Topology & Geometry - LECTURE 01 Part 02/02 - by Dr Tadashi Tokieda

This video forms part of a course on Topology & Geometry by Dr Tadashi Tokieda held at AIMS South Africa in 2014.
Topology and geometry have become useful tools in many areas of physics and engineering, and of course permeate every corner of research in today's mathematics. They often help us make fresh progress precisely because they are very unlike, and complement,traditional differential-equation-based methods. Yet they are almost never taught to students outside advanced pure mathematics. This course teaches a minimal amount of topology and geometry of maximal usefulness in applications, relying on pictures and avoiding abstract algebraic machinery. The motto of the course is: look at the generic situation, spot invariants, solve your problem by
deformation. I hope that the course will train you to THINK IN PICTURES.
Note: Some of you may have studied point-set topology (metric and topological spaces, continuous maps, compactness, etc.). The content of this course is different: it is usually called algebraic and differential topology. This course is designed so that familiarity with point-set topology is unnecessary.

[@aakashchatake]

So the Feynman is alive through you !! It's the best ever anything on mathematics. It's a answer to why and what. I wish one day I could listen you front to front. Live long ..

[@chycho]

WOW! Dr Tadashi Tokieda, you just blew me away. What an amazing teacher. Thank you.

[@missysmithy25]

Ok... This professor is AMAZING. thank you, sir!

[@nuclearnyanboi]

missysmithy25 Check out the channel 'Numberphile'. He features there.

[@upadhyaypriti4712]

@@nuclearnyanboi, else 6lf656jgt5 n5t ,c ,yy

[@talmudrabbi7164]

This professor brings out the essences of mastering the advanced maths, it also applies to physics. Thinking in picture or sketch the image in your mind while studying maths is a vital process or means. Awesome!

[@mllo2003]

I am touched by the music analogy!

[@ydl6832]

It reminds me of Ludwig van Beethoven. He is the Beethoven in math.

[@ryanfranz6715]

He reminds me of my differential equations professor... Who happened to be the best professor I've ever had. They should make all professors watch this guy teach as a prerequisite to being a professor, because honestly most of my professors simply suck at teaching. I'm not sure why universities hire professors that can't teach to teach our future generations.

[@MrFreshboy86]

+Ryan Franz Most professors are hired due to their research and publishings, not teaching ability. To some professors, teaching is just a bother in the middle of their research so they don't really put much effort into it. Other professors, as you've mentioned with your Dif Eq professor are absolutely amazing though.

[@paesanng]

+Ryan Franz Unfortunately, when a person wants to be an academic, they want to devote their lives to dwelling deeper into a subject. However, most unis if not all require that a staff member does BOTH research + Lecturing. It'll make more sense then to just hire people would would like to teach but if a person spends say 10 years (or more) from undergrad to PHD, you kind of expect that person to want to focus on their research as opposed to teaching. But they just have to lecture as that seems to be a requirement to hold that position in the uni, therefore most lecturers just read off the slides. Here in Perth WA, some unis do offer to lecturers (senior ones I suppose) if they want to be, "Only teaching staff." or" Only research staff." But most staff seem to be made to do both. Hopefully, you're not having too much trouble in what you're doing.

[@nal8503]

Blame the universities. As people correctly noticed most professors are forced into teaching regardless of their aptitude for or interest in such.

[@BruinChang]

A incredible man from Uranus.

[@yjrzidovvjsmmra9300]

the teacher that makes you draw. Damn him, my desk is full of drawing now, and thank you. Wish to meet him in person, maybe one day

[@silaskelly604]

Amazing! When young I tried to learn to play piano. My hearing was not good enough to appreciate music and without that, I was unable to learn the piano. When I was 25 y/o and had a degree in engineering and lots of engineering math courses, I found a document that said music was based on mathematics and gave examples. I then understood music (at least in a limited way), and felt I could learn and quickly learned to play the piano and organ. And now some 80 years later I am told that math can be seen so wonderfully that now I can. It is so easy to picture the object formed with A^2+B^2+C^2 or A^2+B^2=C^2. Thanks a bunch.

[@SpeedyBozar]

Numbers + formulas = program. Numbers + formulas + pictures = a mathematician. Numbers + formulas + pictures + meditation = a great mathematician.

[@GreenGoblinCoryintheHouse]

My high school teacher also focused on pictorial representation. Visual memory helps a lot.

[@harshprajapati763]

I really enjoy his lecture like I hear music.

[@paesanng]

That is a very good analogy.

[@MrArtbyart]

I very much appreciate this instructor's emphasis on visualization! Thank you

[@jblaskovich8675]

Dr. Tokieda - Your discussion is inspiring. Thank you.

[@1995yuda]

What a legendary teacher ! Wow !!

[@jabedumar9726]

WOW! Dr Tadashi Tokieda, you just blew me away. What an amazing teacher. Thank you. we want your more and more lectures

[@tabacoryu]

Congratulations...From Brazil, 2016!!!

[@weaya47]

Wow sir! I really admire this genius. The way you teach is so remarkable. These students are so lucky.

[@dhruvsaini1018]

Amazing teachers 👌

[@klong4128]

Excellent mathematician teaching Topology/Geometry . Maths is not just a Numbers/Formulae/Tensor-Abstract-Symbols /Real-Virtual-Pixel-Picture of Nature ! When I was working in a MultiNational semiconductor advanced 3.0 Industry before 2010 , The whole industry just employed one Statistiscian/mathematician per 100000 engineers ! Today 2020 , the limited tasks of PHD maths become normal/better after 4.0 Industrializations .Thus the old picture of PHDdegree-Statistician sitting alone infront of outdated computer is gone ! Maths is just a TOOL used by Sciences . Maths is a Subset of Science in 2020 onwards .But Maths ⇒ Science cannot befound in the Career-Frontal of life . Your teaching MobiusSTRIP is very COMPLETE ! Where I had seen many phd-Scientists teaching Incomplete-Maths . Good job ,keep it up !

[@sangwonpark2833]

Exciting!! I don't believe this class. It did not exist in our University class!!

[@LawsonEnglish]

What a brilliant lecturer.

[@richarddeese1991]

Thanks for the video(s)! I like his message that you must go beyond the numbers & *_see into_* the mathematics. Fact is, the human mind is still largely an animal mind, & it is *_not_* good at math. It jumps to conclusions - sometimes causing its owner to jump too - literally! Fear, the startle reflex, fight or flight... these are things the animal mind does well. When it comes to problem solving, even many animals can be quite clever; escaping from cages, getting into food sources, etc. But for some more refined problem solving tasks, humans are stuck with our animal brains, which tend toward a sort of black box. Our brains (or minds, if you like) tend to leap in the dark, so to speak; to guess at answers without truly thinking it through. In animals, this is useful for survival. It's better to guess that something might be dangerous, & to run away - even if that thing isn't actually dangerous. That way, you live. But even some animals have a crude mathematical sense, which allows them to discern things like relative quantity. That pile has more nuts (or bananas, or whatever) than this pile, so I choose that one. Beyond that, however, our animal brains have to be trained. You cannot use your brain's black box guessing ability to solve quadratic equations! It helps me to think of math as something like a game. Everybody understands games. We play them from an early age. Games have rules. If you obey the rules, & you play correctly & well, you may just win the game. It takes discipline to learn the rules of math. It takes more discipline to *_see into_* the shapes & relationships of numbers, formulas, etc. But - just like anyone who gets good at a game (whether that's soccer, or basketball, or Gin Rummy, or Fortnite), you *_can_* get good at math. Good enough to see into, formulate, & solve, many everyday problems. One very important key is to use your mathematical problem solving skills on a regular basis - outside of the classroom! I strive to see the math in everyday things. Topology, geometry, symmetry; all are right there in front of you. Can you see them? Rikki Tikki.

[@narutosaga12]

Richard Deese nope! Just stop 🛑

[@Krishnajha20101]

This is Awesome!!!

[@Bluedragon2513]

Definitely not boring. Somehow, I can watch and learn with full attention without putting it on 2x speed. There definitely is something special with him

[@DRD363]

tadashis is great!

[@francescos7361]

Thanks , great the link between music and math . I agree.

[@chenalbert2996]

fantastic lecture...

[@bilalahmed-fe5xt]

Finally after searching alott i got good lectures on topology

[@jn4244]

he is really amazing

[@ASMRunning]

Absolutely beautiful and so true

[@jpeterson8646]

This is one of my favorite lectures I’ve ever watched ^_^ I could have lit it better myself

[@rarulis]

Can we get access to the drawing assignments please?

[@chycho]

rarulis This, please.

[@longcat]

i would also appreciate getting access to the drawing assignments please

[@Pete-Logos]

Me three!! Please, give me homework!! (How often do other teachers hear that?) Lol

[@somi11]

I need that too

[@black_jack_meghav]

@@Pete-Logos lol me four

[@nicorobin7666]

Wow all my love and admiration from Libya ❤

[@nimaisarkar3786]

dream class

[@crownieeme7556]

amazing

[@GiR1854]

Inspiring...from India 🇮🇳

[@7177YT]

oh this is brilliant. I hope they knew how lucky they were to sit in that class. (;

[@mustafaali9128]

inspiring..

[@iamyouu]

Wow what an amazing lecture! 👏🏻

[@chunxiaozhou3799]

Really enjoy it! Thank you so much!

[@nuclearnyanboi]

The Drawing Assignments please! I'm even ready to pay.

[@cricketknowall]

Where could we get the drawing assignments, please?

[@muthukrishnanthukkaram313]

I would like this great teacher giving a TED talk. He is great!

[@ganapatibrahma8005]

Amazing activities with pictorial presentation of topological geometry ' HATS OFF' ,Thank you very very much Dr. Tokieda. Brahma G (Gamma).

[@jonadabtheunsightly]

Pictures _by themselves_ are generally not rigorous, that's true. They usually have to be accompanied by an explanation. But pictures are definitely useful and can certainly be part of a rigorous proof; and yes, it would be crazy to not use them at all.

[@Pete-Logos]

You are amazing! Did you also have an awesome teacher(s), or did a mediocre teacher(s) inspire you to be awesome, (or is there a 3rd possibility and reason why you're great? (I don't want to create a False Dilemma, Lol) But, I do want to remain inspired (and maybe even inspire others someday.)

[@anthbenit2576]

numbers and formulas are important in the same sense that words and letters are important ..but words and letters don't make the story ..I believe he was trying to say..

[@maimagdi184]

Is there any reference that can be added to these lectures?

[@deepjoshi356]

can we get the drawing assignments?

[@athosliu]

terrific! btw, why the video is so noisy..

[@folgeende5637]

He is cool...

[@johnconrardy8486]

like a lot

[@raydencreed1524]

18:58 It was actually 4:15 for me when he said the time was 4:15 for him at that part of the video. Cue X-files theme............

[@tobiaszb]

Great talk, although Bachs fugue (d-minor or art of fugue) would be have more understandable connection of writting/listenning. Some symmetries You can see there as well. ^^

[@nal8503]

I was actually surprised he didn't bring Bach. Some of his techniques are analogous to aligning the theme on a Moebius strip.

[@andrewcao8728]

3:06 turn on captions

[@arribarriba20]

What are the mathematical prerequisites to take this course?

[@nal8503]

Linear Algebra and Analysis are sufficient for introductory courses in Topology.

[@thecritiquer9407]

what's maths all about importance of picture

[@richardcarew4708]

mathematics helps understand the Symphony of our lovely Universe, in the great here and now of reality.. as past becomes the future... mathematics is not the language of science.. science cannot exist without it... we measure the Universe... numbers don't lie...

[@richardcarew4708]

I take pictures of everything.. it is a measurement.. that can be repeated.. and I bring in near and far infrared and ultraviolet with Snapseed HDR, free from Google... pictures help us visualize... another useful tool is the abacus 🧮 Richard Carew StarFire Family Industries 👪 [e-mail] Peace ✌ 🙏 Namaste pin.it/4mdw5Su ☆☆ ✌ ☮ ☆☆ I uploaded 18,000 images to a remote drive this evening.. 6 months of photos and videos.. cell phone cameras work well.. I have not used a "real" camera in 8 years 😳.. the best camera is the one in your hand

[@richardcarew4708]

Dr Takeshi Tokieda-sama.. it's been a pleasure, sir 🙏 😊.. I don't suppose you do a course in the abacus?... I would like to understand it better... achieve fluency, as it were.. Harvard and Cambridge should teach the abacus 🧮... people who grow up using the abacus see mathematical relationships more easily... 4 decimals accuracy in engineering... I program my applications like that... errors are cumulative.. so is accuracy

[@dankazmarek1259]

Why is not there a love option for youtube videos?

[@ngocha5354]

What happened to these students? Did they end up doing a PhD in Math?

[@vincentverbaandert4659]

La même conférence (1 et 2) en français svp. The same in french pleeeeaaaase

[@arthurrouquan708]

+Vincent Verbaandert Sa prononciation est pourtant limpide. Puis il y a les sous-titres automatiques que tu peux activer.

[@adabhussain1350]

It's said to be teacher in real meaning.

[@VictorHugo-xn9jz]

Piano scores produce orchestra.... noice

[@sudhaman5141]

The first 5 min were very romantic

[@NevilleEkka]

Please, Professor ACCEPT ME AS UR DISCIPLE

[@black_jack_meghav]

Accepted the moment you clicked on the video

[@johnhammer8668]

Is pictures so important. to maths. Huh.. who knew

[@vaishnavkumars966]

先生！！宇宙人！？

[@varshagarg7743]

Then painters are good pseudomathematician!

[@NiftyFingers]

How to think in 4 dimensions? Brain capped out at 3. I can only think of one 3 dimensional space at a time. I can think of a sequence of 3 dimensional spaces pretty easy but that takes up all my brainpower. Thinking in 5 dimensions requires thinking of a sequence of sequences of 3 dimensional spaces and that's pretty much impossible. I can only pretend I can imagine it and follow out the logical consequences but I still have to chop 5 dimensions into 2 or 3 dimensions. Yet nature has more dimensions than anyone can count, let alone picture.

[@GrandGobboBarb]

practice. you can think beyond three dimensions if you practice repeatedly for years. it's very fun/painful

[@citizencj3389]

Tessaracts are seen in 4 dimension..it depends on what kind of dimension being discussed...space or time?

[@goulchat1]

Nowadays computers are better than humans in many respect

[@LuisRamirez-gc5ds]

He's teaching black people xD

[@PhysicsMathMan]

+Luis Ramírez ?

[@hellothere848]

You know you viewed a Video uploaded by South african institute right?