Set, relation, map and integers

1. set concept
2. set operations
3. symmetric difference
4. equivalence relation
5. equivalence class
6. partitions
7. abstraction lemma
8. application = map = function = transformation = functor
9. basic types of maps: constant, injective, surjective, bijective
10. image, preimage, rank and fiber of a mapping
11. combinations
12. binomial theorem
13. modular arithmetics
14. division algorithm
15. greatest common divisor
16. Euclides algorithm
17. prime number
18. arithmetic fundamental theorem
19. coprime integers

Algebraic estructures

1. binary operation in a set
2. simple algebraic structure
3. associative binary operation
4. neutral element of a binary operation
5. inverses in a binary operation
6. semigroup
7. monoid
8. group
9. ring
10. field
11. skew-field
12. module
13. vector space
14. algebra
1. commutative algebras
2. alternating algebras
3. Lie algebras
15. groupoid
16. universal algebra