Combinatorics and probability

Combinatorics

An introduction to combinatorics: the addition rule and the product rule. The two basic rules behind all other counting methods, with examples.

Probability

How to calculate the probability of a random event. Probability experiments, events, calculating probabilities and plenty of worked examples with dice.

Paradoxes

The Monty Hall problem, also known as the three doors problem. Why it pays to change your choice of door and what your real chance of winning the car is.

Password security

The maths behind why a strong password is worth it. How many guesses a brute-force attack needs and how password length changes the time it takes to crack.

Basics of statistics

The basics of statistics: data set, individual and variable, frequencies, arithmetic and geometric mean, mode and median in one place.

Binomial theorem

The binomial theorem generalises formulae such as (a+b)^2 to any power. Derivation, the link with Pascal’s triangle and worked examples.