COMP9020

outline:

numbers, sets, functions week 1
logic week 2–3
relation theory week 5–6
graphs and trees week 8
induction and recursion week 9
order of growth of functions week 10
counting (combinatorics) and probability week 11-13

week 01 numbers, sets, functions

⌊ x ⌋: R −→ Z — floor of x, the greatest integer ≤ x
⌈ x ⌉  : R −→ Z — ceiling of x, the least integer ≥ x

‘m|n’ — m is a divisor of n, defined by n = k · m for some k ∈ Z 整除

m - n — negation of m|n

质数、最大公约数、最小公倍数

Numbers > 1 divisible only by 1 and itself are called prime.

Greatest common divisor gcd(m, n)
Numbers m and n s.t. gcd(m, n) = 1 are said to be relatively
prime.
Least common multiple lcm(m, n)

gcd 和 lcm 永远是正数，即使原值是负数

gcd(m, n) · lcm(m, n) = |m| · |n|