Question
A metric space is complete if every sequence named for this mathematician converges. For 10 points each:
[10m] Name this French mathematician, who also names an inequality bounding the inner product of two vectors with Hermann Schwarz (“sh’VARTS”).
ANSWER: Augustin-Louis Cauchy (“ko-SHEE”) [accept Cauchy sequences; accept Cauchy-Schwarz inequality]
[10e] If a complex function satisfies the Cauchy-Riemann equations, then a form of this operation can be performed on it. Integration is the inverse of this operation.
ANSWER: differentiation [or word forms such as differentiating; or taking the derivative; accept complex differentiation or complex derivative; prompt on holomorphic or analytic or entire functions by asking “What operation can be performed on such a function?”]
[10h] Cauchy used the mean value theorem to prove this theorem, which states any differentiable function that takes the same value at two different points must have a stationary point between the two points.
ANSWER: Rolle’s theorem [or Rolle’s lemma]
<Other Science>
Summary
| 2024 ACF Fall at Ohio State | fall | Y | 9 | 16.67 | 100% | 44% | 22% |
| 2024 ACF Fall at Washington | fall | Y | 7 | 17.14 | 100% | 57% | 14% |
| 2024 ACF Fall at Georgia | fall | Y | 12 | 13.33 | 92% | 25% | 17% |
| 2024 ACF Fall at North Carolina | fall | Y | 9 | 12.22 | 89% | 22% | 11% |
| 2024 ACF Fall at Rutgers | fall | Y | 7 | 20.00 | 100% | 57% | 43% |
| 2024 ACF Fall at Illinois | fall | Y | 10 | 19.00 | 100% | 60% | 30% |
Data
| CWRU A (UG) | Miami A (UG) | 10 | 10 | 10 | 30 |
| Miami B (UG) | CWRU B (DII) | 10 | 10 | 0 | 20 |
| CWRU C (UG) | Michigan State B | 0 | 10 | 0 | 10 |
| Michigan State A | Michigan A (UG) | 10 | 10 | 10 | 30 |
| Ohio State A (UG) | Michigan C | 0 | 10 | 0 | 10 |
| Ohio State B (DII) | Michigan B (UG) | 0 | 10 | 0 | 10 |
| West Virginia A (UG) | Ohio State C (DII) | 0 | 10 | 0 | 10 |
| Miami C (DII) | West Virginia B (UG) | 0 | 10 | 0 | 10 |
| Jefferson County Scholars (DII) | Michigan D (UG) | 10 | 10 | 0 | 20 |