Name the Equation
x = (-b ± sqrt(b2 - 4ac))/(2a)
Quadratic Formula
Determine the x-intercept of 4x - 2y2 = 3.
(3/4, 0)
Find the derivative of x4/2 - 3x2 + 2x - e7 with respect to x.
2x3 - 6x + 2
Who is the "Father of Geometry"?
Euclid
Calculate 29.
512
∫ab f(x) dx = F(b) - F(a)
Fundamental Theorem of Calculus
Determine a value for x that makes the following vectors orthogonal: (x, -4) & (10, 5).
x = 2
∫ dx / (1 + x²)
arctan(x) + C
Name a Millennium Prize Problem.
Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture.
What are the first 5 digits of pi?
3.1415
eiθ = cos(θ) + i⋅sin(θ)
Euler's Formula
What's the lowest degree polynomial without a general formula for the roots?
5
What is the Maclaurin series expansion for ex?
1 + x + x²/2! + x³/3! + ...
Name the two mathematicians who independently made significant contributions to the development of calculus.
Sir Isaac Newton & Gottfried Wilhelm Leibniz.
What is Dan's least favorite math class?
Calculus II
P(A|B) = P(B|A)⋅P(A)/P(B)
Bayes' Theorem
Calculate the argument of √(i - 1).
3π/8
State the criteria that must be satisfied for Rolle's Theorem to hold.
A given function f(x) must be continuous on the closed interval [a, b], differentiable on the open interval (a, b), and satisfy f(a)=f(b).
Who first introduced the concept of complex numbers and coined the term "imaginary" for the square root of -1?
René Descartes
What’s the LaTeX code for the “∩” (intersection) symbol?
\cap
∇⋅u = 0
ρ(du/dt) = -∇p + μ∇2u + F
Navier-Stokes Equations
Name one of the group axioms.
Well defined associative binary operation, each element has an inverse, existence of identity element.
List at least 5 of the 7 indeterminate forms.
0/0, ±∞/±∞, ∞-∞, 0(∞), 00, 1∞, ∞0.
Who was the German mathematician who proved Fermat's Last Theorem in 1994?
Andrew Wiles
What is the value of ζ(-1)?
-1/12