Mon., Jan. 23
The main video evaporated. This is only a fragment from the end.
Wed., Jan. 25
Fri., Jan. 27
Mon., Jan. 30
The video was lost. Most of today was a clumsy attempt at the proof given in the next two days.
Wed., Feb. 1
Fri., Feb. 3
I blew the recording process! The day was devoted to finishing the proof of Birkhoff's representation theorem for finite distributive lattices, which you can find in the book.
Mon., Feb. 6
Wed., Feb. 8
The recording didn't happen; I don't know what went wrong. The class was mostly about the matrix of blanks (which should be 0's) and *'s in section 1.5, anticipating some of Chapter 2. I also explained abstract closure operators and specializations like topological and vector-space closure.
I forgot to start recording this online class. The class was informal.
§1.5: Regarding abstract closure, the useful Prop. 1.5.2. Galois connections; they will re-appear. Algebra of relations: We care about converse, complement, and composition.
Ch. 2: 0/1 matrix vs. matching in bipartite graph vs. system of distinct representatives. 0/1 matrices with same row and column sums (oversimplified).
Mon., Feb. 13
Wed., Feb. 15
Fri., Feb. 17; today we have two recordings because the first ended after half an hour; the class continues in the second.
Mon., Feb. 20
Wed., Feb. 22
Fri., Feb. 24
Mon., Feb. 27
Wed., Mar. 1
Mon., Mar. 6
Wed., Mar. 8
Fri., Mar. 10
Mon., Mar. 13
Wed., Mar. 15
Fri., Mar. 17
Mon., Mar. 20.
Today I explained the chromatic polynomial of a graph and its connection with the Möbius function (but no proof). For more about this see Exercise 3.5.2.
Wed., Mar. 22.
I forgot to turn on recording until after class. The first part was the proof of Theorem 3.1.4 by the partitioning method in the book. The second part was important examples (power set of a set, divisibility lattice, power set of a multiset), shown in the blackboard captures in the video.
Fri., Mar. 24
Mon., Mar. 27
Wed., Mar. 29
Fri., Mar. 31. There are two videos for the two halves of the class. First half:
Second half:
Wed., Apr. 12
Fri., Apr. 14
Mon., Apr. 17. I forgot to record. The first half of class concerned the Jordan-Dedekind chain condition and rank (page 162). The second half was about the main example of a matroid, namely a finite set of vectors in a vector space. The short video shows all the board work for that half.