power series - Northeast - Buzzpoints App

Question

Answer the following about the construction of the p-adic numbers, for 10 points each.

[10e] The p-adic numbers can be formally defined as one of these constructs expressed using a rational times all powers of p. Taylor and Maclaurin name examples of these expansions used to represent smooth functions.

ANSWER: power series [accept formal series; prompt on infinite summation]

[10m] Under the p-adic norm, the p-adics are a completion of the rationals, meaning that each of these sequences converges to a limit in the set. In one of these sequences, all terms past a certain point become arbitrarily close.

ANSWER: Cauchy (“KO-shee”) sequences

[10h] To obtain other completions in the field of fractions, one can localize a type of integral domain named for this mathematician. A construction named for this mathematician partitions the rationals into “left” and “right” sets.

ANSWER: Richard Dedekind [accept Dedekind domain or Dedekind cut]

<AR, Other Science>

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Summary


California	2025-02-01	Y	3	16.67	100%	33%	33%
Florida	2025-02-01	Y	3	13.33	67%	33%	33%
Lower Mid-Atlantic	2025-02-01	Y	6	15.00	100%	17%	33%
Midwest	2025-02-01	Y	6	18.33	100%	33%	50%
North	2025-02-01	Y	3	20.00	100%	33%	67%
Northeast	2025-02-01	Y	5	22.00	100%	60%	60%
Overflow	2025-02-01	Y	5	14.00	100%	20%	20%
South Central	2025-02-01	Y	2	20.00	100%	50%	50%
Southeast	2025-02-01	Y	4	12.50	75%	0%	50%
UK	2025-02-01	Y	10	21.00	100%	70%	40%
Upper Mid-Atlantic	2025-02-01	Y	8	18.75	100%	25%	63%
Upstate NY	2025-02-01	Y	3	16.67	100%	33%	33%

Data


BU	UMass Boston	10	0	0	10
Harvard A	Brandeis A	10	10	10	30
Harvard B	Brandeis B	10	10	10	30
Brown A	Dartmouth A	10	10	10	30
Tufts A	MIT A	10	0	0	10