Abstract Algebra
In the group of integers paired with standard multiplication, 1 is called this.
What is the identity element?
Among 100 people, at least this many were born in the same month.
What is the ceiling of 100/12=9?
ln(e)= to this number.
What is 1?
μ is used to refer to this, which is not very nice.
What is mean?
This cipher involves shifting the letters down the alphabet. It was also named after a famous Roman dictator.
What is Caesar?
There are three requirements for a nonempty set together with a binary operation to be a group. Name one of them.
Binary operation is associative
There exists an identity element
All elements have an inverse
Let S={1,2,3}. Find a permutation of S.
1,2,3
1,3,2
2,1,3
2,3,1
3,1,2
3,2,1
Using the power law, logb(np) is equal to this.
What is p logb(n)?
Taking the square root of the variance gives you this.
What is standard deviation?
Given A B True C false, find the truth value of:
¬((A^B) v C) -> A
What is True?
A ring is a set along with this number of binary operations.
What is 2?
A derangement is a permutation of objects that leave exactly this number is the original positions.
What is 0 or none?
log27(9)=x. Find x.
What is 2/3?
Out of 24 students, a president, vice president, and treasurer need to be selected. This number is the total number of permutations.
What is (24)(23)(22)=12,144?
To integrate by parts, follow this formula.
What is uv - integral(vdu)?
A group is said to be abelian if for all elements in the group, they are commutative about the binary operation. Groups that are not abelian are called this.
Non-abelian
This number is the coefficient of x2y6 when (x+y)8 is expanded.
What is 56?
log2(x+1) - log2(2x+8)=log2(6)
Find x such that this is true.
What is -(47/11)?
This is the total number of possible five card hands in poker.
What is 52!/(5!47!)=2,598,960?
This formula is for this in baseball:
(Batting Runs + Base Running Runs +Fielding Runs + Positional Adjustment + League Adjustment +Replacement Runs) / (Runs Per Win)
What is wins above replacement (WAR)?
This number is the order of this group:
ℤ 2 × ℤ 2:
What is 4?
The recurrence relation:
an=20an-5 + 4an-1
has this number of degrees.
What is 5?
Simplify the following logarithm:
log4(8) - log27(3)
What is 7/6?
Factorials are typically limited to integers, but this function extends factorials into the complex plane.
What is the gamma function?
See picture.