Intro to Group Theory

Common set names:

• N: natural numbers {1,2,…∞}
• Z: integers {-∞,…-3,-2,-1,0,1,2…∞}
  • Z⁻={-1,-2,-3,…-∞}
  • Z⁺={1,2,3,…∞}
• Q: rational numbers {p/q; p,q∈Z}
  • Q* = Q-{0}
• R: real numbers
• I: imaginary numbers
• C: set of complex numbers ‘a+bi’

Linking #

Algebraic Structure #

https://youtu.be/_i_XRDXcCJY?list=PLxCzCOWd7aiH2wwES9vPWsEL6ipTaUSl3:

Algebraic Structure

Semigroup #

https://youtu.be/CxffkidIty4?list=PLxCzCOWd7aiH2wwES9vPWsEL6ipTaUSl3:

Semigroup

Monoid #

https://youtu.be/wYPEEJLVjXg?list=PLxCzCOWd7aiH2wwES9vPWsEL6ipTaUSl3:

Monoid

Group #

https://youtu.be/JAvICe01xj0?list=PLxCzCOWd7aiH2wwES9vPWsEL6ipTaUSl3:

Group

Abelian Group #

https://youtu.be/vAEK1d6KFog?list=PLxCzCOWd7aiH2wwES9vPWsEL6ipTaUSl3:

Abelian Group