Recursive Definitions and Structural Induction 151 Strings of Matched Brackets 155 Recursive Functions on Nonnegative Integers 158 Arithmetic Expressions 161 Induction in Computer Science 166 Ordinary Induction 99 Strong Induction 108 Strong Induction vs. Sets 73 Sequences 77 Functions 77 Binary Relations Finite Cardinality 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
Well Ordering Proofs 25 Template for Well Ordering Proofs Factoring into Primes 28 Well Ordered Sets 29 Propositions from Propositions 38 Propositional Logic in Computer Programs Equivalence and Validity 44 The Algebra of Propositions 46 The SAT Problem 51 Predicate Formulas 52 The Well Ordering Principle 25 2.1 2.2 2.3 2.4 Mathematics for Computer Science revised Monday 4th June, 2012, 15:49į Thomson Leighton Department of Mathematics and the Computer Science and AI Laboratory, Massachussetts Institute of Technology Akamai TechnologiesĪlbert R Meyer Department of Electrical Engineering and Computer Science and the Computer Science and AI Laboratory, Massachussetts Institute of TechnologyĬopyright © 2012, Eric Lehman, F Tom Leighton, Albert R Meyer.
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