## On Fourier Pseudorandomness

As a final project at the 2010 University of Georgia mathematics REU, I wrote a manuscript discussing the properties and meaning of a mathematical notion called Fourier Pseudorandomness, which provides a quantitative measure of the randomness (in some sense) of a finite set of integers. Some of the more involved proofs require a first course . . . [Read More]

## A Statement of the Riemann Hypothesis

The Riemann Hypothesis, a longstanding unsolved conjecture in analytic number theory, is considered by many mathematicians to be one of the most important unsolved problems in theoretical mathematics. To understand the statement takes only a typical undergraduate mathematics education, but to find a proof would be the capstone of a mathematical career.

The Riemann zeta function . . . [Read More]

## An Equation With Squares

Let k ≥ 0, and let n = k(2k + 1). Then we have:

n2 + (n+1)2 + … + (n+k)2 = (n+k+1)2 + … + (n+2k)2.

For example,
02 = 0,
32 + 42 = 52,
102 + 112 + 122 = 132 + 142,
212 + 222 + 232 + 242 = 252 . . . [Read More]