Week1 - Mathematical Thinking in Computer Science

Discrete Mathematics

Why proofs?

Course Objectives

• learn by examples how to understand proofs
• how to invent
• how to explain
• how to enjoy proofs

Can a chessboard(8 * 8) be tiled by dominos (1 * 2) ?
So after I tried the external tool, the puzzle, in some cases, I could not find a tiling.
There are two problems:

• I cannot find a tiling and prove that it exists.
• I cannot prove a tiling that does not exist neither.

Proof of possiblity

this one can be proved impossible easily, because the remainder is always 1, an odd number.

so,the board without arbitrary two cells of different colors can be tiled by dominos.

Words List

more skeptical
cryptographic protocol
a by-product
tile tiled tiling
domino
an odd number
mission provably impossible
spoiler
recap
theorem
proofs for existential statements
tensegrity