Abstract Algebra, Lec 2B: Equivalence Relations, Partitions, Induction, Foundational Number Theory

(0:00) Equivalence Relations and Partitions.
(9:57) Story about Gauss adding up the first 100 integers in his head.
(13:03) Use (the first principle of) mathematical induction to prove that the sum of the first n integers is n(n+1)/2.
(23:15) Mention well-ordering principle is an axiom.
(23:25) Number theory: division algorithm, dividend, divisor, quotient, remainder, divides, factor, multiple, prime, composite, fundamental theorem of arithmetic, greatest common divisor (gcd), gcd is a linear combination, gcd in terms of prime factorization, relatively prime (coprime) integers.

Bill Kinney, Bethel University mathematics department

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[ShwetankT]

hey bill, I want to thank you and congratulate you for being such a good teacher.

[plaustrarius]

Why would i need to use strong induction to prove a statement if strong induction follows from weak induction?

I'm currently trying to prove (basically) that 1*) a^n - b^n is divisible by (a-b) for all n using induction.

I can prove it (sort of) by assuming that 1*) is a polynomial, that implies (a-b) is always a factor or 'root' of that polynomial for all n.

but that's not really a proof unless I can prove the inductive step i'm guessing?

[plaustrarius]

(script)A is the set of (disjoint) partitions of S under tilde! @8:55 its so beautifulll

[ericrendon]

Does anyone have the homeworks for this course? Please help I tried emailing @Bill Kinney