Sets, Logic and Maths for Computing

Springer Science & Business Media

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 a" concepts such as set, relation, function, and structures such as trees and well-founded orders. They are also in part quantitative a" 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:a [ Explains the basic mathematical tools required by students as they set out in their studies of Computer or Information Sciencea [ Explores the interplay between qualitative thinking and calculationa [ Teaches the material as a language for thinking, as much as knowledge to be acquireda [ Uses an intuitive approach with a focus on examples for all general conceptsa [ Provides numerous exercises, solutions and proofs to deepen and test the readera (TM)s understandinga [ Includes highlight boxes that raise common queries and clear away confusionsa [ Tandems with additional electronic resources including slides on author's websitehttp: //david.c.makinson.googlepages.comThis 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.
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About the author

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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Additional Information

Springer Science & Business Media
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Published on
Dec 31, 2008
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Computers / Computer Science
Mathematics / Discrete Mathematics
Mathematics / Logic
Mathematics / Set Theory
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area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic.
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduate students need to enter the world of computer and information sciences. 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. In ten chapters on these topics, the book guides the student through essential concepts and techniques.

The extensively revised second edition provides further clarification of matters that typically give rise to difficulty in the classroom and restructures the chapters on logic to emphasize the role of consequence relations and higher-level rules, as well as including more exercises and solutions.

Topics and features: teaches finite mathematics 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 away confusions; provides numerous exercises, with selected solutions, to test and deepen the reader’s understanding.

This clearly-written text/reference is a must-read for first-year undergraduate students of computing. Assuming only minimal mathematical background, it is ideal for both the classroom and independent study.

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