The Fibonacci Sequence and Beyond

The Fibonacci sequence, where each term in the sequence is defined to be the sum of previous two terms $F_{n+1}=F_n+F_{n-1}$, is the most famous example of a recurrence relation. We will give a short introduction to recurrence relations and discuss two methods for solving them. In particular we will see the relationship of the golden ratio to the Fibonacci sequence. If there is time, we will state and discuss Poincare's theorem.

The only prerequisite knowledge is the quadratic formula and how to multiply 2x2 matrices.