Columbia University W4995: Introduction To Cryptography, Fall 2003 Instructor: Professor Malkin Lecture 0, Notes takes by Ariel Elbaz

Abstract

This document gives a few examples for using L^{A}TEX. You should use the given file (ITC0.tex) as a template for writing your scribes - change the name to have the correct lecture number that you’re scribing, such as ITC7.tex if you’re scribing lecture 7.

1 Examples of Theorems, Claims, Lemmas, and Proofs

Theorem 1 text of a theorem...

Proof starting a proof... and ending it

Claim text of a claim Sketch of Proof (Informal) text of a proof sketch

We can also emphasize parts of the text

1.1 A subsection on primes

Definition 1 p is a prime if p is an integer that has no integral factors but itself and 1.

More examples

Lemma 1 text of a lemma

Example 1 text of an example

2 Mathematical Equations

Math equations can either be mixed with text,, such as y = x + 2 or 2^{2^{13}} or \frac{17!}{2^{34}} , or else they can be in a sepeate line

P r[x ≥ y] ≤ \frac{1}{3}

or on an automatically numbered equation

∀x|x ≤ y ⇒ y ≥ 0  (1)

and the text continues in the next line.

More advanced equations

V_{s,0}^{{q_{0},q_{1}}} = V_{s,0}^{{q_{0}}} ∪ V_{s,1}^{{q_{0}}} ∘ (V_{1,1}^{{q_{0}}})^{∗} ∘ V_{1,0}^{{q_{0}}}
V_{s,2}^{{q_{0},q_{1}}} = V_{s,2}^{{q_{0}}} ∪ V_{s,1}^{{q_{0}}} ∘ (V_{1,1}^{{q_{0}}})^{∗} ∘ V_{1,2}^{{q_{0}}} = V_{s,1}^{{q_{0}}} ∘ (V_{1,1}^{{q_{0}}})^{∗} ∘ V_{1,2}^{{q_{0}}}

3 Itemizing

• first item

• second item *** item with my bullet

any bullet will go

1. Items can also be numbered 2. and they can be nested

4 Writing text

The L^{A}TEXcompiler does it’s own pagesetting. It converts any number of spaces to a single space, and concatantes sentences to fill the paragraph. You can spread one sentence over as many lines as you want, it will continue as if it was written in a single line. If you want to break a paragraph you need to leave an empty line.