Abstract Algebra, Lec 3B: Modular Arithmetic on Equivalence Classes, Number Theory Proofs

(0:00) Another example of modular arithmetic on equivalence (congruence) classes (this time mod 5). It's isomorphic to Z5 (cyclic group of order 5).
(2:52) Review division algorithm and notion of what it means for one number to divide another.
(5:07) Review primes, composites, Fundamental Theorem of Arithmetic.
(6:59) Second (Strong) Principle of Mathematical Induction to prove the existence portion of the Fundamental Theorem of Arithmetic.
(17:07) Animation of Sieve of Eratosthenes for finding primes.
(19:29) There are infinitely many primes and the idea of its (most beautiful) proof by contradiction.
(23:09) Prove Euclid's Lemma based on the fact that the greatest common divisor (gcd) of two integers is a linear combination of the integers (and therefore two relatively prime (coprime) integers have a linear combination that equals the unity 1).

Bill Kinney, Bethel University mathematics department

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[webster]

Thank you for the video! definitely helps understanding my class, also... who puts a light switch in the middle of a whiteboard?