Скачать или смотреть GR1 What is a poset? What is a Hasse diagram? What is a lattice?

What is a partially ordered set? What is a totally ordered set? What is a Hasse diagram? What is a lattice? Definitions and Examples from Combinatorics, Linear Algebra, and Group Theory. #combinatorics #abstractalgebra Subscribe ‪@Shahriari‬ for math for college students
00:00 Introduction
00:21 Example: The integers are totally ordered
01:02 Example: Subsets of {1, 2, 3} form a poset
01:51 Example: Divisors of 24 form a poset
02:38 What is a poset informally?
03:09 What is a relation?
04:08 Definition: What is a poset?
05:21 Example of a poset: students and gummy bears
07:20 Boolean Lattices prototypical examples of posets
07:56 Definition: Comparability and Cover Relations
09:32 Definition: Hasse diagram of a poset
11:24 Examples: Hasse diagrams of Boolean Lattice of order 6, the integers, divisors of 24
12:14 Subspaces of a vector space form a poset
13:35 Subgroups of a group from a poset
14:26 Definition: What is a lattice?
16:02 Definition: Poset isomorphism
17:40 All posets of size 4

A series of lectures on general topics in undergraduate mathematics.

This particular lecture is useful for both Combinatorics and Abstract algebra and is partially based on two of my books

Shahriar Shahriari, An Invitation to Combinatorics, Cambridge University Press, 2022.
DOI: https://doi.org/10.1017/9781108568708

Shahriar Shahriari, Algebra in Action, A Course in Groups, Rings, and Fields, American Mathematical Society, 2017. https://bookstore.ams.org/amstext-27/

An annotated list of videos for Combinatorics:
https://pomona.box.com/s/by2ay2872avx...
YouTube Playlist:    • Combinatorics, An Invitation  

An annotated list of Abstract Algebra Videos: https://pomona.box.com/s/06zu90ewikpn...
YouTube Playlist:    • Abstract Algebra, an intro via Actions  


Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and six time winner of Pomona College's Wig teaching award.