The following calendar will be populated with links to worksheets, videos, activities and daily posts, so you can catch up on anything you’ve missed and revisit important material.

**Monday, August 24th:**- What we did in class: Polyhedron exploration activity. The materials: Exploratory activity and polyhedron pictures. Here are the pictures with vertices, edges, faces counted: first page, second page. Here are the slides from class.
- Here’s an excellent 3blue1brown video a student pointed me to, giving a proof of Euler’s formula V-E+F=2. We will get to some of these ideas later in the course; for now, just enjoy!

- After-class daily post link: Due Wed Aug 26

**Wednesday, August 26th:**- What we did in class: We began discussing sets. We covered the definition of set, element, equality, cardinality and subsets, as well as some standard sets of numbers and the empty set. We did lots of examples.
- In-class notes

- After-class daily post link: Due Fri Aug 28

**Friday, August 28th:**- What we did in class: We did a practice Worksheet on elements and subsets. The correct answers to the first part spell an english message when read backward from bottom to top. We took these up (whiteboard notes). Then we briefly talked about active reading.
- After-class daily post link: Due Mon Aug 31

**Monday, August 31st:**- What we did in class: We shared active reading strategies, we talked about what is a proof, and then we considered the sandbox problem. As a group we decided on the answer, and then we broke into groups to try to write up proofs.
- After-class daily post link: Due Wed Sept 2

**Wednesday, September 2nd:**- What we did in class: We discussed some first examples of proofs based on the sandbox problem (pdf notes). Then we introduced two types of set-builder notation (link to notes).
- After class daily post link: Due Friday Sept 4

**Friday, September 4th:**- What we did in class: We did an activity to practice dealing with set builder notation.
- Here are some brief whiteboard notes.
- Set Builder Activity: Caller Cards and Bingo Sheet.
- After class daily post link: Due Wed Sept 9

**Wednesday, September 9th:**- What we did in class: We finished up with some lecture about set builder notation in the contexts of the real line (interval notation), the Cartesian plane (where you draw graphs for example), and the universe of subsets of some set. Then we began discussing a proof of the fact that if n is odd, then n^2 is odd. We only got as far as deciding on our definitions. Here are class notes.
- After class daily post link: Due Fri Sept 11

**Friday, September 11th:**- What we did in class: We finished up about the n^2 odd proof. Then we introduced and discussed Cartesian products. Here are notes.
- After class daily post link: Due Mon Sept 14th

**Monday, September 14th:**- What we did in class: We continued Cartesian products, talking about the Multiplication Principle, and we also discussed Power Sets and proved a formula for the cardinality of a Power Set. Here are notes.
- After class daily post link: Due Wed Sept 16

**Wednesday, September 16th:**- What we did today: We discussed more examples of proofs. Here are notes.
- After class daily post link: Due Fri Sept 18

**Friday, September 18th:**- What we did in class: We talked about Venn diagrams and then did an introduction to counting via a first worksheet on counting.
- After class daily post link: Due Mon Sept 21

**Monday, September 21st:**- What we did in class today: We took up some set builder notation, and then did counting (multiplication principle) based on the first worksheet on counting. Here are notes.
- After class daily post link: Due Wed Sept 23

**Wednesday Septmber 23rd:**- What we did in class today: More on counting: addition principle, overcounting, binomial coefficient, binomial theorem. Here are notes.
- After class daily post link: Due Fri Sept 25

**Friday, September 25th:**- What we did in class today: More on combinatorial proof, and counting, including a worksheet, and then an introduction to inclusion-exclusion. Here are notes.
- After class daily post link: Due Mon Sept 28

**Monday, September 28th:**- What we did in class today: More on inclusion-exclusion (a proof) and then an introduction to graphs. Here are notes.
- After class daily post link: Due Wed Sept 30

**Wednesday, September 30th:**- What we did in class today: We did more examples of how graphs show up in mathematics and then we introduced Boolean algebra. Here are notes.
- After class daily post link: Due Fri Oct 2

**Friday, October 2nd:**- What we did today: We got deeper into Boolean algebra and discussed why “if-then” is so tricky. We did the Wason Selection Task. Here’s a Wikipedia article about it. Here are notes.
- After class daily post link: Due Mon Oct 5

**Monday, October 5th:**- What we did in class today: A LaTeX introduction!
- After class daily post link: Due Wed Oct 7

**Wednesday, October 7th:**- What we did in class today: We discussed “if and only if” as a boolean operation.
- We covered Boolean algebra identities, and talked about the contrapositive and contradiction as proof methods. Here are notes.
- After class daily post link: Due Fri Oct 9

**Friday, October 9th:**- What we did in class today: We covered a cheat-sheet of logical equivalences and showed how to use them to turn one expression into another. Then we began a negation worksheet and talked about examples of negation.
- Cheat-sheet of important logical equivalences.
- Negation worksheet.
- After class daily post link: Due Mon Oct 12

**Monday October 12th:**- What we did in class today. We worked through examples of negation, and quantifiers. We talked about the idea of an example and a counterexample. Then for the last ten minutes we did a worksheet on quantifiers, example and counterexample.
- Negation worksheet.
- Quantifiers Negation worksheet
- After class daily post link: Due Wed Oct 14

**Wednesday, October 14th:**- What we did in class today: We did a counting example, did examples with quantifiers, and proved the square root of 2 is irrational by contradiction.
- Here are notes.
- Quantifiers Practice and solutions from class for the first few.
- Set up contradiction worksheet.
- Set up contrapositive worksheet.
- After class daily post link: Due Fri Oct 16

**Friday, October 16th:**- What we did in class today: Took up the worksheets from last time, did another example of proof by contradiction and then some Contradiction Puzzles. Here are notes.
- After-class daily post link: Due Mon Oct 19

**Monday, October 19th:**- What we did in class today: We took up contradiction puzzle solutions. Then we started on existence proofs. Here are notes.
- After-class daily post link: Due Wed Oct 21

**Wednesday, October 21st:**- What we did in class today: We took up solutions for some of the badges. We continued talked about existential proofs. Here are notes.
- After-class daily post link: Due Fri Oct 23

**Friday, October 23rd:**- What we did in class today: We considered the definitions of convergence and continuity, and we used them to prove something converges and something is continuous (we didn’t quite finish the latter). Here are notes.
- After-class daily post link: Due Mon Oct 26

**Monday, October 26th:**- What we did in class today: We took up the proof that f(x)=x^2 is continuous at 0, and then we introduced functions, injectivity, surjectivity and bijectivity. Here are notes.
- After-class daily post link: Due Wed Oct 28

**Wednesday, October 28th:**- What we did in class today: We did examples of functions, injectivity, bijectivity, surjectivity. Here are notes.
- Here’s Functions Worksheet 1 and Solutions.
- Here’s Functions Worksheet 2 and Solutions.
- After-class daily post link: Due Fri Oct 30

**Friday, October 30th:**- What we did in class today: We explored injectivity, surjectivity and bijectivity, and then introduced composition of functions. The lectures were inspired by the worksheets listed above (Oct 28). Here are notes.
- After-class daily post link: Due Mon Nov 2

**Monday, November 2nd:**- What we did in class today: Composition, inverses. We began the proof that a function is bijective if and only if it is invertible. Here are notes.
- After-class daily post link: Due Wed Nov 4

**Wednesday, November 4th:**- What we did in class today: We finished the proof from last class, and then talked about cardinalities of sets. Here are notes.
- After-class daily post link: Due Fri Nov 6

**Friday, November 6th:**- What we did in class today: Cardinalities — examples of showing things are countable or not. Here are notes.
- After-class daily post link: Due Mon Nov 9

**Monday, November 9th:**- What we did in class today: More cardinalities, and a discussion of axiom systems. Here are notes.
- The axioms of the integers
- After-class daily post link: Due Wed Nov 11

**Wednesday, November 11th:**- What we did in class today: Relations and their properties. Here are notes and the annotated worksheet (blank relations worksheet).
- After-class daily post link: Due Fri Nov 13

**Friday, November 13th:**- What we did in class today: Equivalence relations, equivalence classes, and partitions. Here are notes.
- After-class daily post link: Due Mon Nov 16

**Monday, November 16th:**- What we did in class today: Defining rationals, reals, and integers mod n using equivalence classes. Here are notes. Here are multiplication tables.
- After-class daily post link: Due Wed Nov 18

**Wednesday, November 18th:**- What we did in class today: We finished up talking about modular arithmetic and how to divide mod n. Then we introduced the pigeonhole principle and did pigeonhole problems. Here are notes, the Modular Arithmetic worksheet I used in class, and some Pigeonhole problems.
- After-class daily post link: Due Fri Nov 20

**Friday, November 20th:**- What we did in class today. We finished up pigeonhole problems, and then I did a bit of office hour on badges questions.
- After-class daily post link: Due Mon Nov 23

**Monday, November 23rd:**- What we did in class today: Graph Theory! We introduced topics like path, walk, cycle, tree, connected, complete, adjacent, degree. Here are notes.
- After-class daily post link: Due Wed Nov 25

**Wednesday, November 25th:**- What we did in class today: Introduction to induction using a theorem on trees. Here are notes.
- After-class daily post link: Due Mon Nov 30

**Monday, November 30th:**- What we did in class today. More practice with induction. Here are notes.
- Worksheet on the format of induction.
- Solutions as presented in class.
- After-class daily post link: Due Wed Dec 2

**Wednesday, December 2nd:**- What we did in class today: Two induction proofs. First, 2- and 5- cent stamps. Second, Euler’s formula. Here are notes.
- After-class daily post link: Due Fri Dec 4

**Friday, December 4th:**- What we did in class today: Half-length class in which we discussed some false induction proofs.
- Hildebrand’s False Induction Proofs.
- After-class daily post link: Due Mon Dec 7

**Monday, December 7th:**- What we did in class today: Review games.