Elementary Math Challenges

Title: Elementary Math Challenges 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.

Mathematical Induction is a mathematical proof technique used to prove that a property \(P(n)\) holds for every natural number \(n\), i.e. for \(n = 0, 1, 2, 3,\) and so on. The idea is to prove a base case \(P(0)\), and then prove the induction step \(P(n)\) implies \(P(n+1)\). We will look at various applications of this technique.

A recurrence is a description of a function or sequence in terms of itself. A well known example is the Fibonacci sequence \(F_{n+2} = F_{n+1} + F_{n}\) for \(n \geq 0\), with initial conditions \(F_{0} = 0\), \(F_{1} = 1\). Some challenging problems can be naturally posed and solved using recurrences.

Date: Tuesday, October 15, 2019
Time: 6:30pm
Where: Lunt 104
Contact Person: Putnam Coordinator
Contact email: putnam@math.northwestern.edu
Contact Phone:
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