Augustin-Louis Cauchy - 2024 ACF Fall

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 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	9	17.78	89%	56%	33%

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
Jefferson County Scholars (DII)	Michigan D (UG)	10	10	0	20
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
Alberta	UW Chastity	10	10	0	20
Arizona State A	Arizona State B	10	10	0	20
UBC B	UBC A	10	10	0	20
UW Gluttony	UW Greed	0	10	0	10
UW Envy	UW Lust	0	10	0	10
UW Wrath	UW Pride	10	10	10	30
Boise State	UW Sloth	0	10	0	10
Georgia A	Alabama A	0	10	0	10
Clemson B	Auburn B	0	10	0	10
Belmont	Auburn C	0	0	0	0
Emory A	Vanderbilt A	0	10	10	20
Georgia Tech D	Georgia Tech A	10	10	10	30
Georgia Tech C	Furman	0	10	0	10
Auburn A	Georgia Tech E	10	10	0	20
Mississippi State A	Emory Oxford	10	10	0	20
South Carolina A	Tennessee A	0	10	0	10
Georgia Tech B	South Carolina B	0	10	0	10
Tennessee B	Southern	0	10	0	10
Clemson A	Vanderbilt B	0	10	0	10
Appalachian State B	James Madison A	0	10	0	10
Duke A	James Madison B	0	10	0	10
Liberty B	Tusculum	0	10	0	10
Duke B	Liberty C	0	10	0	10
NC State	William & Mary	0	0	0	0
Liberty A	UNC A	0	10	0	10
UNC C	Virginia Tech A	10	10	0	20
UNC D	Virginia	0	10	0	10
Virginia Tech B	VCU	10	10	10	30
Rowan A (DII)	Bard A (UG)	0	10	0	10
Rutgers A (UG)	Columbia A (UG)	0	10	10	20
Fordham A	NYU A (UG)	0	10	0	10
Lehigh A (UG)	Maryland B (DII)	0	10	0	10
NYU B	Lehigh B (DII)	10	10	0	20
Columbia J (DII)	Maryland A (DII)	10	10	10	30
Rutgers B	Princeton A (UG)	10	0	0	10
Rutgers B	Princeton A (UG)	10	0	0	10
Rutgers B	Maryland B (DII)	10	0	0	10
Rutgers B	Maryland B (DII)	10	0	0	10
Penn B (DII)	Columbia B	10	10	10	30
Rutgers B	Princeton A (UG)	10	10	0	20
Rutgers B	Princeton A (UG)	10	10	0	20
Rutgers B	Maryland B (DII)	10	10	0	20
Rutgers B	Maryland B (DII)	10	10	0	20