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Quadratic Equation
The general solution to the quadratic equation $$ax^2 + bx + c$$ is $$x = (-b \pm \sqrt{b^2 - 4ac}) / 2a$$

Conditional Probability
Theorem 1: For all events A and B, $$P(A \mid B) + P(A \mid \bar{B}) = P(A)$$

Proof: Assert that event A happens, and denote the probability of this event as $$P(A)$$. If the probability that $$B$$ happened is $$P(B)$$, then the probability that $$B$$ did not happen is $$P(\bar{B}) = 1 - P(B)$$, because these two events encompass *all* the possibilities (by the Law of the Excluded Middle). Thus, the probability of blah, blah, blah, finish me.

More math


Theorem 1: Every function with a left inverse is injective.

Proof: Let $$f: X \to Y$$ be a function and suppose that f has a left inverse $$g: Y \to X$$. That is, if $$f(x) = y$$, then $$g(y) = x$$. To say that f is injective, we need to show that $$f(a) = f(b)$$ can be true if and only if $$a$$ and $$b$$ are the same number.

Given any two elements $$a, b \in X$$, suppose that $$f(a) = f(b) = c$$. Then since f has a left inverse g, we have $$g(c) = a$$ and $$g(c) = b$$. By this we immediately conclude that a = b, and so f is an injective function. $$\Box$$.

Citiation
Example from http://toolserver.org/~verisimilus/Scholar/Cite.php

Example from http://toolserver.org/~magnus/makeref.php

Newspaper article example

Quotes
""Все счастливые семьи похожи друг на друга, каждая несчастливая семья несчастлива по-своему" (All happy families are alike; each unhappy family is unhappy in its own way.)"

- Tolstoy

Templates
My Labrador Abby is the best dog in the world.

Instrumental case
For masculine nouns, add -ом/-ём/ем, for example, Иван Иванович becomes Иваном Ивановичем.