Quizbowl Math Quantities/Values I

Fg’ - gf’

Determinant

Wronskian __

Determinant

Unchanged by row replacement

Determinant

Weighted sum of minors

Determinant

Gaussian elimination

Determinant

Descartes’ rule of signs

Zeroes

Abel-Ruffini Theorem

Zeroes

Newton’s method/identity

Zeroes

Vieta’s formulas

Zeroes

Cardon

Zeroes

Little Bezout’s Theorem

Remainders

= error for Taylor polynomials

Remainders

Denoted epsilon

Error

“Family-wise” rate

Error

“Irreducible” form cannot be mitigated

Error

Endogeneity

Error

Jacobian type

Determinant

Cofactor expansion

Determinant

Ad-bc for 2x2 matrix

Determinant

= 1 for every element of special linear group

Determinant

Sylvester’s criterion/theorem

Determinant

Constant term of the characteristic polynomial

Determinant

Cramer’s Rule

Determinant

Abel’s Identity

Determinant

Roots are eigenvalues w/ lambda

Determinant

matrix is invertible if __ != 0

Determinant

Hadamard problem

Determinant

Rule of Sarrus

Determinant

Defined using Leibniz formula

Determinant

Derivative found by Jacobi’s formula

Determinant

Dodgson condensation

Determinant

Corresponds to value of parallelepiped

Determinant

Vandermonde type

Determinant

Sign of __ indicates whether linear transformation preserves orientation

Determinant

Cayley-Menger type

Determinant

Fundamental Theorem of Algebra

Zeroes

Cardano’s Formula

Zeroes

Namesake “dilution” in which regression coefficients are underestimated

Error

Sole parameter of geometric and Bernoulli distributions

Probability

Logit function

Probability

Converges to maximal value in sunrise problem

Probability

Laplace smoothing contributes beta-distributed prior weight to

Probability

Expressed within asymmetric Wilson score interval

Probability

= 1 / # of microstates

Probability

= square of wave function for particles

Probability

“Cumulative density” in orbitals

Probability

Frenet–Serret formulas calculate derivatives taken with respect to

Arc Length

Elliptic integrals

Arc Length

sum of the distances between adjacent values in a partition of the domain

Arc Length

Jackknife method

Variance

Must be finite for CLT

Variance

= number of trials in binomial distribution

Variance

sqrt(lambda) in Poisson distribution

Standard Deviation

Squared as “k” in denominator of Chebyeshev’s Inequality

Standard Deviation

Second central moment ^ 2

Standard Deviation

Empirical Rule

Standard Deviation

Denoted by lowercase sigma

Standard Deviation

T-scores and z-scores

Standard Deviation

Denominator of Cohen’s d

Standard Deviation

Pearson’s correlation coefficient

Standard Deviation

Used to find SEM

Standard Deviation

Differ by n and n-1 in “sample” and “population” forms

Standard Deviation

Bessel’s correction

Standard Deviation

Squared = variance

Standard Deviation

Squared = eX^2 - (e(X))^2

Standard Deviation

Multiplied by sqrt(2pi)

Standard Deviation

Slope of regression equation related to ___

Standard Deviation