David Makinson - Sets, Logic and Maths for Computing

'Undergraduate Topics in Computer Science' (UTiCS) delivers high-quality instructional content for undergraduates studying in all areas of computing and information science. From core foundational and theoretical material to final-year topics and applications, UTiCS books take a fresh, concise, and modern approach and are ideal for self-study or for a one- or two-semester course. The texts are all authored by established experts in their fields, reviewed by an international advisory board, and contain numerous examples and problems, many of which include fully worked solutions.

The UTiCS concept relies on high-quality, concise books in softback format, and generally a maximum of 275300 pages. For undergraduate textbooks that are likely to be longer, more expository, Springer continues to offer the highly regarded Texts in Computer Science series, to which we refer potential authors.

More information about this series at http://www.springer.com/series/7592

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The first part of this preface is for the student; the second for the instructor. Some readers may find it helpful to look at both. Whoever you are, welcome!

You have finished secondary school and are about to begin at a university or technical college. You want to study informatics or computing. The course includes some mathematicsand that was not necessarily your favourite subject. But there is no escape: a certain amount of finite mathematics is a required part of the first-year curriculum, because it is a necessary toolkit for the subject itself.

What is in This Book?

That is where this book comes in. Its purpose is to provide the basic mathematical language required for entering the world of the information and computing sciences.

It does not contain all the mathematics that you will need through the several years of your undergraduate career. There are other very good, often quite massive, volumes that do that. At some stage you will 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 a compendium is, beginning students tend to feel intimidated, lost, and unclear about what is in it to focus on. This short book, in contrast, offers just the basics that you need to know from the beginning, on which you can build further as needed.

It also recognizes that you may not have done much mathematics at school, may not have understood very well what was going on, and may even have grown to detest it. No matter: you can learn the essentials here, and perhaps even have fun doing so.

How Should You Use It?

Without an understanding of basic concepts, large portions of computer science remain behind closed doors. As you begin to grasp the ideas and integrate them into your thought, you will also find that their application extends far beyond computing into many other areas. So, there is work to be done.

The good news is that there is not all that much to commit to memory. Your sister studying medicine, or brother going for law, will envy you terribly for this. In our subject, the two essential things are to