polynomials - 2024 ARCADIA

Question

Rings of these objects are denoted k[x] (“k-x”), where their coefficients come from the field k. For 10 points each:

[10e] Name these mathematical expressions that sum terms of the form “a-sub-n times x-to-the-n.” The quadratic formula solves equations involving these expressions of degree two.

ANSWER: polynomials

[10m] This set can be represented as a quotient field by constructing as the ring of polynomials in one variable mod the ideal generated by x-squared plus one. This set is the algebraic closure of the real numbers.

ANSWER: complex numbers [prompt on C]

[10h] Ideals of polynomial rings are related to the geometric structure of their zero sets by this theorem of algebraic geometry. For example, this theorem states that maximal ideals in polynomial rings correspond to individual points in affine space.

ANSWER: Hilbert’s Nullstellensatz (“nool-SHTELL-lun-zots”)

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Summary


2024 ARCADIA at BU	2024-12-06	Y	7	15.71	100%	43%	14%
2024 ARCADIA at Duke	2024-12-06	Y	3	20.00	100%	67%	33%
2024 ARCADIA at Missouri S&T	2024-12-06	Y	1	20.00	100%	100%	0%
2024 ARCADIA Online	2025-05-17	Y	5	16.00	100%	60%	0%
2024 ARCADIA at Penn State	2024-12-06	Y	2	20.00	100%	100%	0%
2024 ARCADIA at Florida Tech	2024-12-06	Y	4	15.00	100%	50%	0%
2024 ARCADIA at UC Berkeley	2024-12-06	Y	2	25.00	100%	100%	50%
2024 ARCADIA at Waterloo	2024-11-09	Y	6	20.00	100%	83%	17%
2024 ARCADIA at GT	2024-12-06	Y	5	14.00	100%	20%	20%
2024 ARCADIA at GT	2024-12-06	Y	1	10.00	0%	100%	0%
2024 ARCADIA at GT	2024-12-06	Y	1	20.00	100%	0%	100%
2024 ARCADIA at Illinois	2024-11-09	Y	4	22.50	100%	100%	25%
2024 ARCADIA at Warwick	2024-12-06	Y	5	20.00	100%	80%	20%
2024 ARCADIA at Claremont	2024-11-02	Y	3	20.00	100%	67%	33%

Data


Boston College A	BU	10	0	0	10
Harvard	Boston College B	10	0	0	10
Tufts A	Bowdoin B	10	10	0	20
Amherst	Bowdoin C	10	10	0	20
MIT	Bowdoin A	10	10	10	30
Tufts B	Brandeis A	10	0	0	10
Yale	Clark House	10	0	0	10
North Carolina B	North Carolina A	10	10	10	30
Virginia Tech A	Virginia Tech B	10	10	0	20
Squidward Community College	WashU	10	10	0	20
South Carolina	Virginia Tech C	10	0	0	10
Old and Young	ASU->Stanford->ASU pipeline	10	0	0	10
Paddington in Peru (2024)	Madmen and Specialists	10	10	0	20
Social credit go vroom	The cult of SGA	10	10	0	20
Toyota Tundra Turbos — Twisting Truths - Tackling Trivia - Taming Titans	In the Mood for Buzz	10	0	0	10
she limp on my waltz till i feel pathetique	bingy academy	10	10	0	20
RIT	Maryland	10	10	0	20
Pitt	Penn State	10	10	0	20
UCF B	Valencia	10	10	0	20
UF A	UF C	10	10	0	20
Florida Tech	USF	10	0	0	10
UF B	UCF A	10	0	0	10
Berkeley Past	Berkeley B	10	10	0	20
Berkeley A	Stanford	10	10	10	30
Waterloo Aspidistra	McMaster ApocolocyntosisBidii	10	10	0	20
Ottawa Absolomabsolomabsolom	Carleton A	10	0	0	10
Toronto A	Waterloo Basic	10	10	0	20
Toronto B	Toronto Chestnut Rice and Kamehameha	10	10	10	30
Toronto Disband the Club 2k24	Toronto Metropolitan A	10	10	0	20
Waterloo Cloze	McGill A	10	10	0	20
Georgia Tech B	Milton	10	10	0	20
Georgia Tech B	Milton	10	10	10	30
Georgia Tech B	Mississippi State	0	10	0	10
Lambert	Georgia Tech C	10	0	0	10
Georgia Tech D	Innovation Academy C	10	0	0	10
Innovation Academy A	Innovation Academy B	10	0	0	10
Georgia Tech A	Johns Creek	10	0	0	10
Georgia Tech B	Milton	10	10	0	20
Georgia Tech B	Milton	10	10	10	30
Georgia Tech B	Mississippi State	0	10	0	10
Georgia Tech B	Mississippi State	0	10	10	20
Innovation Academy B	Georgia Tech C	10	0	10	20
Georgia Tech B	Mississippi State	0	10	10	20
Purdue A	Chicago A	10	10	0	20
Purdue B	Chicago B	10	10	0	20
Illinois Blue	SIUE	10	10	0	20
Notre Dame	Illinois Orange	10	10	10	30
Warwick A	Bristol	10	10	0	20
Cambridge A	Cambridge B	10	10	10	30
LSE A	Imperial A	10	10	0	20
Warwick B	Southampton	10	10	0	20
Imperial B	Warwick C	10	0	0	10
SGV Ventures	Claremont	10	0	0	10
Anderson et al.	Jason et al.	10	10	10	30
ALCU	U[C]SD	10	10	0	20