Logic and Discrete Mathematics: A Concise Introduction

A concise yet rigorous introduction to logic and discrete mathematics.

This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade.

 The chapters on logic - propositional and first-order -  provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy to understand and use deductive systems of Semantic Tableaux and Resolution. The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in the accompanying solutions manual.

Key Features:

• Suitable for a variety of courses for students in both Mathematics and Computer Science.
• Extensive, in-depth coverage of classical logic, combined with a solid exposition of a selection  of the most important fields of discrete mathematics
• Concise, clear and uncluttered presentation with numerous examples.
• Covers some applications including cryptographic systems, discrete probability and network algorithms.

Logic and Discrete Mathematics: A Concise Introduction is aimed mainly at undergraduate courses for students in mathematics and computer science, but the book will also be a valuable resource for graduate modules and for self-study.

Keywords:

discrete mathematics, logic, first-order logic, propositional logic, predicate logic, set theory, combinatorics, counting techniques, graph theory, number theory, cryptography, probability, binomial theorem, cardinality, Chinese remainder theorem, deductive system, Diophantine equations, Euclidean algorithm, inclusion&ndash, exclusion principle, inference rule, algorithm, arithmetic, arrangement, axiom, bijection, Boolean, cardinal number, clausal form, combination, congruence, countable set, Deduction, logical, digraph, directed graph, disjunction, divisibility, divisor, equivalence, equivalence relation, Euler&rsquo, s theorem, Fibonacci numbers, first-order language, first-order structure, formula, function, fundamental theorem of arithmetic, generating function, graph, graph colouring, greatest common divisor, implication, incidence matrix, infinite set, law of excluded middle, linear congruence, linear order, logical connective