Abstract Algebra Video #1: Introduction and Prerequisites

This is the first video in my abstract algebra series. The content may be somewhat dry, but we are trying to lay the groundwork for a serious study of groups, rings, and fields that will be appropriate for undergraduate or even graduate students in mathematics, or just people with a strong interest in the subject. Today, we consider the unique factorization properties of the integers and then give an example of a set of numbers that does not possess this seemingly fundamental property.

NOTE: I erroneously stated that "Zahlen" refers to the natural numbers. I meant to say that this word is for the integers. Apologies!

0:00 Introduction and Agenda
1:12 1.1: Historical Motivation
4:13 1.2: The Integers
7:30 Divisibility
9:17 Stating the Division Algorithm
10:18 Proving the Division Algorithm
17:36 Examples of Division Algorithm
18:16 Greatest Common Divisor
19:16 Bezout's Lemma
20:12 Proof of Bezout's Lemma
24:34 Corollary to Bezout's Lemma
25:17 Euclid's Lemma
26:45 The Fundamental Theorem of Arithmetic
28:50 A "Bad" Example
32:30 Closing Remarks

I know my voice sounds funny- I have breathing problems...