Algebra
The determinant of a diagonal matrix
Product of all its elements.
This number, ten to the power of one hundred, inspired the name of a famous Internet company.
a googol
I pick 2 crayons out of 5, each a different color. What is the total number of unique color combinations I can pick?
10
The expected value of a Bernoulli Random Variable with hyperparameter p = 0.3 is this number.
0.3
This integer is divisible by all other integers.
0
A commutative ring with unity 1 ≠ 0 in which every nonzero element has a multiplicative inverse.
Field
At this number, floating point arithmetic reaches its limit and calls it “Infinity”.
2^1024 (I’ll also accept something like 10^308)
What is true about every third Fibonacci number (F₃, F₆, F₉, ...)?
They are even
This distribution is known for its uses in continuous time Poisson processes, a common problem statement it is used for is the time between machine parts failing.
Exponential Distribution
The birth of graph theory came from the 7 bridges problem (is there a way to cross each of the seven bridges exactly once and return to the starting point). Who solved the problem?
Euler
The special vectors that make a basis when a matrix is diagonalizable.
Eigenvectors
Multiplication is repeated addition, exponentiation is repeated multiplication, and this operation is repeated exponentiation.
Tetration
What is the smallest number n where 1+1 = 0 in a modulo n system?
2
The expression using expectation as sqrt(E[(X - E[X])^2]) is called the blank of X.
Standard Deviation
A trillion has this many zeroes in the long scale.
18
The class of numbers that are not the root of a nonzero polynomial (like e or pi)
Transcendental
This is the “profession name” that online hobbyists that study really big numbers use to describe themselves.
Googologists
Every number that is a palindrome (the same written forwards and backwards like 123454321) and has an even number of digits is divisible by what integer?
11
The expression using expectation as E[e^(tX)] is called the blank of X.
Moment generating function
In these number systems, there can be infinitely many digits to the left of the decimal point instead of to the right.
p-adics
This theorem guarantees that every non-constant single-variable polynomial with complex coefficients has a complex root.
Fundamental Theorem of Algebra
For online hobbyists that study really big numbers, this system is used as a “measuring stick” to compare them against each other based on how many layers of repetition it takes to get to them.
The fast-growing hierarchy
What is required for all integers x, y, and z to satisfy x^n + y^n = z^n if n>2?
All three integers must be not positive.
A distribution is said to have this property if prior failures or elapsed time does not affect the future conditional distribution.
Memorylessness
In the Collatz Conjecture (set of rules to any positive integer that will eventually reach the number 1), what do you do when you're on an odd number?
Multiply it by 3, then add 1