Sets, Logic and Maths for Computing

Description

This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions. Front Matter....Pages i-xxi Collecting Things Together: Sets....Pages 1-25 Comparing Things: Relations....Pages 27-56 Associating One Item with Another: Functions....Pages 57-78 Recycling Outputs as Inputs: Induction and Recursion....Pages 79-111 Counting Things: Combinatorics....Pages 113-136 Weighing the Odds: Probability....Pages 137-164 Squirrel Math: Trees....Pages 165-188 Yea and Nay: Propositional Logic....Pages 189-215 Something About Everything: Quantificational Logic....Pages 217-241 Just Supposing: Proof and Consequence....Pages 243-274 Back Matter....Pages 275-283