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]
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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] 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, |
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