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

Georgia AAlabama A010010
Clemson BAuburn B010010
BelmontAuburn C0000
Emory AVanderbilt A0101020
Georgia Tech DGeorgia Tech A10101030
Georgia Tech CFurman010010
Auburn AGeorgia Tech E1010020
Mississippi State AEmory Oxford1010020
South Carolina ATennessee A010010
Georgia Tech BSouth Carolina B010010
Tennessee BSouthern010010
Clemson AVanderbilt B010010