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CSE 321 Discrete Structures

In this Winter 2008 lecture, we explore key concepts of induction and recursion, fundamental principles in discrete mathematics. We'll cover induction proofs, including examples using public key cryptography (Alice and Bob) and provide a theorem related to harmonic numbers. The winning strategy for the game Chomp is also discussed, showcasing the practical application of induction. Students are reminded of the midterm date, grading weights, and readings from the 5th edition textbook chapters 4.1-4.3. Join us for an engaging session on critical elements in discrete structures.

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CSE 321 Discrete Structures

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  1. CSE 321 Discrete Structures Winter 2008 Lecture 12 Induction

  2. Announcements • Readings • Monday, Wednesday • Induction and recursion • 4.1-4.3 (5th Edition: 3.3-3.4) • Midterm: • Friday, February 8 • In class, closed book • Estimated grading weight: • MT 12.5%, HW 50%, Final 37.5%

  3. Highlights from Lecture 11 • Public Key Cryptography ALICE BOB

  4. Induction Example • Prove 3 | 22n -1 for n  0 Examples to show its true P(0) P(k)  P(k+1)

  5. Induction as a rule of Inference P(0)  k (P(k)  P(k+1))  n P(n) Formal steps Show P(0) Assume P(k), Prove P(k+1), Conclude P(k) P(k+1) Conclude  k (P(k) P(k+1)) Conclude  n P(n)

  6. 1 + 2 + 4 + … + 2n = 2n+1 - 1

  7. Harmonic Numbers

  8. Cute Application: Checkerboard Tiling with Trinominos Prove that a 2k 2k checkerboard with one square removed can be tiled with:

  9. Strong Induction P(0)  k ((P(0)  P(1)  P(2)  …  P(k))  P(k+1))  n P(n)

  10. Player 1 wins n  2 Chomp! Winning strategy: chose the lower corner square Theorem: Player 2 loses when faced with an n  2 board missing the lower corner square

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