Sets, Logic and Maths for Computing

1. Front Matter

   Pages i-xv

   PDF

2. Collecting Things Together: Sets

   • David Makinson

   Pages 1-28

3. Comparing Things: Relations

   • David Makinson

   Pages 29-62

4. Associating One Item with Another: Functions

   • David Makinson

   Pages 63-86

5. Recycling Outputs as Inputs: Induction and Recursion

   • David Makinson

   Pages 87-121

6. Counting Things: Combinatorics

   • David Makinson

   Pages 123-152

7. Weighing the Odds: Probability

   • David Makinson

   Pages 153-187

8. Squirrel Math: Trees

   • David Makinson

   Pages 189-217

9. Yea and Nay: Propositional Logic

   • David Makinson

   Pages 219-264

10. Something about Everything: Quantificational Logic

    • David Makinson

    Pages 265-296

11. Back Matter

    Pages 297-301

    PDF

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.

• Computer
• Computer Science
• Computing
• Discrete Mathematics
• Information Science
• combinatorics
• logic
• sets

From the reviews:

"The book covers the very basic concepts of sets, relations, functions, induction and recursion, combinatorics, probability, trees, propositional logic, and elementary concepts of predicate logic. The text is easy to read, and the concepts are presented in an understandable way using many examples. The book contains exercises with solutions, gives several further exercises, and hints for further selected reading. … the book is recommended for undergraduates as a very first introduction to the basic ideas of finite mathematics and logic." (D. Seese, ACM Computing Reviews, January, 2009)

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.

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