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”)
<VD, Other Science>
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
| 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 | 10 | 30 |
| Georgia Tech B | Milton | 10 | 10 | 10 | 30 |
| Georgia Tech B | Mississippi State | 0 | 10 | 10 | 20 |
| Georgia Tech B | Mississippi State | 0 | 10 | 10 | 20 |
| Innovation Academy B | Georgia Tech C | 10 | 0 | 10 | 20 |
| Georgia Tech B | Milton | 10 | 10 | 0 | 20 |
| Georgia Tech B | Milton | 10 | 10 | 0 | 20 |
| Georgia Tech B | Mississippi State | 0 | 10 | 0 | 10 |
| Georgia Tech B | Mississippi State | 0 | 10 | 0 | 10 |