University studies in computing require the ability to pass from a concrete problem to an abstract representation, reason with the abstract structure, and return with useful solutions to the specific situation.

The tools for developing these skills are in part qualitative - concepts such as set, relation, function, and structures such as trees and well-founded orders. They are also in part quantitative - notably elementary combinatorics and finite probability. Recurring in all of these are instruments of proof, both purely logical ones (such as proof by contradiction) and mathematical (the various forms of induction).

Features:

. Explains the basic mathematical tools required by students as they set out in their studies of Computer or Information Science

. Explores the interplay between qualitative thinking and calculation

. Teaches the material as a language for thinking, as much as knowledge to be acquired

. Uses anintuitive approach with a focus on examples for all general concepts

. Provides numerous exercises, solutions and proofs to deepen and test the reader's understanding

. Includes highlight boxes that raise common queries and clear away confusions

. Tandems with additional electronic resources including slides on author's website

http://david.c.makinson.googlepages.com

This easy-to-follow text allows readers to carry out their computing studies with a clear understanding of the basic finite mathematics and logic that they will need. Written explicitly for undergraduates, it requires only a minimal mathematical background and is ideal for self-study as well as classroom use.

David Makinson is currently Visiting Professor at London School of Economics (LSE). Previous affiliations include the Department of Computer Science at King's College London, UNESCO in Paris, and the American University of Beirut in Lebanon. He is well known for his early research in modal and deontic logics, and more recently in the logic of belief change (as one of the founders of the AGM paradigm) and nonmonotonic reasoning.

The first part of this preface is for the student; the second for the instructor. But whoever you are, welcome to both parts. For the Student You have finished secondary school, and are about to begin at a university or technical college. You want to study computing. The course includes some mathematics { and that was not necessarily your favourite subject. But there is no escape: some finite mathematics is a required part of the first year curriculum. That is where this book comes in. Its purpose is to provide the basics { the essentials that you need to know to understand the mathematical language that is used in computer and information science. It does not contain all the mathematics that you will need to look at through the several years of your undergraduate career. There are other very good, massive volumes that do that. At some stage you will probably find it useful to get one and keep it on your shelf for reference. But experience has convinced this author that no matter how good the compendia are, beginning students tend to feel intimidated, lost, and unclear about what parts to focus on. This short book, on the other hand, offers just the basics which you need to know from the beginning, and on which you can build further when needed.

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.- Something about Everything: Quantificational Logic.