harmonic - 2025 ACF Fall - Buzzpoints App

Question

A function in Euclidean space has a property described by this adjective if it satisfies Laplace’s equation. For 10 points each:

[10m] Give this adjective that also names a divergent series defined as the sum over n of 1 over n.

ANSWER: harmonic [accept harmonic function; accept harmonic series]

[10h] For a holomorphic function, the real and imaginary parts are both harmonic because they satisfy this pair of doubly-eponymous partial differential equations, which are a necessary and sufficient condition for a complex function to be complex differentiable.

ANSWER: Cauchy–Riemann equations [reject partial answers]

[10e] Cauchy also names a theorem regarding this operation in complex analysis, which states that this operation applied to any closed contour is zero. By the fundamental theorem of calculus, this operation is the inverse of differentiation.

ANSWER: integration [accept word forms: accept performing an integral; accept Cauchy’s integral theorem; accept contour integral]

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Summary


Northern California	Main	Y	4	20.00	100%	100%	0%
Southern California	Main	Y	7	17.14	100%	57%	14%
Eastern Canada (1)	Main	Y	4	15.00	100%	50%	0%
Eastern Canada (2)	Main	Y	9	14.44	100%	22%	22%
Florida	Main	Y	4	12.50	100%	25%	0%
Great Lakes	Main	Y	11	17.27	100%	64%	9%
Lower Mid-Atlantic	Main	Y	9	14.44	100%	44%	0%
Upper Mid-Atlantic	Main	Y	12	17.50	100%	58%	17%
Midwest	Main	Y	9	14.44	100%	33%	11%
North	Main	Y	4	15.00	100%	50%	0%
Northeast	Main	Y	12	17.50	100%	58%	17%
Pacific	Main	Y	8	13.75	100%	38%	0%
South Central	Main	Y	6	11.67	67%	33%	17%
Southeast	Main	Y	12	17.50	100%	67%	8%
UK (North)	UK	Y	5	20.00	100%	60%	40%
UK (South)	UK	Y	7	15.71	100%	43%	14%
Upstate NY	Main	Y	5	12.00	100%	20%	0%

Data


Berkeley Boss Bandit	Berkeley Archer Queen	10	0	10	20
Berkeley Little Prince	UCSC	10	0	10	20
Berkeley Mighty Miner	Stanford A	10	0	10	20
Stanford B	Berkeley Skeleton King	10	0	10	20
Claremont C	UCLA F	0	0	10	10
UCLA C	UCSD A	10	0	10	20
UCSD B	USC A	10	0	10	20
UC Santa Barbara	USC B	0	0	10	10
McGill A	Carleton B	10	0	10	20
McGill C	Carleton A	10	0	10	20
Ottawa D	McGill E	0	0	10	10
Ottawa C	Ottawa B	0	0	10	10
McMaster A	Brock A	0	10	10	20
Guelph A	McMaster C	0	0	10	10
McMaster B	Queen's A	10	0	10	20
Toronto D	Toronto A	0	0	10	10
Toronto G	Toronto B	0	0	10	10
Toronto E	Toronto F	0	0	10	10
Waterloo A	Toronto I	10	0	10	20
Toronto H	Waterloo B	0	0	10	10
Toronto C	Waterloo C	0	10	10	20
UCLA E	UCLA A	10	0	10	20
UCLA B	UC Irvine	10	0	10	20
Claremont B	UCLA D	0	10	10	20
Florida B	Florida Tech B	0	0	10	10
Florida A	Florida Tech A	10	0	10	20
South Florida A	ERAU Daytona A	0	0	10	10
UCF A	Florida State A	0	0	10	10
CWRU A	Ohio State D	0	0	10	10
Michigan A	CWRU C	10	0	10	20
Kentucky	WVU A	10	10	10	30
Duke A	JMU B	10	0	10	20
Liberty A	UNC B	0	0	10	10
Liberty B	NCSU A	10	0	10	20
JMU A	NCSU B	0	0	10	10
UNC C	Tusculum A	0	0	10	10
Virginia Tech C	UNC D	0	0	10	10
Virginia Tech B	VCU A	10	0	10	20
Virginia A	William & Mary B	10	0	10	20
William & Mary C	Virginia Tech A	0	0	10	10
Lehigh A	Columbia A	0	10	10	20
George Mason A	Columbia B	0	0	10	10
Lehigh B	Maryland B	0	0	10	10
Rutgers D	Maryland C	10	0	10	20
NYU A	NYU B	10	0	10	20
Rutgers B	Penn	10	10	10	30
Princeton	George Mason C	10	0	10	20
Johns Hopkins	Rowan	10	0	10	20
Rutgers C	George Mason B	0	0	10	10
Maryland A	Stony Brook	10	0	10	20
Vassar A	NYU C	0	0	10	10
Rutgers A	Vassar B	10	0	10	20
Illinois Blue	Rose-Hulman A	10	10	10	30
Illinois Orange	Chicago B	0	0	10	10
Purdue A	Iowa A	10	0	10	20
Iowa B	Illinois Canada	0	0	10	10
WashU Grolars	Purdue B	0	0	10	10
Indiana B	Purdue C	0	0	10	10
Purdue D	Illinois Champaign	10	0	10	20
WashU Grizzlers	Illinois Urbana	0	0	10	10
William Woods University A	Indiana A	0	0	10	10
Louisville D	Michigan D	0	0	10	10
Michigan B	Louisville B	10	0	10	20
Michigan C	CWRU B	0	0	10	10
Ohio State B	Michigan State C	10	0	10	20
Michigan State D	Michigan State B	0	0	10	10
Ohio State A	CWRU D	10	0	10	20
Louisville C	Pittsburgh	10	0	10	20
Michigan State A	WVU B	10	0	10	20
Michigan Tech	Minnesota	0	0	10	10
Iowa State	St. Thomas	10	0	10	20
Macalester	Wisconsin B	0	0	10	10
Wisconsin A	Wisconsin C	10	0	10	20
Amherst A	Vermont A	10	0	10	20
Boston College A	Williams A	10	0	10	20
Dartmouth A	Brandeis Mozart	10	0	10	20
Brown A	Brandeis Bach	10	10	10	30
Brown B	Amherst B	0	0	10	10
Boston College B	Dartmouth C	0	0	10	10
MIT A	Brandeis Beethoven	10	10	10	30
Tufts A	Boston University B	10	0	10	20
Dartmouth B	Tufts C	10	0	10	20
Tufts B	Harvard	0	0	10	10
Williams B	MIT B	0	0	10	10
Boston University A	Williams C	0	0	10	10
Alberta A	Washington Coho	10	0	10	20
Washington Steelhead	Arizona State B	10	0	10	20
Washington Chum	Boise State	0	0	10	10
British Columbia A	Washington Chinook	0	0	10	10
Texas	Washington Atlantic	0	0	10	10
British Columbia C	Washington Masu	0	0	10	10
Washington Pink	Alberta B	10	0	10	20
Washington Sockeye	Washington State	0	0	10	10
Nebraska C	Central Oklahoma A	10	0	10	20
Kansas State B	Harding	0	0	0	0
Murray State College A	Kansas State A	0	0	10	10
Murray State College B	Nebraska B	0	0	0	0
Nebraska A	Tulsa B	0	0	10	10
Tulsa A	Central Oklahoma B	10	10	10	30
Auburn A	Auburn C	10	0	10	20
Clemson A	Clemson C	10	0	10	20
Emory A	Auburn B	10	0	10	20
Durham D	Edinburgh A	10	10	10	30
Edinburgh B	Durham C	0	0	10	10
Edinburgh C	York	10	0	10	20
Durham A	Sheffield A	10	10	10	30
Sheffield B	Edinburgh D	0	0	10	10
Cambridge A	Imperial B	0	0	10	10
Cambridge C	Oxford	10	0	10	20
Cambridge D	Imperial C	10	10	10	30
Cambridge E	Birmingham	0	0	10	10
Cardiff	Warwick	10	0	10	20
LSE	Bristol	0	0	10	10
Southampton	Imperial D	0	0	10	10
Georgia A	Georgia Tech B	10	0	10	20
Chipola College	Georgia Tech C	0	0	10	10
South Carolina A	Georgia Tech D	10	0	10	20
Georgia Tech A	Georgia Tech E	10	10	10	30
Georgia Tech F	Tennessee A	0	0	10	10
Mississippi State A	Sewanne	0	0	10	10
Vanderbilt A	Montevallo	10	0	10	20
Tennessee Tech	Vanderbilt B	10	0	10	20
Alabama A	Vanderbilt C	0	0	10	10
RIT B	Binghamton B	0	0	10	10
Binghamton A	Binghamton C	0	0	10	10
Cornell D	Cornell B	10	0	10	20
Cornell A	RIT A	0	0	10	10
ESF	Rochester	0	0	10	10