Lecture 9
Relative primes, prime numbers, no largest prime and other results. Unique factorisation theorem. Discussion of modern applications in number theory and encryption.
Lecture 10
Congruence modulo an integer, congruence classes, Z_n. Beginning group theory.
Lecture 11
The group axioms, abelian groups. Examples: S_3, cyclic groups, Z_n, GL(n).
Lecture 12
Show some properties of groups: unique identity element, unique inverse for each element etc.