Math Club event Wed., Feb. 9, 12 noon in 139 Exley
Feb. 9, 2011 by kcollins
Math Club Event Wed., Feb. 9, 12 noon in 139 Exley.
Joel Specter will give a talk, Oh How You’ve Failed Us, Induction.
Abstract. Proving that this formula holds isn’t too hard. One way is by induction. In fact, proving the validity of such formulae is exactly why induction exists.
However, what if you hadn’t been given the expression on the right, could you find an expression for the sum of the squares of the first N numbers?
Unfortunately induction offers no aide in this endevor. For while induction is great at proving that a formula is true, it is useless in finding such a formula. Therefore, to find such formulae we must develop other tools.
In this talk, I will develop the theory of generating functions, a tool which will allow us to effortlessly find closed form expressions for a myrid of different problems including the sum of the squares of the first N numbers. But more than this, I will show how the mere act of finding such formulae though the use of generating functions proves their validity. Thus, generating functions allow us to effortlessly find and prove formulae – an act of which induction can only dream.
No background beyond high school algebra
will be needed to enjoy this talk
All are invited. Lunch will be provided.
