Titlebook: Mathematics of Discrete Structures for Computer Science; Gordon J. Pace Textbook 2012 Springer-Verlag Berlin Heidelberg 2012 discrete math

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en I started working on this domain years ago, I became somehow fr- tratedtoseethatmyfriendsworkingonmodelingwhereproducingexistence, uniqueness, and stability results for the solution of their equations, but that I was most of the time limited, because of the nonlinearity of the problem, to proveth

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Predicate Calculus, which a predicate holds requires a formalism richer than propositional logic. This chapter introduces the notion of predicates and extends the axiomatic approach presented in the previous chapter for propositional logic to allow formal reasoning about them.

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More Discrete Structures,alised are multisets, which enable reasoning about collections of objects similar to sets, but which allow multiple copies of the same item. Sequences or lists of objects are also formalised, enabling proofs of laws about them. Finally, graphs are formalised and examples of their use in computer sci

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Numbers,c operators such as addition and multiplication. Using the natural numbers, the notions of mathematical and strong induction are formalised and illustrated through examples. Other classes of numbers, such as the integers, rational numbers and real numbers are also discussed. The notion of cardinalit

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Reasoning About Programs,. Three main applications are given: (i) Correctness of algorithms: While an algorithm says how an answer can be calculated, a specification states what the answer should look like. But how can one prove that an algorithm really satisfies a specification? (ii) Giving meaning to programs: Without giv

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Gordon J. PaceAuthor takes an unusual approach, starts by defining ways of calculating operators and then proves that they satisfy various properties.Treatment is largely self-contained, and even students without p