DISCRETE COMPUTATIONAL STRUCTURES

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Presentation transcript:

DISCRETE COMPUTATIONAL STRUCTURES CSE 2353 Fall 2010 Most slides modified from Discrete Mathematical Structures: Theory and Applications

CSE 2353 OUTLINE Sets PART I Logic PART II Proof Techniques Relations Functions PART III Number Theory Boolean Algebra

CSE 2353 OUTLINE Number Theory Sets PART I Logic PART II Proof Techniques Relations Functions PART III Number Theory Boolean Algebra

Learn the basic counting principles— multiplication and addition Learning Objectives Learn the basic counting principles— multiplication and addition Explore the pigeonhole principle Learn about permutations Learn about combinations Learn about Prime numbers

Basic Counting Principles

Basic Counting Principles

Pigeonhole Principle The pigeonhole principle is also known as the Dirichlet drawer principle, or the shoebox principle.

Pigeonhole Principle

Permutations

Combinations

Combinations

Prime Number An integer p is prime if p>1 and the only divisors of p are 1 and p itself. An integer n>1 that is not prime is called composite.

Finding Primes Sieve of Eratosthenes http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Fundamental Theorem of Arithmetic Every integer n>1 can be written as the product of powers of distinct primes.

CSE 2353 OUTLINE Boolean Algebra Sets PART I Logic PART II Proof Techniques Relations Functions PART III Number Theory Boolean Algebra

Two-Element Boolean Algebra Let B = {0, 1}.

Two-Element Boolean Algebra

Boolean Algebra

Boolean Algebra

Logical Gates and Combinatorial Circuits

Logical Gates and Combinatorial Circuits

Logical Gates and Combinatorial Circuits

Logical Gates and Combinatorial Circuits