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DaniilRudenko
Добавлен 25 окт 2011
Lecture 2.7: Classification of Affine Transformations
This is lecture 2.7 of the REU Apprentice program 2021 at the University of Chicago. We discuss the classification of affine transformations.
Просмотров: 413
Видео
Lecture 2.6: Affine Transformations
Просмотров 5573 года назад
This is the Lecture 2.6 of the REU Apprentice program 2021 at the University of Chicago. We discuss affine transformations.
Lecture 2.5: Cyclic Groups
Просмотров 1723 года назад
This is the Lecture 2.5 of the REU Apprentice program 2021 at the University of Chicago. We discuss cyclic groups.
Lecture 2.4: Symmetries of Regular Polygons.
Просмотров 2043 года назад
This is the Lecture 2.4 of the REU Apprentice program 2021 at the University of Chicago. We discuss symmetries of regular polygons.
Lecture 2.3: Chasles' Theorem
Просмотров 1,6 тыс.3 года назад
This is the Lecture 2.3 of the REU Apprentice program 2021 at the University of Chicago. We discuss Chasles' Theorem.
Lecture 2.2: Rotations
Просмотров 1683 года назад
This is the Lecture 2.2 of the REU Apprentice program 2021 at the University of Chicago. We discuss rotations.
Lecture 2.1: Isometries
Просмотров 6873 года назад
This is the Lecture 2.1 of the REU Apprentice program 2021 at the University of Chicago. We discuss isometries of the plane..
Lecture 1.7: Generating Functions
Просмотров 2493 года назад
This is the seventh lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss generating functions.
Lecture 1.6: An explicit formula for Catalan numbers
Просмотров 2423 года назад
This is the sixth lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss an explicit formula for Catalan numbers.
Lecture 1.5: Catalan numbers
Просмотров 3403 года назад
This is the fifth lecture of the REU Apprentice program 2021 at the University of Chicago. We begin to discuss Catalan numbers.
Lecture 1.4: Binomial Coefficients
Просмотров 1653 года назад
This is the fourth lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss the cyclic structure of a permutation.
Lecture 1.3: Cyclic Structure of a Permutation
Просмотров 2703 года назад
This is the third lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss the cyclic structure of a permutation.
Lecture 1.2: The Group of Permutations
Просмотров 3093 года назад
This is the second lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss the group of permutations.
Lecture 1.1: Bijections and Permutations
Просмотров 1,2 тыс.3 года назад
This is the first lecture of the REU Apprentice program 2021 at the University of Chicago
Group Theory, lecture 6.2: Second Sylow Theorem
Просмотров 6094 года назад
Group Theory, lecture 6.2: Second Sylow Theorem
Group Theory, lecture 6.1: First Sylow Theorem
Просмотров 1,3 тыс.4 года назад
Group Theory, lecture 6.1: First Sylow Theorem
Group Theory, lecture 5.4: Projective Geometry (II)
Просмотров 8944 года назад
Group Theory, lecture 5.4: Projective Geometry (II)
Group Theory, lecture 5.3: Projective Space (I)
Просмотров 2,5 тыс.4 года назад
Group Theory, lecture 5.3: Projective Space (I)
Group Theory, lecture 5.2: Orbits and Stabilizers
Просмотров 2,1 тыс.4 года назад
Group Theory, lecture 5.2: Orbits and Stabilizers
Group Theory, lecture 5.1: Group actions
Просмотров 8 тыс.4 года назад
Group Theory, lecture 5.1: Group actions
Group Theory, lecture 4.5: Quadratic residues
Просмотров 3274 года назад
Group Theory, lecture 4.5: Quadratic residues
Group Theory, lecture 4.4: Abelian groups
Просмотров 2994 года назад
Group Theory, lecture 4.4: Abelian groups
Group Theory, lecture 4.3: Properties of Euler function
Просмотров 2584 года назад
Group Theory, lecture 4.3: Properties of Euler function
Group Theory, lecture 4.2: Euler function
Просмотров 3344 года назад
Group Theory, lecture 4.2: Euler function
Group Theory, lecture 4.1: Cyclic groups
Просмотров 3124 года назад
Group Theory, lecture 4.1: Cyclic groups
Group Theory, lecture 3.7: Lattice of subgroups
Просмотров 1,4 тыс.4 года назад
Group Theory, lecture 3.7: Lattice of subgroups
Group Theory, lecture 3.8: Correspondence Theorem
Просмотров 3,3 тыс.4 года назад
Group Theory, lecture 3.8: Correspondence Theorem
Group Theory, lecture 3.6: First Homomorphism Theorem
Просмотров 4374 года назад
Group Theory, lecture 3.6: First Homomorphism Theorem
Group Theory, Lecture 3.5: Quotient group
Просмотров 4754 года назад
Group Theory, Lecture 3.5: Quotient group
Group Theory, lecture 3.4: Normal subgroups of S4
Просмотров 4 тыс.4 года назад
Group Theory, lecture 3.4: Normal subgroups of S4
What is the proof that if we change the order, still bijection exists
I think it’s |G|^p-1
2:56 Title 🗿
Great video
thank you for this course I think is better to say psi_e=id_X not=e
Every goddamned lecture on this topic provides the same half as$ed description using cr@ppy notation. Don't use product notation to denote a freaking function output.
It is proper notation. It is not a product notation, it's a *, which stands for any binary operator - which groups do require
Ramsey Bolton being this good at math makes him even scarier
The video is low quality @5:52 a video called "some history" skips the history @9:57 please prepare your examples
why if we have a transposition on the sub it becomes the whole group?
Thank you for the explanation ❤
Cheers Thanks
this channel is really under rated
thank u so much for vdos can u please tell me which textbook was used, and is there any link to the coursepage for assignments
Is it the S3 Group or the Dieder Group D3 ?
Amazing
f a i l
why are you saying that?
Great lectures. Pity about the squeaky marker.
Thank you for uploading.
Балдеж
Thanks Danni, Loved your explanation, helped me connecting dots of Projective space from (algebra, analysis & geometry), indeed VectorSpace keeps it simple & concrete, Appreciate the effort, looking forward. 😃😃
Fórmula of quadratic is wrong
Nice video Sir Ji . Love from INDIA 🇮🇳.
Great video!
great video! made things really clear!
Wow😘
How u write backwards
It is mirrored
I love the dramatic exit at 2:48 xD honestly I needed it ! I'm currently studying Geometry with a Klein Erlangen Program flavor and Projective Geometry in particular, and this series is helping me out a lot, thank you very much !
Thanks for your work! Hello from Irkutsk 😉
how do you write backwards?
Most likely he wrote it normally and then mirrors the video
You made the explanation really easy to follow, I just have a tiny complain/observation . . . The way you wrote Z/2Z in the video, doesn't it make it look like a Quotient Group? Isn't the Set of elements of mod 2 supposed to be identified with the notation 2Z?
I know we can find the smallest subgroup containing some elements, but does anyone ever go the other way and find the smallest set that generates the group? Would it even be useful? And is there a better way to do it than brute force and checking all possibilities? That would be a very expensive computational problem.
man really made up a variable for his example number omg
wow this man is writing all of this inversely thats impressive
Thank you sir, very informative.
I almost skipped this lecture, thinking it would be just a revision of relations. I'm glad I din't, the last part on conjugation was very interesting
I'm curious, is there any method to count the number of groups of order n?
Very nice explanation! the examples are really helpful :)
Wonderful presentation!
Dr. Rudenko, Thank you for posting this excellent video. Could you please tell me what textbook you used for the course. Thanks!
When I took the course with him a year prior, he used Dummit & Foote.
@@sillystrings Thanks! The book along with his lectures will be a fun.
@@dewookus No problem, enjoy!
Un superbe travail qui permet de bien comprendre la théorie des groupes . Jusque là toutes ces notions restaient bien compliquées pour moi . Vous apportez enfin un éclairage intense avec des exemples très parlants. Je vais vous suivre régulièrement . Merci pour tout.
This was so helpful. Thank you!