Long-time no see, thank you all for the supportive messages during my hiatus (I completed my master thesis and have worked one year at my first job)! This video is dedicated to all of you, but also specific @Sarah _ that have waited an awful amount of time for me to complete this one. Conformal mapping is one of the hardest concepts to grasp in complex analysis and I also struggled with it a fair bit in school but I think this video will be able to show you that it is easier than one thought!
Camtasia for editing and recording my screen while I write on a canvas I made in photoshop. I'm using a Wacom tablet and then I record my audio with a Blue Yeti and edit it in Audacity :)
Seriously, you just saved my day. I had a hard time while understanding fluid flow on object with conformal mapping, and this video grasped concept for me. thx a lot.
I just came here to understand definition of conformal mapping but couldn't stop myself to grasp the whole concept..credit goes to you. Keeping helping us man
Another truly incredible masterpiece! Sadly I have reached the end of the playlist, but I will eagerly look forward to any and all new content in the future. Thank you again, so so much!
@@TheMathCoach You are most welcome, and I found your content *very* useful! I've got notifications turned on so I'll be ready. In the meantime, I'm exploring more math on TH-cam, including integration techniques and differential equations on Mathematics MI ( th-cam.com/channels/ZDkxpcvd-T1uR65Feuj5Yg.htmlplaylists ), along with Numberphile, Flammable Maths and Socratica.
Dear TheMathCoach, I hope this message finds you well. I am writing to express my heartfelt gratitude for the enlightening lecture you delivered on [specific topic or date]. Your ability to convey complex concepts with clarity and enthusiasm is truly remarkable and has greatly enhanced my understanding of the subject. The depth of knowledge you shared, along with your engaging teaching style, has left a lasting impression on me. I particularly appreciated the practical examples and real-world applications you included, which made the material much more relatable and easier to grasp. Thank you once again for your dedication and effort in providing such a valuable learning experience. I look forward to attending more of your lectures in the future. Warm regards
Have the bots started leaving comments on my videos now! I have reached a new audience (sorry if you are a human, I noticed [Insert Text here bracket])
So elegantly explained. Thank you for the effort and I hope you can find the time to continue making content. Perhaps a series on undergrad abstract algebra.
In class we were just given definitions and formulas, not a single drawing, and I didn’t get what Möbius Transformations were. Now I understand everything. Thank you so much!!
The video is really great. The teacher didn't teach us, she let us read the textbook and the written textbook was very difficult to understand, but after watching your video, I understood the problem! Thank you so muchh
I love how well you explain everything, even when it may seem obvious. In my prof's lecture, he just said that a conformal mapping is a function that preserves "the angle" and pointed to two intersecting curves on his slides. But then I thought "how do you even get an angle between curves????" And then he proceeded to show more complicated mappings with circles and I just zoned out. Thanks for clarifying that it's the angle between the tangents at the point lol
One of the first times I directly subscribed to a TH-cam channel. Quality video, thank you for the additional resources such as the course map, the different methods and the links to go further. Very good compromise between rigor and simplicity.
Hi ketya, I'm happy to hear that my content can be useful to more people! Welcome to my channel and just let me know in the comments if you have any questions :) I'm also glad that you find my level of explanation appropiate to this kind of educational videos, always a tricky road to go between 30+ mins of proving all the statements in the video and somewhat of a more general approach and just going over the key aspects, short and concised.
Hello. Adobe Photoshop for the writing (and a lot of patience) while I record my screen with Camtasia, which is also my editing program. The audio is later recorded over the video by using Audacity and then I match the video and audio files with Camtasia :) Just let me know if you are interested in knowing about my settings in either program. I'm making a video right now about "how I make educational videos" which will walk you through all these things in detail and that one should be out within one month!
@@TheMathCoach That's good stuff. If you have the time or inclination, I'd watch a tutorial video of your editing process. I have all the programs mentioned and I'd like to up my video editing skills and perhaps make videos similar to this in the future. Great content. I subscribed and will be watching your complex analysis series. It's been forever and I should brush up.
you are right and it is a quick simplification on my part, it should ofc be that "f(z) goes to infinity when z goes to 1". But in short the function will have infinity big values when we approach z=1.
Very helpful. I am a physicist and need conformal mapping for solving Laplace equations for electric field. This vieo clarifies a lot for me :) I would like to present material in such clarity myself. I like neet writing and higlighting/shadowing part of formulas. Where did you learn to write like this, and how do you excecute this?
Thank you so much for the amazing video. I have a question. We said that a circle that passes through the origin is mapped to a line, why that didn't happen in 12:53
Hello, I think my explaination in the video needs one additional mark. It is not that the circle passes through the origin that is the important part, it is that we use a mappning that makes us *divide with zero* at at least one point, which happended at 07:57 with the inversion mapping (1/z) if and only if the line or circle passes through the origin (z = 0 -> 1/0). Hope it clarifies!
Interesting! I had not realized that the derivative was affected by the (ad-bc) condition. I thought it was just the determinant not being zero. Thanks!
Happy to hear that! Maybe in the future, focusing right now on my little book about complex analysis and to finish this playlist, which is not so far away.
Excellent video. However, I'm interested in how a finite area (circle) got mapped to an infinite area. Doesn't that break some rules? Also, is the reverse also possible? i.e. mapping an infinite area to a finite one? What does that actually mean? 🤔
Glad you found it useful! The summary is that astonishing things happens when you divide by zero. In this case, some points on the circle created division with zero and therefore these gets mapped to infinity, which means that the length of the line must be infinite in length (since we have to reach some point at infinity), hence the area must follow the same principle to connect all the points in the mapping. Then again you could say that the circle is not finite in area to start with in the same way that there are infinite many numbers between two numbers on the real number line.
Hello, happy you found it useful! I made a video where I explain everything in detail: th-cam.com/video/5PGj1Sh4Lk0/w-d-xo.html I hope it helps and let me know if you have any follow upp questions. Happy Holidays :)
@TheMathCoach, I have a question. What Mobius transform maps the whole interior of a rectangle to another rectangle? Will it always be an affine transform? Thank you so much for this excellent video.
Hello! Thankyou so mush for sharing these videos. It is a superb complement for the lectures given on my university. I have a question at (16:33) and forward when you transform the circle to a line. I don't get it when you insert the points in your given f1(z) = 1/z+1 to get the four new points. I did a similar problem in my course where i transform a domain D1(0,2)\D2(1,1)onto the horizontalstrip{w∈C: 3
Hello, happy to hear that my content can be useful for you! I used the function *f(z) = 1/(z-1)* and I used that one since I needed to divide by zero to get a line. I think you are probably going to be able to create the same result from your example since each radius is going to be mapped to its own line. For example in the video, you could see that z-values with radius 1 are mapped to the line and then all the other points are mapped to the left, you will probably be able to achieve kind of the same result. The first transformation of the big circle D1 will give you all the points to the left of some line AND then you will have to subtract the points that makes up the smaller circle D1 so you will end up with a *band*. After that I guess you have to rotate it and translate it to match the final image. Best of luck!
Hello, first of all thank you so much for this great video. I want to ask you that when you change the elementary transformation order the final Möbius transformation result also changes. How will we understand which one is true?
Hello, if the transformations still make your mapping end up in the same desired spot then it is also a valid Möbius Transformation. Often the question will ask you for "a" möbius transformation and not "the" möbius transformation since there often exist more then one.
Hello! I use Adobe Photoshop for the writing (and a lot of patience) while I record my screen with Camtasia, which is also my editing program. The audio is later recorded over the video by using Audacity and then I match the video and audio files with Camtasia :)
@@TheMathCoach thank you very much, the "a lot of patience part" must be the most important one lol. Actually I thought you would use some unknown crazy good program, but actually the tools are normal ones, guess I'll grab my patience and try to do something like this as well.
@@nicolasdellano280 haha yea, I probably have around 10-20 hours of me writing on the canvas and end up using only around 1-2 hours since most of it is mistakes before you get just the right one! Best of luck to you!
Hi, Can we express difference of two figures numerically by using conformal mapping? For example: how are a circle and an ellipse far each other numerically? Or a circle and triangle, or square... A circle resembles a circle %100. Can you lead me?
Hi, there probably exist an conformal map. Regarding the second thing, the key thing to get a circle to map to a line is that the image needs to contain infinity and that was succeded in the video at the origin since we had the function 1/z so the origin is not the condition for all examples only for this one.
Not sure, since I think that area is quite well covered at the moment. I think I need to target more niche areas of mathematics for people to find my videos :)
Hello, sorry no in the foreseen future. I have a plan to start a course about GROUP and RING Theory after this playlist so that thing will probably include some information since they both are defined from a set.
Long-time no see, thank you all for the supportive messages during my hiatus (I completed my master thesis and have worked one year at my first job)! This video is dedicated to all of you, but also specific @Sarah _ that have waited an awful amount of time for me to complete this one.
Conformal mapping is one of the hardest concepts to grasp in complex analysis and I also struggled with it a fair bit in school but I think this video will be able to show you that it is easier than one thought!
wow, congratz! you deserve it!
What software are you using to create these helpful videos?
Camtasia for editing and recording my screen while I write on a canvas I made in photoshop. I'm using a Wacom tablet and then I record my audio with a Blue Yeti and edit it in Audacity :)
If i map a half plane to a quadrant what transformation would i use
Mind blowing........ thank you from my bottom of my heart friend
Seriously, you just saved my day. I had a hard time while understanding fluid flow on object with conformal mapping, and this video grasped concept for me. thx a lot.
Happy to hear that DeepDark, now you will able to continue to master your fluid flows while having a great day!
Best of luck with your studies mate.
i spent over 5 hours not knowing my professor's explanation, but after your awesome video, im totally speechless. thank you so much!!!!
happy to be able to help out! sometimes you just need it explained in some other way for everything to click! :)
I just came here to understand definition of conformal mapping but couldn't stop myself to grasp the whole concept..credit goes to you. Keeping helping us man
I'm just happy to help and that you shared your progress with me :)
Another truly incredible masterpiece! Sadly I have reached the end of the playlist, but I will eagerly look forward to any and all new content in the future. Thank you again, so so much!
Thanks for the watch, glad my content could be useful to you. It will come more with time :)
@@TheMathCoach You are most welcome, and I found your content *very* useful! I've got notifications turned on so I'll be ready. In the meantime, I'm exploring more math on TH-cam, including integration techniques and differential equations on Mathematics MI ( th-cam.com/channels/ZDkxpcvd-T1uR65Feuj5Yg.htmlplaylists ), along with Numberphile, Flammable Maths and Socratica.
well i dont even know how to thank you.you just explained to me what no one else could.i am really greatful for your dedication
I'm just happy to help! Good luck with the rest of your studies :)
Dear TheMathCoach,
I hope this message finds you well. I am writing to express my heartfelt gratitude for the enlightening lecture you delivered on [specific topic or date]. Your ability to convey complex concepts with clarity and enthusiasm is truly remarkable and has greatly enhanced my understanding of the subject.
The depth of knowledge you shared, along with your engaging teaching style, has left a lasting impression on me. I particularly appreciated the practical examples and real-world applications you included, which made the material much more relatable and easier to grasp.
Thank you once again for your dedication and effort in providing such a valuable learning experience. I look forward to attending more of your lectures in the future.
Warm regards
Have the bots started leaving comments on my videos now! I have reached a new audience (sorry if you are a human, I noticed [Insert Text here bracket])
So elegantly explained. Thank you for the effort and I hope you can find the time to continue making content. Perhaps a series on undergrad abstract algebra.
Thank you for the kinds words. I also hope that :)
In class we were just given definitions and formulas, not a single drawing, and I didn’t get what Möbius Transformations were. Now I understand everything. Thank you so much!!
The drawings are kind of necessary in my opinion! Happy to help mate :)
I watched so many of your videos and you saved my life so thank you. i still might not pass tomorrow but the odds for success are so much greater now.
Happy to hear that, I hope your exam went well! :)
I can’t express how grateful I am. Great video
Happy to help!
The video is really great. The teacher didn't teach us, she let us read the textbook and the written textbook was very difficult to understand, but after watching your video, I understood the problem! Thank you so muchh
You are a wonderful human being. Thank you.
Just happy to help!
I love how well you explain everything, even when it may seem obvious.
In my prof's lecture, he just said that a conformal mapping is a function that preserves "the angle" and pointed to two intersecting curves on his slides. But then I thought "how do you even get an angle between curves????" And then he proceeded to show more complicated mappings with circles and I just zoned out. Thanks for clarifying that it's the angle between the tangents at the point lol
Happy to help and yes, it is really not so obvious xD
One of the first times I directly subscribed to a TH-cam channel. Quality video, thank you for the additional resources such as the course map, the different methods and the links to go further. Very good compromise between rigor and simplicity.
Hi ketya, I'm happy to hear that my content can be useful to more people! Welcome to my channel and just let me know in the comments if you have any questions :) I'm also glad that you find my level of explanation appropiate to this kind of educational videos, always a tricky road to go between 30+ mins of proving all the statements in the video and somewhat of a more general approach and just going over the key aspects, short and concised.
simply a thrill.words will fall short of the description.
Happy you liked it!
Any one can solve problems,but only genius can reveal the concept 👍🏻👍🏻👍🏻👍🏻❤️
Happy I could help! This is such a great area and I hope my explaination could help others understand it more easily! Happy Holidays!
you are a savior, lots of love and respect!!
Thank you for all the love and respect!
Thank you very much sir 🙏 I am currently an engineering first year student and u r video helped me a lot today! Greetings from India 🇮🇳
Happy to hear that my content was useful to you! best regards from sweden :)
You are my savior, young man!
this young man was happy to help out!
congrats for the amazing video. I'm a physics student and it helps me a lot.
Happy to hear that! Good luck with your studies :)
For Mathematical Physics ?
@@den_rmdani yes!
Thanks so much for saving my time and you've literally made my day!!!
Found it!!! God bless you forever!
Nice one! :D
Excellent presentation. You are a great teacher. Thank you.
Glad that it could be useful to you Anil and thank you for the kind words :)
I was trying hard to grasp the idea of conformal maps... You helped me alot... Thanks 🙂
I'm happy to help :)
that was simply OUTSTANDING!
THANK YOU!
th-cam.com/video/QMi0wYFrse4/w-d-xo.html geometric approach of conformal mapping
Thank you so much for explaning the concept so nicely!
Glad it was helpful!
Beautifull Explanation.
Thank you, I think it worked out really great for this topic!
@@TheMathCoach It sure did.
Thank you so much for the video lesson and examples. Very well presented and simply explained.
Thank you for the kind words, happy it could be useful to you!
It looks really good! What software do you use to make these videos?
Hello. Adobe Photoshop for the writing (and a lot of patience) while I record my screen with Camtasia, which is also my editing program. The audio is later recorded over the video by using Audacity and then I match the video and audio files with Camtasia :)
Just let me know if you are interested in knowing about my settings in either program. I'm making a video right now about "how I make educational videos" which will walk you through all these things in detail and that one should be out within one month!
@@TheMathCoach That's good stuff. If you have the time or inclination, I'd watch a tutorial video of your editing process. I have all the programs mentioned and I'd like to up my video editing skills and perhaps make videos similar to this in the future. Great content. I subscribed and will be watching your complex analysis series. It's been forever and I should brush up.
Happy to hear that and I will get back to work on my tutorial then :)
This was very helpful. thank you.
thank you so much, what an amazing video!! really helpful !!!
I'm just glad it could be useful for someone :)
thank you so much for making this video it is very helpful to me ....
Glad it was helpful! This is one of my favorite videos, so really happy that it can be useful to people!
Very very good work, thanks for it man!
My pleasure
thanks very much brother. your video is very productive
I'm happy you found my video useful :)
Thank you very very much!! Great video
Glad you liked it and thank you for the kind words!
Your videos are incredible, thank you. I was reading a dusty old tome on this and it was killing me :(
most of the texts are dusty indeed, I had to visit the old archives myself when I created this video! But happy to help out mate!
Thanks for all you did!
Happy to help!
17:05 Here you mentioned that f(1) = infinity, I think its because its 1/(1-1) = 1/0, but isn't 1/0 undefined?
you are right and it is a quick simplification on my part, it should ofc be that "f(z) goes to infinity when z goes to 1". But in short the function will have infinity big values when we approach z=1.
Thank you so much!!!
That was awesome
Happy to help and it was kind of fun to make it, so glad to hear that it got rating awesome :)
Thank you very much! This video was great 😀
Happy to hear that, this one is one of my proudest work :)
This is so helpful, thank you!
Glad it was helpful!
Very helpful. I am a physicist and need conformal mapping for solving Laplace equations for electric field. This vieo clarifies a lot for me :) I would like to present material in such clarity myself. I like neet writing and higlighting/shadowing part of formulas. Where did you learn to write like this, and how do you excecute this?
Glad it helped! I have an video on my channel where I show "how I make my videos", but the short version is photoshop and a lot of patience!
excellent explanation sir
Thank you and Happy to help out!
Well done, very helpful
Glad it was helpful!
Keep on making videos on complex analysis!
That's the plan!
@@TheMathCoach Eagerly waiting for transformation videos ❤️
You are amazing teacher!!!
Glad you think so!
I just subscribed.
Golden channel
Amazing content, thanks for uploading.
My pleasure!
Thank you so much for the amazing video. I have a question. We said that a circle that passes through the origin is mapped to a line, why that didn't happen in 12:53
Hello, I think my explaination in the video needs one additional mark. It is not that the circle passes through the origin that is the important part, it is that we use a mappning that makes us *divide with zero* at at least one point, which happended at 07:57 with the inversion mapping (1/z) if and only if the line or circle passes through the origin (z = 0 -> 1/0). Hope it clarifies!
Thank you so very much. It was helpful
Glad it was helpful!
Interesting! I had not realized that the derivative was affected by the (ad-bc) condition. I thought it was just the determinant not being zero. Thanks!
I'm happy to help out Karl :)
This is amazing!
Is there a possibility to share some more complicated examples with exponents and inversions?
Happy to hear that! Maybe in the future, focusing right now on my little book about complex analysis and to finish this playlist, which is not so far away.
Thank you soooooooooo much!!!!! Why do i have to waste 1-2h before understanding the topic with just 1 video ...
That is the point with my videos, short and straight to the point with examples.
It was very helpful, Thanks a lot😉
Glad to hear that!
Great work! Well done
Happy you liked it!
Excellent video. However, I'm interested in how a finite area (circle) got mapped to an infinite area. Doesn't that break some rules? Also, is the reverse also possible? i.e. mapping an infinite area to a finite one? What does that actually mean? 🤔
Who said Circle is a finite area? 😏
Welcome to set theory where both areas are actually infinite
@@ivank4766 In the quiet words of the Virgin Mary, come again?
Glad you found it useful!
The summary is that astonishing things happens when you divide by zero. In this case, some points on the circle created division with zero and therefore these gets mapped to infinity, which means that the length of the line must be infinite in length (since we have to reach some point at infinity), hence the area must follow the same principle to connect all the points in the mapping. Then again you could say that the circle is not finite in area to start with in the same way that there are infinite many numbers between two numbers on the real number line.
@@TheMathCoach This is beyond me 😅
Hi! What a wonderful job, a masterpiece!!!! Would you describe what software and hardware do you use for handwriting? Thank you!
Hello, happy you found it useful! I made a video where I explain everything in detail: th-cam.com/video/5PGj1Sh4Lk0/w-d-xo.html I hope it helps and let me know if you have any follow upp questions. Happy Holidays :)
@TheMathCoach, I have a question. What Mobius transform maps the whole interior of a rectangle to another rectangle? Will it always be an affine transform?
Thank you so much for this excellent video.
Happy that you found this video helpful, but I don't know enough regarding your question to answer it.
thank you so much, so helpful !
I'm happy to help!
Hello! Thankyou so mush for sharing these videos. It is a superb complement for the lectures given on my university. I have a question at (16:33) and forward when you transform the circle to a line. I don't get it when you insert the points in your given f1(z) = 1/z+1 to get the four new points. I did a similar problem in my course where i transform a domain D1(0,2)\D2(1,1)onto the horizontalstrip{w∈C: 3
Hello, happy to hear that my content can be useful for you!
I used the function *f(z) = 1/(z-1)* and I used that one since I needed to divide by zero to get a line. I think you are probably going to be able to create the same result from your example since each radius is going to be mapped to its own line. For example in the video, you could see that z-values with radius 1 are mapped to the line and then all the other points are mapped to the left, you will probably be able to achieve kind of the same result. The first transformation of the big circle D1 will give you all the points to the left of some line AND then you will have to subtract the points that makes up the smaller circle D1 so you will end up with a *band*. After that I guess you have to rotate it and translate it to match the final image.
Best of luck!
Best of bests video on You Tube🎉🎉🎉🎉
Thank you for all your videos!! Could you do one on the Dirichlet problem?
nothing planned right now, maybe in the future!
Just excellent!
Glad that you found it useful Gungör!
Amazing video.
Glad you found it useful!
amazing video!
Glad you think so Adriel, this is one of my best work so far if I can say so myself :)
Thank u so much sir
Amazing explanation
Thank you!
Thanks 👍
Happy to help 👍
Hello, first of all thank you so much for this great video. I want to ask you that when you change the elementary transformation order the final Möbius transformation result also changes. How will we understand which one is true?
Hello, if the transformations still make your mapping end up in the same desired spot then it is also a valid Möbius Transformation. Often the question will ask you for "a" möbius transformation and not "the" möbius transformation since there often exist more then one.
Thanks you, this video help me.
I'm happy to hear that!
Hey bro love your videos. But i currently can't find one which you are teaching "finding image of a strip" in conformal mapping. Please help me
It was clear sir 🙂
I'm happy that you found it useful!
Hey, very good video, just by curiosity, what software do you use to make the videos?
Hello!
I use Adobe Photoshop for the writing (and a lot of patience) while I record my screen with Camtasia, which is also my editing program. The audio is later recorded over the video by using Audacity and then I match the video and audio files with Camtasia :)
@@TheMathCoach thank you very much, the "a lot of patience part" must be the most important one lol. Actually I thought you would use some unknown crazy good program, but actually the tools are normal ones, guess I'll grab my patience and try to do something like this as well.
@@nicolasdellano280 haha yea, I probably have around 10-20 hours of me writing on the canvas and end up using only around 1-2 hours since most of it is mistakes before you get just the right one!
Best of luck to you!
excellent thanks a lot!!!
You're welcome!
You are wonderful teacher, you are amazing , thank you from deep heart 🤍
Happy to be able to help and glad that you found my video helpful :) you make a teacher happy over here!
masterpiece really! Could you please make another video about Exponential mapping? Thank you so much
Happy to hear that you liked it, maybe in the future. Not heard of it before.
Awesome vid
Happy to help!
Really nice
Glad you liked it!
Thank you ❤
Happy to help!
Best Explanation
Glad you liked it!
what happened at 17:12 ? it went over my head
8:26 I tell myself, okay may be since the line goes to infinity. 8:27 it's confirmed. Looks like I still got some math cells active.
haha, that is one of the best feelings ever mate! You seems to still got it!
Thank you sir
I'm happy to help :)
This reminds me of geometry transformations taught to Y8 students. ie. rotation, reflection, translation
That is great to hear since this area is just a way to use those elementary transformations. It is pretty beautiful how everything comes together.
great dude
great mate!
Hi,
Can we express difference of two figures numerically by using conformal mapping?
For example: how are a circle and an ellipse far each other numerically? Or a circle and triangle, or square...
A circle resembles a circle %100.
Can you lead me?
Hello, not sure about that sorry. Conformal mappings is a property for a function and is not used to compare properties between two functions.
Please come back, i love your videos.
I'm still here - lurking in the comments, just slow at making videos :)
@@TheMathCoach Okay, take your time :)
i have one question can the distribution of this transformation is normal?
very helpful
Glad you liked it!
Ω={z=x+iy∈C:y
Hi, there probably exist an conformal map. Regarding the second thing, the key thing to get a circle to map to a line is that the image needs to contain infinity and that was succeded in the video at the origin since we had the function 1/z so the origin is not the condition for all examples only for this one.
THANKS SIR
Happy to help!
What is image of unit disk under f(z)=z/(1-z^2) ile ilgili aramalar
what have you tried so far? and keep it in English if you want me to understand it.
Sir please upload more vedios on COMPLEX ANALYSIS
I'm on it, next video about Deformation of Contours should be up in the next couple of days!
Sir, could you make videos for real analysis as well?🙏
Not sure, since I think that area is quite well covered at the moment. I think I need to target more niche areas of mathematics for people to find my videos :)
thanks, love u
My pleasure to help out!
Why are we not funding this??? ❤️💚💙
That would be a blessing :)
Tq so much
No problem!
Can you start a video series on metric space?
Hello, sorry no in the foreseen future. I have a plan to start a course about GROUP and RING Theory after this playlist so that thing will probably include some information since they both are defined from a set.
@@TheMathCoach wow that will also helpful sir, please start that course and also provide the intuitions.
@@prithwishbhattacharya9481 glad to hear that, but it is not something I can start this year and this is only the plan, nothing is decided yet :)
❤❤❤❤❤❤❤
Theorem link is broken
Thanks for the notice, the page had been removed by the publisher. I have updated with another link in the description :)