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CS 345 Lecture 1 Introduction and Math Review

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CS 345 Instructor – Qiyam Tung TA – Sankar Veeramoni

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Administrivia Webpage – http://www.cs.arizona.edu/classes/cs345/summer14/ Syllabus – http://www.cs.arizona.edu/classes/cs345/summer14/syllabus.html

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Sets Union Intersection

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Sets (cont’d) Membership Defining sets – Even numbers – Odd numbers

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Sets Power set

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Sequences Summation Products

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Closed form equivalents Triangular numbers Sum of powers of 2

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Logarithms Product Quotient

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Logarithms (cont’d) Power Change of base

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Logical Equivalences De Morgan’s Law – Propositions – Sets

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10 minute break

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Proofs Deductive Contrapositive Inductive

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Proofs (cont’d) Contradiction pq~pp->q~p V q

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Proofs (cont’d)

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Deduction (example) Conjecture: If x is even, then 5x is even

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Deduction (cont’d) Conjecture: If x is even, then 5x is even

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Contrapositive (example) Conjecture: If x^2 is odd, then x is odd

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Contrapositive (cont’d) Conjecture: If x^2 is odd, then x is odd

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Inductive (example) Conjecture:

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Inductive (cont’d)

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Contradiction (example 1) Conjecture: There are infinite prime numbers

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Contradiction (example 1 cont’d)

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Contradiction (example) Conjecture: The square root of 2 is irrational

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Contradiction (cont’d)

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Extra 1

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Extra 2

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Extra 3

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Extra 4

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Extra 5

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CS 345 Lecture 1 Introduction and Math Review

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CS 345 Instructor – Qiyam Tung TA – Sankar Veeramoni

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Administrivia Webpage – http://www.cs.arizona.edu/classes/cs345/summer14/ Syllabus – http://www.cs.arizona.edu/classes/cs345/summer14/syllabus.html

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Sets Union Intersection

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Sets (cont’d) Membership Defining sets – Even numbers – Odd numbers

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Sets Power set

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Sequences Summation Products

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Closed form equivalents Triangular numbers Sum of powers of 2

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Logarithms Product Quotient

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Logarithms (cont’d) Power Change of base

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Logical Equivalences De Morgan’s Law – Propositions – Sets

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10 minute break

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Proofs Deductive Contrapositive Inductive

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Proofs (cont’d) Contradiction pq~pp->q~p V q

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Proofs (cont’d)

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Deduction (example) Conjecture: If x is even, then 5x is even

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Deduction (cont’d) Conjecture: If x is even, then 5x is even

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Contrapositive (example) Conjecture: If x^2 is odd, then x is odd

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Contrapositive (cont’d) Conjecture: If x^2 is odd, then x is odd

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Inductive (example) Conjecture:

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Inductive (cont’d)

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Contradiction (example 1) Conjecture: There are infinite prime numbers

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Contradiction (example 1 cont’d)

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Contradiction (example) Conjecture: The square root of 2 is irrational

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Contradiction (cont’d)

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Extra 1

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Extra 2

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Extra 3

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Extra 4

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Extra 5

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