Single-Variable Calculus
According to historians, calculus was invented by Leibniz and this physicist who is known for his laws of gravity.
Who is Issac Newton?
Two positive integers are said to be relatively prime if this is their only common factor.
What is 1?
This series of books written by Euclid is considered to be the backbone of Euclidean geometry.
What are The Elements?
A matrix is invertible (i.e has an inverse) if and only if its determinant doesn't equal this value.
What is 0?
1,1,2,3,5,?
What is 8? (This is the Fibonacci sequence)
According to the power rule for derivatives, this function is the derivative of x^2
What is 2x?
If a and b are integers and d is a positive integer such that d|b-a, then a is said to be this to b
What is congruent(mod d)?
Out of the five axioms posed by Euclid, this is the one axiom that couldn't be proved and thus, this axiom is ignored in non-Euclidean geometries.
What is the parallel postulate?
Interestingly, matrix multiplication doesn't generally have this property that matrix addition and real number multiplication both have.
What is the commutative property?
1,4,27,256,?
What is 5^5? (The sequence is (n^n)).
In general, sequences in the real numbers can have at most this many limits.
What is 1?
In the positive integers (or any commutative ring if we wish to be abstract), for any two elements x and y; an element d is said to be this if d|x, d|y, and for any element c, if c|x and c|y, then c|d
What is a greatest common divisor?
Former US President James Garfield was said to have come up with his own proof of this fundamental triangle theorem.
What is the Pythagorean Theorem?
For any natural number n, the nxn identity matrix has one 1 in every row, one 1 in every column, and 0s elsewhere. This means that the identity matrix is a special kind of these types of matrices.
What are permutation matrices?
2.7,2.71,2.718,2.7182,?
What is 2.71828? (the nth element is e truncated to n decimal digits)
While Archimedes was investigating parabolas, he found the area between a parabola and a defined rectangle by basically calculating an early form of this and then taking its limit of sorts.
What is a Riemann sum?
The Fundamental Theorem of Arithmetic states that every positive integer can be uniquely factored into these types of numbers.
What are prime numbers?
A straight line from the center of a circle to its edge is a radius. A straight line from the geometric center of a regular polygon to one of its vertices is known as this.
What is an apothem?
A matrix is said to be this if for any i,j A(ij)=A(ji) where A(ij) is the entry in the ith row and jth column.
What is a symmetric matrix?
(1), (1 1), (1 2 1), (1 3 3 1), ?
What is (1 4 6 4 1)? (These are the rows of Pascal's triangle)
If a differential equation can be written in the form dy/g(y)=f(x)dx, it is said to be this kind of differential equation.
What is separable?
A positive integer is called n-smooth if all of its prime factors are less than or equal to n. With that in mind, these are the first six 5-smooth numbers.
What are 2,3,4,5,6, and 8?
A tesseract is the four dimensional analogue of this six sided 3D figure.
What is a cube?
If we think of the columns of a matrix as vectors, this is the vector space spanned by the columns.
What is the column space?
1,1,2,3,3,?
What is 4? (This sequence is known as Hofstadter's Q-sequence. Interestingly, we don't know if this sequence is infinite or finite.)