Transcription of Mathematics for Computer Science - MIT OpenCourseWare
{{id}} {{{paragraph}}}
Mcs 2015/5/18 1:43 page i #1 Mathematics for Computer Science revised Monday 18th May, 2015, 01:43 Eric Lehman Google Inc. F Thomson LeightonDepartment of Mathematics and the Computer Science and AI Laboratory, Massachussetts Institute of Technology; Akamai Technologies Albert R MeyerDepartment of Electrical Engineering and Computer Science and the Computer Science and AI Laboratory, Massachussetts Institute of Technology 2015, Eric Lehman, F Tom Leighton,Albert R Meyer. This work is available under the terms of theCreative CommonsAttribution-NonCommercial-ShareAl ike license. mcs 2015/5/18 1:43 page ii #2 mcs 2015/5/18 1:43 page iii #3 Contents I Proofs Introduction 3 References 4 1 What is a Proof? 5 Propositions 5 Predicates 8 The Axiomatic Method 8 Our Axioms 9 Proving an Implication 11 Proving an If and Only If 13 Proof by Cases 15 Proof by Contradiction 16 Good Proofs in Practice 17 References 19 2 The Well Ordering Principle 27 Well Ordering Proofs 27 Template for Well Ordering Proofs 28 Factoring into Primes 30 Well Ordered Sets 31 3 Logical Formulas 41 Propositions from Propositions 42 Propositional Logic in Computer Programs 45 Equivalence and Validity 48 The Algebra of Propositions 50 The SAT Problem 55 Predicate Formulas 56 References 61 4 Mathematical Data Types 81 Sets 81 Sequences 86 Functions 87 Binary Relations 89 Finite Cardinality 93
I Proofs Introduction 3 0.1 References 4 1 What is a Proof? 5 1.1 Propositions 5 1.2 Predicates 8 1.3 The Axiomatic Method 8 1.4 Our Axioms 9 1.5 Proving an Implication 11 1.6 Proving an “If and Only If” 13 1.7 Proof by Cases 15 1.8 Proof by Contradiction 16 1.9 Good Proofs in Practice 17 1.10 References 19 2 The Well Ordering Principle 27
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document:
{{id}} {{{paragraph}}}