# ESP Biography

## DREW HAVEN, MIT freshman studying math and computer science

Major: Mathematics

College/Employer: MIT

Year of Graduation: Not available.

Not Available.

## Past Classes

(Clicking a class title will bring you to the course's section of the corresponding course catalog)

M1970: Generating Functions in Splash! 2008 (Nov. 22 - 23, 2008)
Did you know that the nth Fibonacci number is $$F_n = \frac{1}{\sqrt{5}} \left[ \left(\frac{1 + \sqrt{5}}{2}\right)^n - \left(\frac{1-\sqrt{5}}{2}\right)^n \right]$$? What does this have to do with the infinite polynomial $$f(x) = 1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + \cdots$$? Generating functions are a beautiful tool for messing with sequences and figuring out recurrence relations. Armed with these and some arithmetic, we can come up with formulas like these with ease!