Slide Set 08: Generating Functions and their Delightful Applications to Random Networks
We absorb the dark powers of Generatingfunctionomancy.
Simple, flat slides:
25M
; Last updated: 2019/01/14, 23:14:28
Printable handout:
6.2M
; Last updated: 2019/01/14, 22:50:59
Slides with all reveals for lectures:
41M
; Last updated: 2019/01/14, 22:05:08
Covered in these episodes:
11g: The Dark Art of Generatingfunctionomancy (12:42)
11h: Generating functions: Example calculations (3:43)
11i: Generating functions: Computing the average degree (4:27)
11j: Generating functions: Higher moments and more (4:09)
12b: Generting function recap (3:04)
12c: Inversion formula for probability generating functions (9:07)
12d: Generating function deliciousness for sums of variables (1:55)
12e: Giant component condition, generatingfunctionally (16:48)
12f: Component size distributions (4:27)
12g: Recursion story with pictures (13:01)
12h: Sneaky generating function story for random sums of randomness (16:59)
13c: Generating function refresh (6:22)
13d: Simple V = U + 1 generating function rule (3:01)
13e: Recursive equations for finite component size p.g.f.'s (11:32)
13f: Giant component size calculation (3:41)
13g: Component size distributions for standard random graphs (14:55)
13h: A very pleasing simple network calculation (25:47)
14d: Finding finite component size distributions with generating functions (6:47)
14e: Distribution of finite component sizes: Standard random networks (7:50)
14f: Distribution of finite component sizes: Simple mixed network (5:58)