Mathematics for Computer Science

“mcs” — 2015/5/18 — 1:43 — page i — # Mathematics for Computer Science revised Monday 18thMay, 2015, 01: Eric Lehman Google Inc. ...

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Contentsviii “mcs” — 2015/5/18 — 1:43 — page ii — # “mcs” — 2015/5/18 — 1:43 — page iii — # Introduction I Proofs 0.1 Reference ...

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. ...

0.1 References of argument in this vein, Descartes goes on to conclude that there is an infinitely beneficent God. Whether or no ...

1 What is a Proof? 1.1 Propositions Definition. Apropositionis a statement (communication) that is either true or false. For exa ...

Chapter 1 What is a Proof? prime numbers, unless it’s a constant (see Problem 1.17). But the real point of this example is to sh ...

1.1. Propositions 7 Several incorrect proofs of this theorem have been published, including one that stood for 10 years in the l ...

Chapter 1 What is a Proof? For a computer scientist, some of the most important things to prove are the correctness of programs ...

1.4. Our Axioms 9 pair of points”.) Propositions like these that are simply accepted as true are called axioms. Starting from th ...

Chapter 1 What is a Proof? 1.4.1 Logical Deductions Logical deductions, orinference rules, are used to prove new propositions us ...

1.5. Proving an Implication 11 1.4.2 Patterns of Proof In principle, a proof can beanysequence of logical deductions from axioms ...

Chapter 1 What is a Proof? Example Theorem 1.5.1.If 0 x 2 , thenx^3 C4xC1 > 0. Before we write a proof of this theorem, we ...