One could also say that an ideal is represented by a system of equations (or that an ideal is an abstraction for a system of equations). Two systems of equations are equivalent (in the algebraic world) if each equation of the one can be deduced (addition of polynomials of the ideal in question, multiplication with any polynomial) from the equations of the other. In the geometric world, we would like two system of equations to be equivalent exactly if they have the same solutions, which is clarified in the next video.
I'm currently doing research/learning for my final year project on Algebraic curves and Riemann surfaces and thank you so much for these videos. Learning from literature only is virtually impossible for me and Ried's book on the matter is good, but this gives so much needed context that I feel like I might actually be able to complete the project. So glad I found these videos, you and a few other creators are awesome! P.S. do you know the best way to reference a youtube playlist lol
I am glad that you found your way here and that the videos are helpful, thanks for the feedback ☺ I would probably go for “Last name, First Name. "Title of video." RUclips, uploaded by Screen Name, day month year, ruclips.net/user/xxxxx”, potentially replacing the name by the channel name. However, people move slowly and some might be against such references, so a more standard reference is certainly also a good idea.
@@VisualMath Thank you, I'll find a way to reference the series in some way as it has been pivotal :) Also, I've recently changed from using Reid's Undergraduate Algabraic Geometry to Andreas Grathmann's notes. Did you by any chance use these too? I've noticed some similarities in some of the early pacing etc?
Thank you so much for the work you put into this. It's a real treat to open up youtube and find there's a new video in this series!
I am very happy to hear that. I hope you will enjoy AG ☺
One could also say that an ideal is represented by a system of equations (or that an ideal is an abstraction for a system of equations). Two systems of equations are equivalent (in the algebraic world) if each equation of the one can be deduced (addition of polynomials of the ideal in question, multiplication with any polynomial) from the equations of the other. In the geometric world, we would like two system of equations to be equivalent exactly if they have the same solutions, which is clarified in the next video.
Thanks for pointing that out: that viewpoint will come in handy when the Groebner bases enter the game!
I'm currently doing research/learning for my final year project on Algebraic curves and Riemann surfaces and thank you so much for these videos. Learning from literature only is virtually impossible for me and Ried's book on the matter is good, but this gives so much needed context that I feel like I might actually be able to complete the project. So glad I found these videos, you and a few other creators are awesome!
P.S. do you know the best way to reference a youtube playlist lol
I am glad that you found your way here and that the videos are helpful, thanks for the feedback ☺
I would probably go for “Last name, First Name. "Title of video." RUclips, uploaded by Screen Name, day month year, ruclips.net/user/xxxxx”, potentially replacing the name by the channel name. However, people move slowly and some might be against such references, so a more standard reference is certainly also a good idea.
@@VisualMath Thank you, I'll find a way to reference the series in some way as it has been pivotal :) Also, I've recently changed from using Reid's Undergraduate Algabraic Geometry to Andreas Grathmann's notes. Did you by any chance use these too? I've noticed some similarities in some of the early pacing etc?
@@Smigdit78 Yes, I am roughly following Grathmann's notes. They are so excellent 🥰
Have you looked up the recent Algebraic Curves and Riemann Surfaces for Undergraduates by Nerode & Greenberg?
@@julianwilson9919 No, I have not seen that one. I will have a look, thanks for the reference 🤗
Keep up the good work
Thanks, I will try to do my best. I hope you will enjoy AG ☺
The contravariance in one sentence: More constraints yield fewer solutions.
Exactly ☺
What does V(f,g) mean though? Is V an operation acting on two sets?
Ah, I am just lazy 😅 This means V({f,g}), so set brackets are omitted. I hope that makes sense.