Modular Arithmetic: Addition in Motion
Topics Covered (14 minutes 47 seconds):
- Examples of additive dynamical portraits
- Proof that f(x) = x+a is bijective, which proves the pictures contain only cycles
- Proof that the cycles are all the same size
- Process of exploration and conjecture for the cycle size/number
- A full description of the dynamical portrait with proof
- the definitions of function, injectivity, surjectivity, bijectivity
- the ability to use modular arithmetic in practice (see Modular Arithmetic: User’s Manual.)
- the video Modular Arithmetic: In Motion, which introduces dynamical portraits and proves basic properties:
- the portrait consists of cycles if and only if the associated function is a bijection
Materials and links:
- Tool to compute addition and multiplication tables.
- PDF of small addition and multiplication tables.
- Tool to draw modular dynamics pictures.
- Additive Dynamics Exploration (to be done in groups before this video).