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Notes 021508

# Notes 021508 - Dr McCann C Sc 245 Announcements Homework 4...

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February 15, 2008 – Dr McCann – C Sc 245 Announcements: Homework 4 due Monday Exam #1 Review: Wednesday 2/20/08 @ 7-9:00PM – GOULD SIMPSON 906 1 Exam : Friday 2/22 REVIEW:

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5 Important definitions Conjecture Theorem Proof Lemma Definition: A simple theorem whose truth is used to construct more complex theorems: Corollary Definition: A theorem whose truth follows directly from another theorem. Why people fear proofs Proofs are creative, no set steps. Look from different perspectives Practice proofs & expect dead ends Proofs are puzzles, don’t let it bother you when you have dead ends Proof Types Direct Proof END OF EXAM #1 Proof By contraposition Like direct but with a twisth Proof by contradiction A dark road on a foggy night End of exam #2 Direct proofs We’re trying to prove conjectures of the form (p q)
So, to prove p q: Assume p, show Q Proof is valid if q is shown true and p assumed Proof is sound if q is shown true and p is shown true. If P true, Q has to be True FIRST PROOF Conjecture: If n is even, then n 2 is also even, (n Σ Z). Cannot use INDUCTIVE REASONING “oh yeah 6 is even, 36 is even”

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