Series of exercises:
(1) Sets and mappings: Boolean operations with concrete examples, proving equalities between sets; proving statements involving "implication"; calculating with the Boolean operations; products and its geometric content; concrete construction of maps; injectivity, surjectivity, and direct and inverse images; permutations on finite sets; basic combinatorics; families of sets; characteristic functions (logic vs algebraic operations).
(2) Binary relations: equivalence relations; classes and maps on them; working with concrete examples; equivalence and set partitions; ordering (the divisibility order on the integers as a basic example); insights for depth of order theory (well-ordering on the integers, the reals, a primer on logic).
(3) Basic algebraic structures: binary operations; associativity and identity elements; abstract manipulation of binary operations; checking an operation to be a group one; subgroups and equivalence relations.
- Teacher: Yassine GUERBOUSSA