This book equips the student with essential intellectual tools that are needed from the very beginning of university studies in computing. These consist ofabilities and skills - to pass from a concrete problem to an abstract representation, reason with the abstract structure coherently and usefully, and return with booty to the specific situation. The most basic and useful concepts needed come from the worlds of sets (with also their employment as relations and functions), structures (notably trees and graphs), and combinatorics (alias principles of counting, with their application in the world of probability). Recurring in all these are two kinds of instrument of proof – logical (notably inference by suppositions, reductio ad absurdum, and proof by cases), and mathematical (notably induction on the positive integers and on well-founded structures). From this book the student can assimilate the basics of these worlds andset out on the paths of computing with understanding and a platform for further study as needed. Only minimal background in mathematics necessary Careful selection of material that is really needed by students in the first two years of their university life in Computer Science and Information Sciences Brings out the interplay between qualitative thinking and calculation Teaches the material as a language for thinking in, as much as knowledge to be gained INDICE: Collecting Things Together: Sets.- Comparing Things: Relations.- Associating One Item with Another: Functions.- Recycling Outputs as Inputs: Induction and Recursion.- Counting Things: Combinatorics.- Weighing the Odds: Probability.- Squirrel Math: Trees.- Yea and Nay: Propositional Logic.- Somethingabout Everything: Quantificational Logic.
- ISBN: 978-1-84628-844-9
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 290
- Fecha Publicación: 01/08/2008
- Nº Volúmenes: 1
- Idioma: Inglés