I can confirm that 1,2 and 3 are indeed my favourite colours
@ochiruko2874
Жыл бұрын
As a disorganized python user, mine are 0, 1, and 2. My fourth favorite color is red
@edvogel56
2 жыл бұрын
Finally a determinant that determines something I am really interested in! How many crayons I get to use to color a knot. This is awesome!
@alieser7770
3 жыл бұрын
you revived my faith in humanity with these lectures
@lorenzonuti5940
5 жыл бұрын
Very cool, I'm writing my math degree's thesis and it's all about Reidemeister moves , excellent timing for that! Best wishes from Italy!
@MathatAndrews
5 жыл бұрын
Wonderful! Feel free to drop a link here to your thesis when you have it written up. Happy writing!
@mortyhere
3 жыл бұрын
this is the second time I'm watching these lectures, that's how good it is.
@MrGiuse72
3 жыл бұрын
OOOOOHHH a lesson masterfully designed to FINALLY understand this knot theory foundation !!! THANK YOU Prof.
@Pantheonmusic666
3 жыл бұрын
This is so cool...I got turned on to knot theory by diving into another youtube lecture series on quantum physics (kind of a counter intuitive order, I know lol). But the implications of the parallels between topology and theoretical physics are astounding. I'm definitely going to binge watch the rest of this series/class tomorrow when we're all snowed in. Thanks for making quality education accessible for everyone!!
@MathatAndrews
3 жыл бұрын
Glad to hear you're enjoying it! I hope you get a lot out of the videos -- note there are also some problem linked in each video description that you can try. Stay warm!
@schrodinger1cat
2 жыл бұрын
Very enjoyable and easy to follow! Thank you so much!
@xiaolonghanshan1755
4 жыл бұрын
Such a high quality, vivid, and interesting class!
@paulensor9984
7 ай бұрын
This single lecture has got me excited to study knot theory ❤
@SepiaSepiaKR
4 жыл бұрын
To whom it may concern: If the audio bothers you as it does me, you can go to windows options -> ease of access -> audio -> turn on mono audio. Just remember to turn it back off afterwards.
@MathatAndrews
4 жыл бұрын
Thanks! The later lectures don't have this problem.
@SepiaSepiaKR
4 жыл бұрын
@@MathatAndrews It was just a minor inconvenience. The lecture itself is a marvel.
@mhk2167
4 жыл бұрын
you made this very easy to understand
@MichaelJohnson-fd6hu
3 жыл бұрын
When finding the determinant, why is one column and one row automatically crossed out to reduce dimension? Is it because the determinant will be the same either way? Is there a proof for further reading?
@mankritsingh4058
3 жыл бұрын
For real, cannot thank you enough for this amazing resource! God bless!
@swebb01
2 жыл бұрын
you are really good at drawing knots!
@nickfranczak6421
2 жыл бұрын
this is such a great resource! thank you so much :)
@yrosenstein
Жыл бұрын
How do you call these flexible pipes? I want to purchase some?
@musiquinhasdaoras
10 күн бұрын
How does the figure 8 knot is 5-colorable exactly? Why is 5-colorable if you can only paint it with four colors?
@張簡旭凱
5 жыл бұрын
this video is great!!!!! thanks~
@tahayfer
2 ай бұрын
Thank you for your great service bro!
@marwaassem1087
5 жыл бұрын
We need to see connections between knots and Algebraic number theory please ........ your explanation is really beautiful
@kurtw531
4 жыл бұрын
Thumbs up and subscribed. A question. At 1:01 and other times, you are using some sort of plastic tubing. What is that called and where is it sold? I've used whiteboards and extension cords for practice. Didn't really like the extension cords because they seem to want to return to a previous state. Any help would be greatly appreciated.
@MathatAndrews
4 жыл бұрын
They are just long glow sticks!
@kurtw531
4 жыл бұрын
@@MathatAndrews That was fast. Thank you. I checked Amazon. They've got them with the connectors.
@SirLightfire
Жыл бұрын
Is there an infinite knot that is colorable for all primes? Similarly, is there always a knot that is colorable by all primes smaller than p?
@Suav58
3 жыл бұрын
So, how does the concept of luminiferous aether differ from a concept of quantum vacuum or quantum foam? How does the knot concept differ from that of a closed string? Are we going to get to the Kontsetitch Invariant some day?
@JeanDAVID
4 жыл бұрын
what if you can cut at a under crossing and make it an upper crossing ? can a multiple crossing knot by this way be transformed successively to an unknot ?
@MathatAndrews
4 жыл бұрын
Yes, just by changing crossings any knot can be changed into an unknot! You should think about this until you convince yourself that it is true. It may help to recognize that changing crossings is equivalent to letting the knot "pass through itself".
@lookasaw
4 жыл бұрын
Hi sir, very nice video! Could you please tell me where I can find proofs for the theorems you illustrated here and, more in general, a good knot theory book? Greetings from Italy
@MathatAndrews
4 жыл бұрын
Thank you for the kind message! I recommend 'The Knot Book' by Colin Adams; it is very readable. I think you'd enjoy it.
@real_mathematics7573
3 жыл бұрын
my favorit video, Thanks Sir.
@TheDannyAwesome
2 жыл бұрын
Is the determinant always squarefree?
@ln7813
4 жыл бұрын
Thank you! This video is very clear, very good!
@axelyeti
3 жыл бұрын
Amazing video. Thanks a lot. I have a question though: for the last knot you mention (the 7-4), why should we consider a 6x6 matrix when there're 7 crossings? For the Trefoil, there are 3 crossings thus a 3x3 matrix, why should it be different when p goes up?
@ijeremyoliver
3 жыл бұрын
It's not. After writing the overdetermined 3x3 matrix for the trefoil, you delete a row and column before taking the determinant. We only took the determinant of the 2x2 you'll matrix. The same is done for 7_4.
@stephanemami
5 жыл бұрын
not my field at all so I got confused when you went from colors (kindergarden) to number (at least high school). So dumb question, could a not be 5 colorable and not 3 colorable? I sense it's not, but I think everything would be clearer if I know why...
@MathatAndrews
5 жыл бұрын
No worries! It is easy to get knotted up... Yes, a knot can be 5 colorable but not 3 colorable. For instance, if a know has determinant 5, then it would be 5 colorable but not colorable. Here's an example of such a knot: katlas.org/wiki/5_1
@dmytronazaryk681
Жыл бұрын
English language is knot best for not theory
@ΑλεξανδραΦικιωρη
Жыл бұрын
Why in p-colorability p must be a prime ?
@sangchoo1201
2 жыл бұрын
is posible to make a matrix using 0, 1, and -2? because x + y == 2z (mod p) is not only equivalent to 2z - x - y == 0 (mod p), but also x + y - 2z == 0 (mod p)
@xwtek3505
Жыл бұрын
What?
@chevasit
Жыл бұрын
Very Good 👍
@sajateacher
5 жыл бұрын
Can you have knots in complex spaces or higher-dimensional real spaces?
@MathatAndrews
5 жыл бұрын
Good question! In a 4-dimensional setting, every knotted circle would be trivial. This is because you have an extra dimension that allows the knot to "pass through" itself with touching itself. (Convince yourself of this.) However, we can think of knotted spheres in 4-dimensional space! That is, in a 4D universe, it would be possible to have a knotted up a basketball!
For the first couple videos, only high school algebra. As they advance, some of the ideas will become more advanced and abstract, but I try to explain what is needed along the way.
@L0wLevel01
4 жыл бұрын
@@MathatAndrews thank you so much for your quick reply !!! I will watch all of the videos and try to read "the knot book" and ,hopefully, publish a paper.
@MathatAndrews
4 жыл бұрын
@@L0wLevel01 Stay in touch with your progress!
@georglehner407
Жыл бұрын
@23:13 had me laughing
@alexanderying1558
Жыл бұрын
especially because even the correction is wrong in multiple ways
@TheMemesofDestruction
7 ай бұрын
22:24 👀
@alejand5
3 жыл бұрын
Hi! I'm wondering when I can find a proof for the last theorem (the one about p-col and the determinant). Can you give me some refecences? Thanks!!!
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