Transcription of Mathematics for Computer Science - MIT OpenCourseWare
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Mathematics for Computer Science - MIT OpenCourseWare
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 Logic
Mathematics for Computer Science. revised Monday 18. th. May, 2015, 01:43. Eric Lehman. Google Inc. F Thomson Leighton. Department of Mathematics and the Computer Science and AI Laboratory, Massachussetts Institute of Technology; Akamai Technologies. Albert R Meyer. Department of Electrical Engineering and Computer Science
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