EVENT DETAILS AND ABSTRACT

Title: Elementary Math Challeges in Induction and Recurrences
Speaker: Miguel A. Lerma
Speaker Info: Northwestern University
Brief Description: Training session for the Putnam Competition
Special Note: Training session for the Putnam Competition
Abstract:

If a property $P$ is true for number $1$, and $P(n) \Rightarrow P(n+1)$ for every $n \geq 1$, then it is obvious that all positive integers have property $P$. We will see how we can exploit this fact to prove statements that at first look very challenging to prove directly.

A recurrence is an expression relating values of a function or sequence to its previous values, e.g the Fibonacci sequence is defined $F_{1}=0$, $F_{1}=1$, and $F_{n} = F_{n-1} + F_{n-2}$ for $n\geq 2$. Many challenging problems can be easily tackled by using properties of recurrences.