answer 4 36:37 Question 5 38:10 Answer 5 41:48 Probability graph in Desmos 44:08 Revisiting an alternating series sum for ln(2) 47:29 Tip-7 51:08 Tip-8 55:23 Audience questions through tweets 57:28 Tip-9 58:29 Python programming for various probability question 1:04:31 Arts created using Desmos graph tool with mathematical expressions 1:05:54 Thank you, appreciation to team and all. _Water Sip:_ 23:26, 23:36,34:06, 37:28, 1:03:42

@vedantwate4105

4 жыл бұрын

U deserve more than 1k likes ,,so underrated!!!😭

@lightyearahead

4 жыл бұрын

Thank you!

@obnoxious2471

4 жыл бұрын

I'm just here for the water slurps

@61gopalprabhulsm70

4 жыл бұрын

pens used?

@lefudj4236

4 жыл бұрын

*water sips with passion*

Why should you watch his videos? 1. You will learn to think intuitively. 2. You will get better at Mathematics (not just the course work but also the daily life mathematics). 3. Your problem solving skills and spatial thinking abilities will improve dramatically. 4. He is the best teacher possible. 5. He is just awesome :)

@JustFamilyPlaytime

4 жыл бұрын

Sounds like a man crush to me :)

@madhurima3914

4 жыл бұрын

@@JustFamilyPlaytime ;)

@XFreakyDeathX

4 жыл бұрын

@@JustFamilyPlaytime I mean, he sure is pretty handsome

@adityaprasad1322

4 жыл бұрын

And DAT gorilla

@siddharthabrh

3 жыл бұрын

Axomiya ?

Petition requesting Grant to make a series teaching python in his unique way.

@hirakmondal6174

4 жыл бұрын

That will be a dream come true. And moreover I am eager to learn about Manim library that he created. It will be so helpful for young learners like us. So ya, Grant please make some videos on the same. And as always, love u . :)

@subhramitbasu3886

4 жыл бұрын

Yes please.

@billrussell3955

4 жыл бұрын

Grant I'm a major supporter and funder. I would love to see how you would layout the inverse square law with M2 increasing. And the effects on the celestial bodies as M2 acceates mass. With M1 staying reasonably static. Thanks

@52.yusrilihsanadinatanegar79

4 жыл бұрын

Yes

@alfredwillins

4 жыл бұрын

yes yes yes

Problem solving tips 1. Use the defining features of the set up. 2. Give things (meaningful) names 3. Leverage symmetry 4. Try describing one object two different ways 5. Draw a picture. [Have some numbers? Make them coordinates!] 6. Ask a simpler version of the problem 7. Read a lot, and think about problems a lot. 8. Always gut-check your answer! 9. Learn at least a little bit of programming

I just applied your tip on a higher level maths worksheet than mine and holy shit it works!! Hopefully I get better at Maths. Thank you!

@3blue1brown

4 жыл бұрын

Cool, what was the problem?

@saurra3953

4 жыл бұрын

It wasn't just a question. The worksheet had some geometric theorems given which had to be applied on a collection of problem. Turns out, proving the theorems first does help in understanding questions better.

@sudheerthunga2155

4 жыл бұрын

Ooh cool ,Is there a way you coudl share us the Worksheet? It would be fun

@sudheerthunga2155

4 жыл бұрын

@Christian Weissmuller Yeah (P.s., even I'm school going too) :)

@technoultimategaming2999

4 жыл бұрын

@@saurra3953 ikr. If I find a calculus differencial question that requires chain rule, I never remembered it. It felt like "derive the power, multiply by the power, the power has to be divided by x^2 because the power is 5763x. And then we rise it to the 9! power and we subtract the number by pi'th' root of e" But they way 3b1b explained it "We call this power g(x) and we can derive in terms of g(x). Now we derive g(x) in terms of x and solve the thing"

Oh, it's a shame this series has to come to an end. I was fond of it and your constant enthusiasm. As always, you left me astonished at the terrific quality of your content and thus I'd like to thank you for putting your efforts into such a generous project. You're awesome!

@kirikouthemightyandstrong3183

4 жыл бұрын

what a name !

That "double projection" proof of the Pythagorean identity almost took me right out of my seat!

@chicchi1682

4 жыл бұрын

Right! Most beautiful Thing I've ever seen

@vanshajshukla6205

3 жыл бұрын

Correct ,it was opening like a thriller

@Ilportavoce

3 жыл бұрын

goddamn i didnt know it was gonna be that good but GODDAMN

@anitagupta

3 жыл бұрын

Time stamp plzzźzzz

@jordanadkins1828

2 жыл бұрын

@@anitagupta @13:43

Thank you so much for putting together this absolutely splendid lockdown math series. It's been a pleasure to watch each and every one. In particular, it's been extremely gratifying to review (and expand upon) ways to conceptualize exp(x), because it is such a lively function with so much to explore about it. Wishing you happiness during the times of quarantine ahead :)

My professor would say he doesn't need to draw a perfect circle. He just needs to state the curve he drew is a circle.

@gregoryfenn1462

4 жыл бұрын

Yeah true but the proofs are usually easier to explain and understand if your diagrams are at least roughly accurate

@danielpetka446

4 жыл бұрын

Lol

@WanJae42

4 жыл бұрын

In art class, I often have to declare what the sketch is.

Tip 5 : Draw a picture. This tip is also very useful when solving problems related to mechanics. *Grant is like Bertrand Russell, thinks like a mathematician and talks like a poet.*

@jyotisampat3246

4 жыл бұрын

More like Billy Graham, of mathematical cult.

@elliott8175

3 жыл бұрын

To be honest, this is true even for non-mechanical stuff.

@malihareza4754

3 жыл бұрын

Couldn't agree more

@connorkearley7381

2 жыл бұрын

yes 😊

31:22 - 31:42 You are officially the Bob Ross of math. Edit: I don't know why my timestamps were messed up.

Those were great, can’t say more than tank you, thanks Grant.

@migfed

4 жыл бұрын

I cannot agree with you more

@harrypotter-po9yh

3 жыл бұрын

thank you**not tank you

@particleonazock2246

3 жыл бұрын

Ok Matron Carl Friedrich Gauss.

Feels like our favorite TV show just ended with a touching last episode. Thank you so much Grant! You're a wonderful person.

I am grateful for this whole channel and this particular series of lives which brightened my lockdown and most certainly the lockdown of other math fans. Looking forward to re-watching it all and watching the videos coming out later.

I've always struggled with problem-solving. My process usually involves a lot of coffee, degrading into confusion, sleepiness, frustration, and possibly paper violence. Thanks for talking about this stuff.

@gerardomalazdrewicz7514

4 жыл бұрын

well, there is a definition of mathematician as someone who turns coffee into theorems.

@tetraedri_1834

4 жыл бұрын

@@gerardomalazdrewicz7514 And a definition of a comathematictian that turns ffee into cotheorems.

For probability problem, you can also try to find the probability of being even if rounded nearest, or round up as well. The answers are quite surprising in some ways. By the way, you should be able to answer right away for round up, given that you know the answer for round down. Hint for round nearest: there is pi.

@3blue1brown

4 жыл бұрын

Yes! I meant to mention this, then forgot :)

@guyedwards22

4 жыл бұрын

Is it 1-(ln(2)/2) for the round up case and (5-pi)/4 for the round to nearest case?

@elliottmcollins

4 жыл бұрын

Yeah, I spent like 20 minutes figuring this out before watching +3Blue1Brown 's answer, only to realized I'd done the round-to-nearest rather than round-down problem.

@elliottmcollins

4 жыл бұрын

I think that may be why everyone said D, too. That's the right answer if you round to nearest instead of rounding down.

3b1b is hands down one of the most influential youtubers regarding math (and also logic and physics). He always provides intriguing problems and creative solutions to them. What's more, he explains the thought process, ideas and connections to other problems/topics which is incredibly beneficial for people who are interested in mathematics. I just want to express my appreciation and thankfulness, that's all!!

I'm glad you exist, sir. You made calculus so easy for me. Thank you.

Please consider doing more lectures on lockdown math, Grant. You're just awesome at the math and I love the way you look at problems. It breaks my heart to see you go.

Thank you Grant for such beautiful and encouraging sessions during these testing time's... Those new perspectives and visualizations of different functions like exp(x), cos²x, e^(iß) just blew me away.... It's always astonishing and exciting when you think you know the topic and then someone comes up and just changes your thinking... Thank you once again..

Grant, your videos are absolutely incredible! This series has been so helpful for me - I am a high school student from India hoping to pursue Physics at university this year, and I have stayed up for almost all your lectures because they always have little things that are so fascinating and are never taught conventionally. You have really inspired me with this lockdown series, and I just wanted to let you know that what you are doing is something truly amazing. I have been homeschooling for the past four years and your videos, especially the calculus series, have been extremely useful (and very beautiful!). You are one of the reasons I want to study Physics. Thank you so much, and please, for our sake, never stop what you're doing!

Best math tutor in the world, wish I had one in my early years. I started to understand and love math. I then moved on to applying math to solve problems. Hopefully, in the future will get to innovate in math.

This dude made me excited about math all over again, I wish we had you as teach back in highschool..

Thank You so much for this entire series Grant.I developed a deeper understanding and liking in maths thanks to you.I missed a few of the episodes because it is a bit late here .Nevertheless,wanted to thank you for the amazing visual intuitions you always provide

@squibble311

4 жыл бұрын

ℂouldnt agree more!

@sandeepbharadwaj6914

4 жыл бұрын

@@Leonardo-lb6rs Umm why?

@appleslover

4 жыл бұрын

@@Leonardo-lb6rs I am also 19 and now I am thinking of double majoring math(s) a and genetic engineering (it's been 2 years actually but now I am thinking of it seriously).

@Leonardo-lb6rs

4 жыл бұрын

@@appleslover Man! That's sounds so cool and exciting. Genetic engineering is far more revolutionary and necessary than most people realize. Good Luck👍

@sandeepbharadwaj6914

4 жыл бұрын

@@Leonardo-lb6rs Oh I am 17 if you were curious

Your eloquence and flow of speech is stunning (especially in front of the camera filming live!!!)

This series is a must watch for everyone I feel.Grant sir,you are such an awesome teacher!You are my favorite teacher, and also the best from whom I ever learnt!Thank you so much!!!

Thank you Grant for putting up this Lockdown Math series! Watched every single episode, took notes, solved the problems, learned a lot, and had tons of fun! : -D

So useful. Thank you, Grant! Your lectures are brilliant.

What do you mean last lecture!? D: I'm not even a half of a mathematician yet... maybe 𝒊 times a mathematician at best.

@noahtaul

4 жыл бұрын

Well then you’re absolutely a mathematician!

@herrk.2339

4 жыл бұрын

@@noahtaul But the reality of his mathematicianship is 0

@ilke3192

4 жыл бұрын

I can't figure out what you mean, what a complex situation

@squibble311

4 жыл бұрын

very ℂool ;)

@jonnyp1340

4 жыл бұрын

You really did a full 1̶8̶0̶ 90 on that

These were great, thanks. I'll miss them but also I look forward to your usual content. Also, those artworks at the end were incredible!

excellent video ! no one actually thinks of such question that how to become better at problem-solving as it's not having any specific answer ... but the points listed down in the above video are actually promising and helpful but at the same time open-ended, which concludes that "use them and then only you feel that they work!".It helped me actually !!

when he said," throwing things at the screen, getting angry." that made me laugh so much

1:02:45 ARE YOU OUT OF YOUR MIND. Grant, I love you. But that's just absurd. That lingering sneeze that doesn't want to come out is the worst feeling ever.

@wintersfan

4 жыл бұрын

It Always Happens To Me Because My Dad's AC Is Too Cold

@justitroyal7032

3 жыл бұрын

100% agreed

I have always enjoyed Maths. Your channel and this lockdown series really takes the cake in my book. Thank you very much for sharing your talents in such an enjoyable way. You are my Richard Feynman of Mathematics. Please, please keep doing this!

Your content is meaningful and really broadens your viewers' thinking. It competes favourably with anything on KZread for me, even from an entertainment standpoint. Thank you so much for existing, mate.

This is probably the most important 3B1B video of them all. Here, Grant distils all his years of learning and inquiry into a few actionable ideas, expressed simply. As an engineering senior who barely tolerates pure mathematics, I have seen Grant mention these ideas before and noted the similarity to the process of solving an engineering problem. By following a systematic and disciplined method one can make sense of a complicated practical system and solve for all kinds of unknowns. We always define our system, draw a diagram, look for symmetry, find alternate expressions for variables, plot data to look for connections and so on. And the teaching process is designed to take us from simple problems to more complex ones, but often the key to a tricky problem is to imagine a simplified or extreme case ('what it [x] were zero, or infinite?') and generalise from there. Of course we have the luxury as students of saying 'assume [friction, or some other pesky state-dependent variable] is negligible.' And with many mechanical systems, understanding the geometry is often the most important step.

48:37- 48:41 is basically my life as a mathematician and a musician. Don't get me wrong; watching amazing solutions to problems or really talented players really inspires me to get better at what I do, but at the same time it can be quite frustrating because even though you might be 'halfway there' you know it will probably take a while to reach your goal. And when you eventually get there you find someone that's even better and you feel like you're always stuck on someone elses shadow. And truth be told, for the average person, you'll eventually find someone better than you. And although it might hurt your self-esteem a lot (at least if you're like me), it ends up being a good thing, because (then again, if you're like me) once you overcome that feeling of not being good enough it encourages you to keep improving by giving you a new goal. Otherwise you tend to stagnate. Wow, at first it was kind of a joke comment, but I ended up getting all philosophical. As always, awesome videos, Grant! Even if I already know some of these things, I always find at least a tiny bit of beautiful math that inspires me to learn more.

It feels a little sad when the final music starts after your goodbyes but then it leads to an amazing afterthought...Many Thanks!

This series was EPIC. Without your precious help I might have never understood "what Euler's formula is actually saying", even though I have seen other videos explaining the topic (the 5th episode with imaginary interest rates was one of my favourite videos). Thank you!

G.Polya's "how to solve it" is relevant here

@3blue1brown

4 жыл бұрын

Outstanding book.

@justitroyal7032

3 жыл бұрын

@@3blue1brown I feel very jealous looking at all the books in your background

@thomasteepe

3 жыл бұрын

@@3blue1brown Another book worth mentioning here is "How to Solve Problems: New Methods and Ideas" (2008) by Spyros Kalomitsines. In chapter 3, Kalomitsines presents a "spiral method of problem solving", a flowchart-ish combination of three elements: 1) The description method: Try to collect as much information about the problem and its ingredients in a list of short notes. 2) The means-ends analysis method: Find the difference between what is given and the goal, and then cover that distance. 3) The getting out of loops method: If you get stuck, formulate negations to the approaches you've tried so far, and generate new ideas from these negations. The book has a strong emphasis on writing ideas down. In my view, this is a very valuable alternative to the much more famous catalogue of questions given in Polya's "How to Solve It".

51:05 This is me. 100% of the time. During a math exam, when I'm tired I tend to think "Ohh this looks like that!" and sometimes instead of subtracting I add. Then, after the exam I'm like "That was a stupid mistake"

Thank you so much for this incredible series! It helped me develop a different way of thinking about approaching math problems

Thank you for everything! I study Computer Science so I've been learning calculus and algebra etc but I didn't have that deeper understanding. I've watched some of your videos a few years ago but then I rather enjoyed the wonderful quality and lovely pi creatures than content itself(I didn't know back then about integrals and so on). Now during quarantine I have eventually time to understand all that stuff that I was just counting without understanding what actually I am doing so I could pass my exams. Your channel is my Netflix right now :D Love the content, love the animations, it's just pure perfection.

I literally never comment on videos but just wanted to say Thank you Grant for sharing your wisdom and contagious excitement for mathematics. Thanks to you I have been thinking about e, pi and i a lot and what they say about natural phenomena in general. Really appreciate it.

Of course, he is not only smart as hell but also freaking handsome ...

@BlessedForever888

3 жыл бұрын

and has a very pleasant personality and sonorous voice. Altogether making a perfect math teacher.

I just watched your TedxBerkeley presentation and I just want to say that it was absolutely inspiring. I was so nervous to take my schools Calculus series and now I can't wait. Math has always been a struggle for me and you have made me (and i'm sure many others) feel confident and curious. Thank you so much!

Thank you for this lockdown series, it's been very pleasing to follow!

Notably: "Google for the answer" is not one of the steps that you list.

@washieman2445

4 жыл бұрын

thats only for programming (stackoverflow)

@benjaminswartley1803

4 жыл бұрын

@@washieman2445 Until you actually have a situation where you need to ask a question on Stack Overflow and it gets marked as a duplicate of a question that is nowhere close to the one you asked. Not that I wouldn't survive without SO.

@washieman2445

4 жыл бұрын

@@benjaminswartley1803 yeah it can be a really toxic place at times

@grig517

4 жыл бұрын

@@benjaminswartley1803 Relatable...

@Ultiminati

4 жыл бұрын

@@benjaminswartley1803 Why can I relate to that even though I don't use Stack Overflow, lol. uh, I remembered, I once posted a Discord suggestion and it was marked as a duplicate which wasn't even close, then couple months later they actually brought that feature I suggested.

your saying that you get one mistake, people unsubscribe. your job is intense. 4:09

Haven’t solved any problems till now but it would surely help. Earlier when I used to solve tough questions many a times it was not defined on how to interpret the question. This actually works, even before the video came I had one or two techniques in my mind but never used them. Never thought that these are so important. Thanks for changing my perspective

I feel very humbled by your amazing ness, but also inspired to try to become better myself. Thank you so much!

I hope you enjoyed making these. I think the high-quality animation videos risk suffering "perfect is the enemy of good", and we'd get less content. On the other hand, there are other excellent math KZreadrs you've recommended.

Grant i just wanna say how deeply grateful i am for the content you made, you truly inspired me to think deeply about topics in maths rather than brushing them off, growing up i rarely had teachers that knew or understood what they taught, but I'm truly glad to have come across your channel, u really make me appreciate maths Best wishes, from South Africa

First did not understand the prob problem. When Grant started explaining, saying about floor, I totally got the solution way, made the picture and noticed the known series. The problem was solvable in a so sophisticated way I can not tell Thank you Grant so much. You have a good language and very rich vocabulary with so many mots de beau. The journey was really exciting, I will definitely watch anything like this later

I was just complaining to my geometry teacher how random the ways the problems are solved look to me, thank you this really helps.

@51:10 isn't that the mistake, it should be - 1/2*ln(2)+2 , which will be (-0.35+2)/2=1.30/2 =0.65 ...... Also at @51:44 he says he makes purposefully makes mistake. Grant intentionally switch the signs. Such a great series specially the complex number and tetration, Euler identity are great ones to look closely that hardly anyone teaches to the core. Hopefully he will continue with different topics. Thanks a lot to the whole team :)

Hello, thank you for sharing the lesson, I enjoy it! By the way can you please share what camera you're using to focus on the paper?

Subscribed for nearly 3 years now and as fascinated as I am by the other videos, this one is my favorite. 'read a lot, and think about problems a lot', the build up and explanation to that is what teachers need to tell/show the students. I have seen many hardworking students take this statement to mean practice, practice & practice already solved/non-diverse problems, which ultimately leads them to believe that despite practicing, they are not getting better. I would love to see a video on this point being elaborated even further, showing how one should go about this, using(if possible) more basic problems that can be shown to students still in high school as well.

This is better than 99.9% of what you find on YT these days. Often times I even understand what you're talking about, and sometimes I even get the answers right. Makes me feel good actually, fun stuff.

I wonder how long did it take you to think through and prepare these lectures.

Ah, so at last you stepped into a field where I'm more comfortable and could actually say something, rather than listen with my jaw dropped to the floor. :) So asking about tips to solve problems in general is a weaker form of a question about an automated, formal procedure to solve problems in general. And so it might have been nice to point out at the very beginning, that it's already proven that such a procedure cannot exist (precise formulation of the problem was to find a formal procedure, that for any statement in a mathematical theory would indicate whether the statement is true or false), so tips is all that we can ever hope for. It happens to be one of my favourite achievements in 20th century mathematics. It was proven independently in 1930s by two mathematicians in very different ways. One of them was Alan Turing (who imagined the famous Turing Machine and used it for this very proof) and Alonzo Church (who used his own invention of Lambda Calculus). They actually met later and together proved that both solutions are equivalent to each other (if I remember correctly it was Turing's PhD thesis and Church was his supervisor), laying foundation for modern computer science, especially programming. Actually all modern programming languages are in one way or another based either on Turing Machine or Lambda Calculus.

@ehtuanK

4 жыл бұрын

Shouldn't that be equivalent to Gödel's incompleteness theorem? It seams to me that both can be derived from each other: If there are mathematical statements that can neither be proven nor disproven mathematically, that obviously implies that there is no formal procedure that can determine for every statement whether it is true or false, since no procedure can work on undecidable statements. Ergo: Gödel => Turing & Church. If there is no formal procedure that can determine for every statement whether it is true or false, that implies that there are mathematical statements that can neither be proven nor disproven mathematically, since if there weren't such statements, each statement would have a finite string of mathematical symbols that either prove or disprove it, and therefore a formal procedure could consist of iterating through all such strings (which is in principle possible due to the set being countable) until a proof or disproof is found (be that strategy as unpractical as it is). Ergo: Turing/Church => Gödel.

@Sventimir

4 жыл бұрын

@@ehtuanK, I don't remember the details now, but I believe it's not exactly equivalent. According to Wikipedia, Turing explicitly cited Goedel in his paper, which implies, he already knew about Goedel's Incompleteness Theorem, published only 4 years earlier. What I do remember, Turing in his paper described the halting problem and proved it to be unsolvable for a Turing Machine. Then from it he somehow derived proof I referred to earlier. It likely goes along the lines that having a procedure to decide statement's truth would allow you to solve the halting problem, which we already know cannot be done. So the question is equivalent to that about the halting problem, but not to Goedel's theorem. I recommend a great book by C. Petzhold, "The annotated Turing", which cites Turing's paper in extenso and explains it almost sentence-by-sentence.

@randairp

4 жыл бұрын

@@Sventimir I believe ehtuanK's right that they're equivalent. Not only would "having a procedure to decide a statement's truth" ---> "solve the halting problem", but the converse is also true. For intuition: write a computer program that searches for a counterexample to Goldbach's conjecture. It halts if and only if the conjecture is false. So we can prove/disprove theorems by deciding if a program halts. More generally, suppose we have a theorem T, write a computer program that enumerates over every proof in our theory, halting only if T is proved. We can run the same program on the negation, ~T, and now we have "a procedure to decide a statement's truth" by "deciding if a program halts". (This assumes the excluded middle on provability, i.e. if the program diverges for both T and ~T, we end up showing the system is incomplete, and if both halt, unsound).

@Sventimir

4 жыл бұрын

@@randairp But the assumption of excluded middle on provability itself contradicts the Goedel's Incompleteness Theorem. Hence if the program never halts, the statement is true OR unprovable (in which case it can still be either true or false) and you cannot know which. Therefore even having a solution to halting problem does not give you a procedure to decide whether a statement is true or false. Also the rule of excluded middle is generally suspicious. It grants you the ability to show something exists without being able to point out to a concrete example of such object (via proving double contradiction), which isn't worth much. Actually logical systems built into some programming languages designed for theorem proving (like Coq, Isabelle or Idris) are all modelled on intuitionistic logic, which rejects the law of excluded middle. Although I admit it's difficult and I might be mistaken here. The book I referred to earlier explains it, but unfortunately I don't have it with me, so I can't quote.

@randairp

4 жыл бұрын

@@Sventimir "A procedure to decide a statement's truth" does seem ill-defined to me, I'm not sure how it would be specified. I'll look at that book. The interesting thing about dependent type theories like Coq/Agda/Idris is that they effectively guarantee their own incompleteness. They don't necessarily reject excluded middle, it's just unprovable, though still consistent with the theory.

Hi Grant - Thank you for these awesome lectures. They have shown great insight to me despite already being an almost undergraduate student of math. Beyond that it has generally just been truly relaxing and enjoyed. You have a very calm voice and an easy-going pace such that I prepare a good seat and a warm cup for every session. In particular this last lecture and your 7th tip on being a better problem solver enforced the gain that I feel I get from watching your videos. Coupled with exercises I truly do believe that you channel is one of the best pathways to learning available to us in this day and age. For future videos, series and courses you could maybe apply this feature more heavily (which you already have) of introducing a single or a small set of problems (perhaps in a separate video or in text form on either social media or another platform) for viewers to ponder about. I am personally very encouraged to work hard on it knowing that others are doing it as well and it will be covered thoroughly. For what it's worth, you have yourself a new patreon supporter, as soon as I've set up a patreon account. Thank you.

Another tip of yours from previous videos that I find really useful, Grant: sometimes it helps to 'fast forward' to the answer of a problem computationally in something like Python, and then work backwards. This one worked fairly nicely for the probability problem using some basic plotting. I suppose this tip could be abstracted further to 'iterate and observe'

This is the first time I’ve ever been legitimately curious and interested in high level math. Not sure why this was recommended but this guy is a god-tier teacher

1. Use the defining features of the setup 5:58 2. Give things meaningful names 7:48 3. Leverage Symmetry 10:29 4. Try describing one object two different ways 15:17 5. Draw a picture 30:38 6. Ask a simpler version of the problem 32:53 7. Read a lot, and think about math problems a lot 47:29 8. Always gut-check your answer! 51:08 9. Learn at least a little bit of programming 57:28 10. like useful comments ;)

@ti84satact12

4 жыл бұрын

Thank you forthis!

Grant, I've been away from your channel for awhile, and this is the first video I've seen a video that shows you as you teach. I really like it, and I think it's a big improvement.

Thank you for the lectures, you've made them really amazing. **looking forward to new ones**

Already nostalgic

@jinjunliu2401

4 жыл бұрын

for real 😭

I would love to see an essence of group theory series. I think there are great ways to visualize things like cosets and the isomorphism theorem.

Please do consider new videos of a series like this on...anything in the math world. You present it so well and shared some great ways of thinking about the complex plane, e, pi, logs...a ton of stuff and in ways that made it all so much more broadly intuitive and understandable. The community would be so stoked to see these keep going; it's really comforting to have in these times and I hope is helpful to you to share all this stuff too during these times. It's really cool how interactive it is, yet one-on-one you present it to us as students of all backgrounds. Super gifted teacher, and student yourself.

Thanks for all of these videos, you're an incredible teacher!

Grant, please make a series on how teaching math to children! I would love to help my son to learn math the way you teach!

I am always looking for ways to improve my problem-solving skills, this is such a good video! also, you literally look like prince charming

Please keep doing live lectures! These are amazing!

Best mathematics lecture EVER!!! Thank you so much this is so confidence building and with very useful tips to start problem solving. I didn’t quite get the answer but I got a good upper bound on the problem using a different method - and I did spot your mistakes!

Can’t believe we are losing this series due to haircuts... Also Are you going to upload the next part of ‘Probabilities of Probabilities‘?

Please , when the next livestream will be available. I missed a lot of theme ( just replay) . Thank you so much!!

@wassilywsky6333

4 жыл бұрын

I think this is his last stream, maybe, he has mentioned' last lecture ' (of this series)

@abderrahimelouafi1373

4 жыл бұрын

@@wassilywsky6333 thank you sir.

Not five seconds after I finally had the lightbulb moment and realized where we were going I hear the reassurance to those that haven't had it click yet. Thank you for being kind to those of us that are a little slower but are trying! :D

Thanks Grant, good to see that simple strategies can be used to begin solving complex problems, especially the part with we have, what we learn.

3 blue, 2 eyes and his blouse, 1 brown, his hair

Don't know why my brain finds it hard to match your voice with your face

There are great channels but this one is in a category of its own.

You are great. All of the videos of lockdown series were interesting and cool and I think it will help to make a different perspective towards math . Thanks for your videos.

Hey I drop by here, just want to see what the math magician's face looks like

at the x/y question, if it was the ratio, why didnt you solve it by solving [y/x]? It wouldve been less confusing as that is the inclination of the line you've drawn....

Really Amazing approach. I did not expect the problem evolves this way . Bravo.

46:58 "Pattern recognition but wearing a little added clothing" Loved it. Most potent and most honest. I see what you meant by the red now.

I was kind of surprised that Polya's How To Solve it didn't get a mention right at the top. If you don't already have it, kick yourself in the ass and go and buy a copy.

Since we know odd numbers and even numbers share equal symmetry, why that probability question's answer is not 0.5??? Could anyone plss clear my doubt....

@FlyingSavannahs

3 жыл бұрын

It depends on values of the 1st and 2nd draws. Grant labels these as x and y so I will too. One half of the time you would expect x p(total) = p(xy) = 0.5 + (>0.0) p(total) > 0.5

@shahal6657

3 жыл бұрын

@@FlyingSavannahs Thanks bro✔️💯👍

I know Im a couple years late to this, but Ive been told or read this theorm probably 4 dozen seperate times in my life. This is the first time ive seen any proof for it, and now ai will never unsee it. Thank you

These lectures are very helpful in getting the brain to work on very different problems, giving new routes to progress in. Would be amazing if you could do one lecture once per month, talking about multiple subjects, giving "homework", then answering those questions in regular animated videos.

When is the """LOCKDOWN MATHS IS BACK""" series starting? I'm waiting impatiently. Truly loved this series 👍

59:50 I was curious as to how Grant managed to keep his hair looking fabulous this late. He certainly wouldn't agree. The only option now is to pick up the shear yourself and do small meticulous cuts following a video tutorial until a satisfactory cut has been achieved. Best if someone willing to help on this endeavor.

@mistertheguy3073

4 жыл бұрын

Approximate the haircut with increasingly smaller (infinitely small) cuts

These are some great problem-solving tips! I've found tip #8 especially helpful since I often make stupid mistakes, but then I find it helpful to look at my solution and see if it seems reasonable.

Where was this guy when I was in school… These kids today don’t know how good they have it! Excellent job on this video!

It would be great if you can do a series on Mathematics of Machine learning. Thanks.

@hassanakhtar7874

4 жыл бұрын

He has a series on neural networks (classic AI). If you haven't, check it out!

My brain just can't sync his voice to his face!!!!

@conantheseptuagenarian3824

4 жыл бұрын

same here. totally weird.

I really enjoyed this series. THANKS.

Thanks Grant - excellent live series - please do more when you can