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

"Contemporary Abstract Algebra", by Joe Gallian: https://amzn.to/2ZqLc1J Check out my blog at: https://infinityisreallybig.com/ Abstract Algebra Playlist:    • Abstract Algebra Course, Lecture 1: Introd...   (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 AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.