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

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

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

4. 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

5. Basic Counting Principles

6. Basic Counting Principles

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

8. Pigeonhole Principle

9. Permutations

10. Combinations

11. Combinations

12. 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.

13. Finding Primes Sieve of Eratosthenes

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

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

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

20. Two-Element Boolean Algebra

24. Boolean Algebra

25. Boolean Algebra

26. Logical Gates and Combinatorial Circuits

27. Logical Gates and Combinatorial Circuits

28. Logical Gates and Combinatorial Circuits

29. Logical Gates and Combinatorial Circuits