Thanks for watching! Check out my Graph Theory playlist for more, and please share the videos to help out the channel! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html Hundreds more graph theory videos still to come!
My pleasure, and yes it certainly is. I'd like to brush up on my programming eventually to incorporate more CS stuff with the graph theory. The more the channel grows the more time I can spend on it, so it will come in due time!
amazing , just by seeing the problem title , i was able to prove this :D thanks alot sir , i have completed your entire playlist the only thing missing here it about , Symmetric difference in graph
Thanks for watching and that's awesome, good work! I'm so glad you found the playlist valuable, there are still many more lessons planned for it. As for the symmetric difference in graphs, I don't think I've ever heard of that, I'll have to look into it!
thanks bro, please sean could you make a video about "directed graph" (representation of the graphe , representation of the matrixe 'incidence and adjacence', the successor table....etc), thanks a lot god bless you ♥ and I'm sorry for my bad english
Thanks for creating this series, you took a very academic branch of math and made it entertaining! I can't think of many practical problems that this knowledge could be applied to but my interest peaked when you presented the matrix representation. I was disappointed it ended with that. Are there more practical applications of Graph theory using their matrix representation or is this all the graph theory knowledge that currently exists? Also it would be great if you had some videos on Tensor calculus, specifically the Christoffel symbol. No matter how many times I study it, I just can't visualize what it does.
So glad you've enjoyed it, thanks for watching! By "this knowledge" I'm not sure if you mean graph theory or the topic of this lesson specifically, but rest assured it has many applications, which is surely part of why it has grown so much - being a relatively new field of math. I think the first graph theory book was written in the 1900s. I'm not the best to ask about applications because I just enjoy it for its mathematical beauty, but graph theory is used to model social networks, digraphs can be used to represent groups, they can be used for various problems concerning transportation, they have surprising utility! Many problems I have seen I am quite surprised to find they can be solved with graph theory! An example is "Instant Insanity" a very popular puzzle from the 1900s I believe (maybe created by the prolific Sam Lloyd, maybe not, can't remember). The matrix representations also have a lot of utility. It's a good way to communicate with computers about graphs, and my favorite graph theory theorem concerns the repeated multiplication of the adjacency matrix of a graph. Consider the problem of counting the number of paths of length k that exist between two vertices in a graph G with adjacency matrix A. The answer to this question can be found by just looking at the matrix A^k, it's quite beautiful! The result is mentioned on this page if you want to have a look, and the proof is a surprisingly straightforward induction argument: (www.sciencedirect.com/topics/mathematics/multiplication-of-matrix) I will certainly be doing more lessons on graphs and matrices, though I must admit to a slight fear you could say of matrices, I just don't really love working with them. As far as tensor calculus videos - it will be a while because I have never studied it - but hopefully someday I'll have some tensor calculus lessons on the channel!
Thanks for the link it was very helpful. The simple digraph representation as a matrix, and the matrix multiplication for counting paths, seems to really unlock a lot of the information I was missing. If you don't like matrices you may or may not like Tensor calculus. Tensor notation replaces your rows and columns of a matrix with indices. You seem very comfortable with indices so tensor representation will probably make you more comfortable with matrices. For me, most of Tensor calculus made sense once I had a strong grasp on the difference and relationships between vectors and covectors, but that Christoffel symbol still alludes me. I think it relates to graph theory in that it represents a relationship between two points, maybe even the path between those points, I'm not quite sure, it still just looks like a bunch of unrelated indices to me.
Oh but this isn't about the eccentricity of ellipses, this is about vertices in graphs! I've been meaning to do some more ellipse lessons though. Thanks for watching and yes I am American, I hail from the northeastern United States!
Adjacent vertices? More like "Amazing videos; thanks for these!" 🙏 (Also, hopefully at least a few people find my eccentric comments to be entertaining.)
Thanks for watching! Check out my Graph Theory playlist for more, and please share the videos to help out the channel! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Hundreds more graph theory videos still to come!
Thanks. Graph theory is very important in computer science
My pleasure, and yes it certainly is. I'd like to brush up on my programming eventually to incorporate more CS stuff with the graph theory. The more the channel grows the more time I can spend on it, so it will come in due time!
amazing , just by seeing the problem title , i was able to prove this :D thanks alot sir , i have completed your entire playlist the only thing missing here it about ,
Symmetric difference in graph
Thanks for watching and that's awesome, good work! I'm so glad you found the playlist valuable, there are still many more lessons planned for it. As for the symmetric difference in graphs, I don't think I've ever heard of that, I'll have to look into it!
@@WrathofMath sir, can you tell me where can i work out stuffs i have learned :D
thanks bro, please sean could you make a video about "directed graph" (representation of the graphe , representation of the matrixe 'incidence and adjacence', the successor table....etc), thanks a lot god bless you ♥ and I'm sorry for my bad english
Thanks for creating this series, you took a very academic branch of math and made it entertaining! I can't think of many practical problems that this knowledge could be applied to but my interest peaked when you presented the matrix representation. I was disappointed it ended with that. Are there more practical applications of Graph theory using their matrix representation or is this all the graph theory knowledge that currently exists? Also it would be great if you had some videos on Tensor calculus, specifically the Christoffel symbol. No matter how many times I study it, I just can't visualize what it does.
So glad you've enjoyed it, thanks for watching! By "this knowledge" I'm not sure if you mean graph theory or the topic of this lesson specifically, but rest assured it has many applications, which is surely part of why it has grown so much - being a relatively new field of math. I think the first graph theory book was written in the 1900s. I'm not the best to ask about applications because I just enjoy it for its mathematical beauty, but graph theory is used to model social networks, digraphs can be used to represent groups, they can be used for various problems concerning transportation, they have surprising utility!
Many problems I have seen I am quite surprised to find they can be solved with graph theory! An example is "Instant Insanity" a very popular puzzle from the 1900s I believe (maybe created by the prolific Sam Lloyd, maybe not, can't remember). The matrix representations also have a lot of utility. It's a good way to communicate with computers about graphs, and my favorite graph theory theorem concerns the repeated multiplication of the adjacency matrix of a graph. Consider the problem of counting the number of paths of length k that exist between two vertices in a graph G with adjacency matrix A. The answer to this question can be found by just looking at the matrix A^k, it's quite beautiful! The result is mentioned on this page if you want to have a look, and the proof is a surprisingly straightforward induction argument: (www.sciencedirect.com/topics/mathematics/multiplication-of-matrix)
I will certainly be doing more lessons on graphs and matrices, though I must admit to a slight fear you could say of matrices, I just don't really love working with them. As far as tensor calculus videos - it will be a while because I have never studied it - but hopefully someday I'll have some tensor calculus lessons on the channel!
Thanks for the link it was very helpful. The simple digraph representation as a matrix, and the matrix multiplication for counting paths, seems to really unlock a lot of the information I was missing. If you don't like matrices you may or may not like Tensor calculus. Tensor notation replaces your rows and columns of a matrix with indices. You seem very comfortable with indices so tensor representation will probably make you more comfortable with matrices. For me, most of Tensor calculus made sense once I had a strong grasp on the difference and relationships between vectors and covectors, but that Christoffel symbol still alludes me. I think it relates to graph theory in that it represents a relationship between two points, maybe even the path between those points, I'm not quite sure, it still just looks like a bunch of unrelated indices to me.
I dont know why I am watching this though I am in class 12! I know eccentricity of ellipse and that all stuff. Dont mind. Are you American?
Oh but this isn't about the eccentricity of ellipses, this is about vertices in graphs! I've been meaning to do some more ellipse lessons though. Thanks for watching and yes I am American, I hail from the northeastern United States!
Adjacent vertices? More like "Amazing videos; thanks for these!" 🙏
(Also, hopefully at least a few people find my eccentric comments to be entertaining.)