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]
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Summary

2024 ACF Fall at Ohio StatefallY916.67100%44%22%
2024 ACF Fall at WashingtonfallY717.14100%57%14%
2024 ACF Fall at GeorgiafallY1213.3392%25%17%
2024 ACF Fall at North CarolinafallY912.2289%22%11%
2024 ACF Fall at RutgersfallY720.00100%57%43%
2024 ACF Fall at IllinoisfallY1019.00100%60%30%

Data

Appalachian State BJames Madison A010010
Duke AJames Madison B010010
NC StateWilliam & Mary0000
Liberty AUNC A010010
UNC CVirginia Tech A1010020
UNC DVirginia010010
Virginia Tech BVCU10101030
Liberty BTusculum010010
Duke BLiberty C010010