Math 511: Spring, 2023
Presentations

Presentation Topics (in class or in office)

1. Theorem 1.1.1. Theorem 1.1.2 (despite being infinite).
2. Page 5: Prove that a Boolean algebra B, as a (+, ·) algebra, is isomorphic to the vector space of its indicator functions with values in GF(2).
3. Explain what is right and what is wrong with the first sentence on page 10: "There is a bijection...".
4. Lemma 1.2.1. (Linear extensions are important.)
5. The proof of page 12, lines 7-9, on order dimension vs. direct (= Cartesian) products.
6. Exercise 1.1.3(a) and (b) (separate presentations).
7. Exercise 1.2.2(b) and (c) (separate presentations).
8. Lemma 1.3.2.
9. Lemma 1.3.3.
10. Exercise 1.3.3.
11. Exercise 1.3.6.
12. Theorem 1.4.1.
13. Exercise 1.4.2.
14. Exercise 1.4.5(b,c). Do not read the text up to (a). What you need is only the text after (a) and before (b,c).
15. Theorem 2.2.9.
16. Theorem 2.2.10.
17. Exercise 2.2.1.
18. Theorem 2.3.3 proof, and deduce a result that states the exact rank in similar fashion.
19. Exercise 2.3.2(a).
20. Exercise 2.3.2(b).
21. Exercise 2.4.5.
22. Theorem 2.6.3.
23. Lemma 2.6.5.
24. Exercise 2.6.1.
25. Exercise 2.6.9(a).
26. Exercise 2.6.10(a).
27. Exercise 2.7.4(a).
28. Exercise 3.1.1.
29. Exercise 3.1.2(a).
30. Theorem 3.2.4.
31. Theorem 3.2.5.
32. Exercise 3.3.4, Thm. 3.3.1.
33. Exercise 3.3.4, Thm. 3.3.3.
34. Exercise 3.3.5(a).
35. Exercise 3.3.5(b).
36. Exercise 3.3.7(a) (see correction in the errata).
37. Exercise 3.4.2.
38. Exercise 3.5.3(b).
39. Prove that every interval of a (finite) geometric lattice is a geometric lattice.
40. Exercise 4.2.2.