Auxiliary materials
These were developed by Seckin and Andrew to teach Mathematics 220 at UBC during August-December 2020.
- these mostly follow the style, content and order of the PLP text
- the slides were produced using PreTeXt and reveal.js mostly by adapting the textbook source
- the videos were produced using OBS, xournal++, and a greenscreen. Due to covid restrictions at the time and the ensuing space limitations, they were produced in a kitchen pantry - please forgive the resulting idiosyncracies
Slides and videos
| text-chapter | topic-n | title | slides | video |
|---|---|---|---|---|
| 1 | 1 | intro to sets | link | |
| 2 | 2 | logical statements | link | |
| 2 | 3 | and, or, & not | link | |
| 2 | 4 | the implication | link | |
| 2 | 5 | modus ponens | link | |
| 2 | 6 | converse, contrapositive & biconditional | link | |
| 2 | 7 | statement types & some defintions | link | |
| 3 | 8 | a first proof | link | |
| 3 | 9 | more proof examples | link | |
| 4 | 10 | logical equivalence | link | |
| 5 | 11 | contrapositive proof | link | |
| 5 | 12 | proof by cases | link | |
| 6 | 13 | quantifiers | link | |
| 6 | 14 | negating quantifiers | link | |
| 6 | 15 | nested quantifiers | link | |
| 6 | 16 | existence proofs | link | |
| 6 | 17 | disproofs | link | |
| 7 | 18 | induction | link | |
| 7 | 19 | proof of induction | link | |
| 7 | 20 | more induction | link | |
| 7 | 21 | generalising induction | link | |
| 8 | 22 | subsets and power sets | link | |
| 8 | 23 | set operations | link | |
| 8 | 24 | set proofs | link | |
| 8 | 25 | more set proofs | link | |
| 9 | 26 | relations | link | |
| 9 | 27 | properties & congruence | link | |
| 9 | 28 | equivalence relations & classes | link | |
| 9 | 29 | set partitions | link | |
| 9 | 30 | integers modulo n | link | |
| 10 | 31 | functions | link | |
| 10 | 32 | images and preimages | link | |
| 10 | 33 | injections, surjections & bijections | link | |
| 10 | 34 | compositions | link | |
| 10 | 35 | inverse functions | link | |
| 11 | 36 | proof by contradiction | link | |
| 11 | 37 | contradiction examples | link | |
| 11 | 38 | two famous proofs | link | |
| 12 | 39 | cardinality of finite sets | link | |
| 12 | 40 | towards infinite sets | link | |
| 12 | 41 | denumerable sets | link | |
| 12 | 42 | uncountable sets | link | |
| 12 | 43 | more infinities | link |