What is algebraic geometry?
ฝัง
- เผยแพร่เมื่อ 16 ต.ค. 2023
- Algebraic geometry is often presented as the study of zeroes of polynomial equations. But it's really about something much deeper: the duality between abstract algebra and geometry.
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A HUGE HUGE thank you to Faisal Al-Faisal for working with me on the script and storyboard for this video!
And another thank you to Davide Radaelli for helpful conversations when making this video.
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CORRECTIONS:
At 4:26, I mistakenly wrote that g(1,1)=-2. This is a typo! The corrected version is g(1,-1)=-2.
SOURCES and REFERENCES for Further Reading!
(a) “A guide to plane algebraic curves” by Keith Kendig. It’s written in a very elementary style and has lots of really captivating diagrams throughout. If you look at the table of contents, it starts off with lots of examples that only require elementary algebra. And by the end, it actually gets to some pretty deep theorems in algebraic geometry.
(b) "Ideals, Varieties, and Algorithms” by Cox, Little, O’ Shea. This book does not assume any knowledge of abstract algebra and teaches everything from the ground up. It is a very nice book with plenty of computational examples and exercises.
(c) “Algebraic Geometry and Arithmetic Curves” by Qing Liu. This books is all about schemes and Spec. It's a rather terse theorem-proof style book, but it is beautifully written and has lots of exercises.
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MUSIC CREDITS:
The song is “Taking Flight”, by Vince Rubinetti.
www.vincentrubinetti.com/
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What is algebraic geometry?: (0:00)
Coordinate Ring: (3:04)
How algebra detects reducibility: (3:54)
How algebra detects a node: (5:15)
Schemes!: (8:00)
Please please please make more algebraic geometry or commutative algebra videos. These are really great!
Please make more videos on algebraic geometry, please. These videos are treasures.
Best advanced math education channel on TH-cam. I struggled immensely with algebraic geometry in college. The definitions and concepts weren’t properly motivated. So I learned in a painfully mechanical way.
An excellent introductory video. I should have watched it before I took algebraic geometry or read Gathmann's.
Wow, I don't think there is a better introduction to ideals in algebraic geometry.
Individuals that have spare money, if I were one of you, I would consider donating to this man. He has the most simple yet beautiful way of sharing knowledge I've seen since I discovered 3b1b. Give this man a chance to make more videos like this one more frequently. ❤
It's really cool that you talked about schemes! For such an advanced topic it's really nice to see a video even mentioning it
Such a fascinating video! Your videos tend to ignite a spark of curiousity everytime i watch them, thanks so much!
As an algebraic geometer/commutative algebraist, this video describes exactly how we think about shapes and their corresponding rings. Great job!
You really made my day ❤️,
4:25
This is a really nice appetizer, it's so rare for a video on algebraic geometry to actually go far enough to talk about schemes
Appreciable work. Keep on providing introductory videos (+ additional resources) of Advanced Math Courses. As a highly motivated undergrad, it really helped me to study these advanced topics with good intuition and a good introductory recourse (that book you mentioned). Anyway, Thanks and keep on guiding us.☺
I was always too intimidated to begin studying this topic I’ve laways been intrested in, but this video has definitely done a good job at helping me croos that threshold. So thanks!
The best layman presentation of algebraic geometry I have ever seen. Great!
Great video. So nice to see a new video from you. Thank you
wow!! It's so amazing. You are very good at explaining everything! Well done!!!!
Great introduction! Very thoughtful and wise presentation.
Small error but at
excellent quality of explanation. Please more videos on this topic.