Скачать или смотреть GI02 Strong (Mathematical) Induction (and recurrence relations)

#maths What is strong induction and how can you use it in conjunction with a #recurrencerelation? #mathematicalinduction is a proof technique for proving a sequence of (related) propositions. For Strong Induction, when proving one of the statements, we assume that we have already proved all the earlier ones (and not just the one before). We give 4 examples of the use of mathematical induction, three use strong induction, while two prove patterns in the Pingala-Fibonacci numbers. The examples emphasize that recurrence relations work well with induction. Subscribe ‪@Shahriari‬ for math videos at the college level.
00:00 Introduction
00:33 Principle of Mathematical Induction (   • GI01 Mathematical Induction  )
01:39 Strong Induction
02:16 *Example 1*: Using 3 & 5 cent stamps, make n cents. For which n is this possible?
02:57 Finding a pattern for Example 1
03:58 Strong Induction Proof of Conjecture for Example 1
05:30 What were the base cases for Example 1?
06:48 Pingala-Fibonacci numbers. What is in a name?
08:47 *Example 2*: What is the sum of the squares of Pingala-Fibonacci numbers?
09:05 Finding a pattern for Example 2
10:40 Induction Proof of Conjecture for Example 2
13:14 *Example 3*: An upper-bound for Pingala-Fibonacci numbers
14:10 Strong Induction Proof of Claim for Example 3
18:50 *Example 4*: A sequence defined by a recurrence relation
19:17 Finding a pattern for Example 4
20:12 Strong Induction Proof of Conjecture for Example 4

One of a series of lectures by Shahriar Shahriari on mathematical concepts used in undergraduate college mathematics.

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and six time winner of Pomona College's Wig teaching award.