Statistics
The probability of rolling
2 or 4
on a regular 6-sided die.
What is 1/3?
The derivative of e^x
What is e^x?
If x + y = 2y,
x is equal to this.
What is x=y?
This theorem can be used to determine the length of one side of a right triangle, provided the other two are known.
What is the Pythagorean Theorem?
The base of the natural logarithm is represented by this letter, often called Euler's number
What is e?
The probability of rolling "snake eyes" (two dice, each of which is a 1)
What is 1/36?
The rate of change of velocity
What is acceleration?
The inverse of f(x)=1/x
What is 1/x?
The Intermediate Value Theorem states that, for a continuous function f, if f(a)<0 and f(b)>0, then there exists a number c between a and b such that f(c) equals this
What is 0?
Legend has it: Euler discovered how to quickly add up the numbers from 1 to 100 in elementary school. In general, the sum of the integers from 1 to n is this type of number.
What is a triangle number?
If alpha=5% and we calculate a p-value of 0.002, then we may reject this hypothesis.
What is the null hypothesis?
f'(a) is calculated using first principles using the expression
limb→a [f(a)-f(b)] divided by this
What is a-b ?
The solution to this equation:
x^2 - 2x + 1 =0
What is 1?
Andrew Wiles published his 129-page proof of this famous theorem in 1995, showing that
a^n + b^n = c^n has no positive integer solutions for any integer n>2.
What is Fermat's Last Theorem?
Richard Feynman called it "the most remarkable formula in mathematics", relating 5 fundamental mathematical constants
e^(i*π) + 1 = 0
What is Euler's identity?
Given that events are normally distributed
the probability that a new observation
lies within one standard deviation of the mean
What is 68%?
In order to differentiate a relation that is not a function, e.g., x^2 + y^2 = 1, we may use this type of differentiation
What is implicit differentiation?
If cos(x)=1 and tan(x)=0, then sin(x) equals this
What is 0?
This theorem states that "every smooth vector field on a sphere has a singular point". In layman's terms, one could say "you can't comb the hair on a coconut"
What is the Hairy Ball Theorem?
In graph theory, this is a path that traverses all edges exactly once and also has the same starting and ending point
What is an Eulerian circuit?
In a variation of the Monty Hall problem, the contestant selects 1 of 5 doors. The host then reveals 3 incorrect doors. This is the probability that switching to the other unrevealed door is the correct one
What is 4/5 or 80%?
The derivative of this function is 1/(1+x^2)
What is arctan(x)?
This is the value of x in the expression
logx(9) = 2
What is 3?
(equvalent to x^2 = 9, x>0)
Determining the value of a limit by bounding it above and below with equal limits uses this "squishing" theorem
What is the Squeeze Theorem?
Euler's method is the most basic explicit method for numerical integration of these equations and is the simplest Runge–Kutta method
What are ordinary differential equations?