11:31
Group Theory 1: Axioms
AUT literacy for assessments
5:32
Group Theory 2: Example of a group: Positive real numbers under multiplication
6:00
Group Theory 3a: Addition modulo 2 NO SOUND
10:09
Group Theory 3b: Addition modulo 3
9:25
Group Theory 4a: 2x2 matrices integer valued with unit determinant
3:01
Group Theory 4b: nxn matrices nonzero determinant
1:55
Group Theory 4c: z1 powers
4:54
Group Theory 4d: z2 cyclic group
3:04
Group Theory 4e: z3 definition of order
7:43
Group Theory 4f: z4 direct product of groups or cartesian product
11:03
Group Theory 5a: Complex numbers under multiplication
4:28
Group Theory 5b: z1 free group
13:55
Group Theory 5c: z2 symmetric group
6:28
Group Theory 6: Left identity and left inverse is group proof
2:03
Group Theory 7: Definition of subgroup
2:21
Group Theory 8: Trivial subgroups identity and whole Group
3:08
Group Theory 9: Z subgroup of R
4:36
Group Theory 10: C2 subgroup of C4
5:30
Group Theory 11: Complex plane subgroup of modulus 1
7:11
Group Theory 12: Centre definition
2:10
Group Theory 13: Centre meaning
7:06
Group Theory 14: Centre of GL2
4:09
Group Theory 15: Definition of homomorphism
3:50
Group Theory 16a: Homomorphism of identiy
3:42
Group Theory 16b: Old homomorphism of identiy element
2:23
Group Theory 17: Homomorphism of inverse is inverse of alpha
5:10
Group Theory 18: Definition of isomorphism
2:55
Group Theory 19: Logs of real numbers as homomorphism
4:47
Group Theory 20: Homonorphism even and odd
2:48
Group Theory 21: Definition of cosets
4:43
Group Theory 22: Coset characterised by any member
2:49
Group Theory 23: Cosets are either disjoint or equal
4:21
Group Theory 24: Criterion for equality of cosets
Group Theory 25: All cosets are the same size
6:37
Group Theory 26a: Lagrange's theorem
Group Theory 26b: Left cosets and right cosets are the same size
6:01
Group Theory 27: Definition of normal subgroup
3:21
Group Theory 28: Normal subgroup defined as conjugation
15:55
Group Theory 29: Example of non normal subgroup
Group Theory 30: Center is normal
8:30
Group Theory 31: Kernel of homomorphism is a normal subgroup
16:27
Group Theory 32: Set of automorphisms of a group is a group
4:25
Group Theory 33a: Normal subgroup is kernel of a homomorphism 1
6:29
Group Theory 33b: Normal subgroup is kernel of a homomorphism 2
1:02
Group Theory 33c: Normal subgroup is kernel of a homomorphism 3
2:28
Group Theory 33d: Normal subgroup is kernel of a homomorphism 4
9:01
Group Theory 34: First isomorphism theorem 1
2:32
Group Theory 35: First isomorphism theorem 2
3:33
Group Theory 36: First isomorphim theorem 3
19:27
Group Theory 37: Example of Rsquared with subgroup L
Group Theory 38a: Subgroup generated by a subsest
4:41
Group Theory 38b: Example determinant
Group Theory 39: Subgroups generated by coprime pairs of integers
4:35
Group Theory 40: Definition of group action on a set
7:42
Group Theory 41: Definition of stable and definition of orbit under G
5:17
Group Theory 42: Example of orbits of orthogonal matrices are concentric circles
5:26
Group Theory 43: Definition of symmetric group
Group Theory 44: Cycle notation
4:29
Group Theory 45: Define the shape of a cycle
7:01
Group Theory 46: Conjugacy classes of Sn
Group Theory 47: Generate Sn from cycles
Group Theory 48: Generate Sn from n-1 2-cycles
1:04
Group Theory 49: Every 2cycle is its own inverse
