What is mathematical induction and how it works
  • Introduction to the course
  • What kinds of statements can be proven by induction
  • Induction: this is how it works
  • Both cases are necessary
Examples of proofs by induction
  • Proving formulas, Problem 1
  • Sequences: guess and prove, Problem 2
  • Sequences: guess and prove, Problem 3 with two base cases
  • Proving divisibility, Problem 4
  • Not necessarily for all natural numbers: an inequality, Problem 5
  • A difficult proof, Problem 6
  • Another difficult proof, Problem 7
  • Proofs by induction, Wrap-up
Extras
  • Bonus Lecture