1. A Mathematical Logician By: Hanan Mohammed

2. Objectives: Who is this guy? Why should we know him? Impact on Mathematical and Logical fields (1815-1864) George John Boole (1815-1864)

3. Who is Who is George John Boole ? Sun of shoes a seller and a lady maid John interest in mathematics Start going to school Interests in education? Eldest sibling,…so?

4. Finance obstacles and educational Became teacher assistant to support family Serious mathematics learning start! Establish his own school Published in Cambridge Mathematical Journal Duncan Gregory, editor Who is Who is George Boole- A student & A teacher

5. Queens College Mathematics professor First Mathematics professor Science department Dean Several calculus accomplishments Applied algebra to solve differential equations Who is Who is George Boole- A Star Mathematician

6. Algebra of logic: Boolean algebra Regarded Logic as aspect of Mathematics Mathematical Analysis of Logic Discovered analogy between algebraic symbols and logic forms An Investigation of the Laws of Thought (1854), on Which are Founded the Mathematical Theories of Logic and Probabilities Who is Who is George Boole- Boolean algebra maker

7. Why do we care Why do we care Represent Logic as mathematical formulas Manipulated as normal algebraic expressions Value of input and output is: true/false Horned and sheep example (=x & y)

8. Why do we care Why do we care Boolean Algebra Rules P1: X = 0 or X = 1 P2: 0. 0 = 0 P3: 1 + 1 = 1 P4: 0 + 0 = 0 P5: 1. 1 = 1 P6: 1. 0 = 0. 1 = 0 P7: 1 + 0 = 0 + 1 = 1

9. Idempotent Law –X+X=X –X X=X Involution Law –0’=1 –1’=0 –(X’)’=X Complementarily Law –X+X’=1 –X X’=0 Why do we care Why do we care Boolean Algebra Laws

10. Associative Law –(X+Y)+Z = X+(Y+Z) = X+Y+Z –(X Y) Z = X (Y Z) = X Z Y Distributive Law –X (Y+Z) = X Y+X Z –X+(Y Z) = (X+Y) (A+Z) Commutative Law –X+Y=Y+X –X Y=X Y Why do we care Why do we care Boolean Algebra Laws

11. Claude Shannon after 70 years extends Boole's studies Design system electromechanics through Boolean algebra Solved Boolean Algebra through circuits Why do we care Why do we care Boole's work is the basis of mechanisms