Schedule
The integers and integers mod m
- Nov 21
- Construction of the integers
- Pre-reading
- Nov 28
- Lean’s
Int - Pre-reading
- Project draft due
- Lean’s
- Nov 30
- Modular arithmetic
- Pre-reading
- Dec 2
- A glimpse of groups
- Pre-reading
- Dec 9
- Final project due
Past topics
Induction
- Nov 9
- Peano’s natural numbers
- Pre-reading
- Nov 11
- Recursion
- Pre-reading
- Nov 14
- Induction
- Pre-reading
- Nov 16
- Strong induction
- Pre-reading
- Nov 18
- Other inductive types
- Pre-reading
- HW 12 due
Relations
- Oct 31
- Examples of relations
- Pre-reading
- HW 10 due
- Project & Group Choice due
- Nov 2
- Properties of relations
- Pre-reading
- Nov 4
- Partial and total orders
- Pre-reading
- Nov 7
- Equivalence relations
- Pre-reading
- HW 11 due
Functions
- Oct 21
- Basic ideas around functions
- Pre-reading
- Oct 24
- Injective, surjective, bijective functions
- Pre-reading
- HW 9 due
- Oct 26
- Inverses
- Pre-reading
- Oct 28
- Functions and sets
- Pre-reading
Sets
- Oct 10
- Introducing sets
- Pre-reading
- HW 7 due
- Oct 12
- Operations on sets
- Pre-reading
- Oct 17
- Sets in Lean
- Pre-reading
- HW 8 due
- Oct 19
- More set theoretic proofs in Lean
- Pre-reading
Predicate logic
- Sep 23
- Predicates, quantifiers, and equality
- Pre-reading
- Sep 26
- New rules of inference
- Pre-reading
- HW 5 due
- Sep 28
- Models in predicate logic
- Pre-reading
- Oct 3
- Examples derivations
- Pre-reading
- Oct 5
- Predicate logic in Lean
- Pre-reading
- HW 6 due
- Oct 7
- Examples in Lean
- Pre-reading
Lean
- Sep 12
- Propositions and connectives
- Pre-reading
- HW 3 due
- Sep 14
- Proofs and first rules of inference
- Pre-reading
- Sep 16
- More proofs and rules of inference
- Pre-reading
- Sep 19
- Negation and proof by contradiction
- Pre-reading
- HW 4 due
- Sep 21
- Interactive mode for proving
- Pre-reading
Propositional logic
- Aug 22
- Some puzzles
- No pre-reading
- HW 0 due
- Aug 24
- Propositions and proof
- Pre-reading
- Aug 26
- And, or, implies
- Pre-reading
- Aug 29
- Not
- Pre-reading
- HW 1 due
- Aug 31
- Reductio ad absurdum
- Pre-reading
- Sep 2
- Intepretations and truth tables
- Pre-reading
- Sep 7
- Proof vs truth
- Pre-reading
- HW 2 due
- Sep 9
- Useful formula in propositional logic
- Pre-reading
Welcome and Orientation
- Aug 19
- Introducing the course and ourselves