Mathematics for Computer Science

“mcs” — 2011/5/9 — 20:49 — page i — # Mathematics for Computer Science revised Monday 9thMay, 2011, 20: Eric Lehman Google Inc. ...

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“mcs” — 2011/5/9 — 20:49 — page ii — # “mcs” — 2011/5/9 — 20:49 — page iii — # 1 What is a Proof? I Proofs 1.1 Propositions 1.2 ...

I Proofs ...

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Introduction This text explains how to use mathematical models and methods to analyze prob- lems that arise in computer science. ...

Part I Proofs of argument in this vein, Descartes goes on to conclude that there is an infinitely beneficent God. Whether or not ...

Part I Proofs Bogus proof. aDb a^2 Dab a^2 b^2 Dabb^2 .ab/.aCb/D.ab/b aCbDb aD0:  Problem 0.2. It’s a fact that the Arithmetic ...

Part I Proofs His students first wonder if the quiz could be on Friday of next next. They reason that it can’t: if Albert didn’t ...

1 What is a Proof? 1.1 Propositions Definition.Apropositionis a statement that is either true or false. For example, both of the ...

Chapter 1 What is a Proof? can’t check a claim about an infinite set by checking a finite set of its elements, no matter how lar ...

1.2. Predicates 9 This proposition is true and is known as the “Four-Color Theorem”. However, there have been many incorrect pro ...

Chapter 1 What is a Proof? is a predicate whose truth depends on the value ofn. The predicate is true fornD 4 since four is a pe ...

1.4. Our Axioms 11 Euclid’s axiom-and-proof approach, now called theaxiomatic method, remains the foundation for mathematics tod ...

Chapter 1 What is a Proof? A key requirement of an inference rule is that it must besound: an assignment of truth values to the ...