Content of this Pdf

Set theory

1. Set
2. Some important sets
3. subset
4. empty set
5. finite set
6. cardinality
7. equal set
8. Algecric operations on sets
9. union
10. intersection
11. disjoint sets
12. Some properties of union and intersection
13. Complement of sets
14. Difference
15. De morgan’s law
16. Symmetric difference
17. Power set
18. Partition of a set
19. Cartesian product

Relation and mapping

1. equivalence relation
2. Examples
3. Mapping/function
4. Composition of mapping
5. Summary

Division algorithm

well ordered property

Divisibility

Greatest common divisor

Theorems

Euclid lemma

Euclidean algorithm

Solve problems

Binary composition/operation

Examples

Modular Arithmetic

Properties

Group

Semigroup

Abelian group

Examples

Remarks

Revision