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Mastering Combinatorial Problem Solving Methods

Explore counting principles, arrangements, and selections in MATH 310. Dive into addition, multiplication, and equality principles. Homework assignments and volunteer tasks included.

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Mastering Combinatorial Problem Solving Methods

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  1. MATH 310, FALL 2003(Combinatorial Problem Solving)Lecture 17, Wednesday, October 8

  2. 5.1. Two Basic Counting Principles. • Homework (MATH 310#6W): • Read 5.2 • Do 5.1: All odd numbered exercises. • Turn in 5.1: 34,42,44,46 • Volunteers: • ____________ • ____________ • Problem: 46.

  3. The Addition Principle m y x n

  4. The Multiplication Principle m n y z x

  5. The Equality Principle • (Bijective proof)

  6. The Bookkeper’s Principle

  7. Combinatorial “principles”. • So far we have encountered five methods that we call principles: • The bookkeeper’s principle (2e = sum deg) • The induction principle • The equality principle (Prufer sequences) • The addition principle • The multiplication principle • We will learn several other useful principles.

  8. 5.2. Simple Arrangements and Selections • Homework (MATH 310#6F): • Read 5.3 • Do 5.2: All odd numbered exercises. • Turn in 5.2: 38,48,59,60,70 • Volunteers: • ____________ • ____________ • Problem: 59.

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